Zeilberger, Doron - Department of Mathematics, Rutgers University

• Solutions to the "QUIZ" for Oct. 20, 2008 1. Let f(x) =
• RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION Doron Zeilberger
• Dr. Z's Math151 Handout #3.4 [Derivatives of Trigonometric Functions] By Doron Zeilberger
• Solutions to the "QUIZ" for Oct. 1, 2009 s as functions of r and s , if
• NAME: (print!) Section: E-Mail address
• ALGORITHMS FOR PERMUTATION STATISTICS BY ANDREW MICHAEL BAXTER
• Dr. Z's Math151 Handout #4.5 [Summary of Curve Sketching] By Doron Zeilberger
• RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION Doron Zeilberger
• AN EVEN SIMPLER PROOF OF PASCAL'S HEXAGON THEOREM Ren e DESCARTES 1 and Shalosh B. EKHAD 2
• The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) And PROOF(!!) of Holonomic Determinant Evaluations
• Enumerative and Algebraic Combinatorics
• PROOF OF A DETERMINANT EVALUATION CONJECTURED BY BOMBIERI, HUNT AND VAN DER POORTEN
• You Don't Have To Be an Einstein to Figure Out that Sara Should (Asymptotically) Eat +O(1=n) Dove Bars,
• By Doron ZEILBERGER 1 [Silence for 30 seconds]. I always dreamed about giving a talk about nothing. First, I thought of
• A Proof of the Celebrated Goldbach's Theorem Doron ZEILBERGER1
• Dr. Z's Math151 Handout #2.1 [Limits, Rates of Change, and Tangent Lines] By Doron Zeilberger
• PUBLICATIONS OF DORON ZEILBERGER Last Update: May 4, 2005
• A Direct Combinatorial Proof of a Positivity Result "A simple result deserves a simple proof"
• Dr. Z's Math151 Handout #2.7 [The Intermediate Value Theorem] By Doron Zeilberger
• Finite Versions of Szemeredi's Theorem on Arithmetical Progressions and Doron ZEILBERGER1
• Dr. Z's Math152 Handout #9.1 [Modeling with Differential Equations] By Doron Zeilberger
• A PROOF OF GEORGE ANDREWS' AND DAVID ROBBINS' q-TSPP CONJECTURE
• MATH 250 (1,2), Fall 2010, (Dr. Z.) , Full Solutions Only to the Theoretical Questions of Practice Problems for Exam 2
• Dr. Z's Math152 Handout #6.3 [Volumes by Cylindrical Shells] By Doron Zeilberger
• Automatic CounTilings Doron ZEILBERGER1
• A New Proof that there are 2n Possible Outcomes on Tossing a Coin n Times
• Dr. Z's Math251 Handout #16.5 (2nd ed.) [Surface Integrals of Vector Fields] By Doron Zeilberger
• MATH 250 (1,2), Fall 2010, (Dr. Z.) , Practice Problems for Exam 2 1. (a) Find an LU decomposition of the matrix
• The COMBINATORIAL ASTROLOGY of Rabbi ABRAHAM IBN EZRA Doron ZEILBERGER 1
• Automatic Generation of Generating Functions for the Number of Spanning Trees for Grid Graphs (and Much More General Creatures) of Fixed (but arbitrary!) Width
• A Fibonacci-Counting Proof Begged by Benjamin and Quinn Doron ZEILBERGER
• In How Many Ways Can n (Straight) Men and n (Straight) Women Get Married, if Each Person Has Exactly k Spouses?
• What Is Experimental Mathematics? Doron ZEILBERGER 1
• PROOF OF THE ALTERNATING SIGN MATRIX CONJECTURE 1 Doron ZEILBERGER 2
• CHOMP, RECURRENCES, and CHAOS(?) Doron ZEILBERGER 1
• \Book Review of \Kepler's Conjecture\ by George G. Szpiro\ Doron ZEILBERGER 1
• A PROOF OF JULIAN WEST'S CONJECTURE THAT THE NUMBER OF TWO-STACK-SORTABLE PERMUTATIONS OF LENGTH n IS 2(3n)!/((n+1)!(2n+1)!)
• PROOF OF A q-ANALOG OF A CONSTANT TERM IDENTITY CONJECTURED BY FORRESTER
• In How Many Ways Can You Reassemble Several Russian Dolls? Doron ZEILBERGER1
• ADVANCESIN APPLIED MATHEMATICS3, 377-383 (1982) T. L. Hill's Graphical Method for Solving
• Lieber Opa Paul, Ich Bin Auch Ein Experimental Scientist! Doron ZEILBERGER 1
• Dr. Z's Math251 Handout #17.1a (2nd ed.) [Green's Theorem] By Doron Zeilberger
• MATH 251 (4-6,11), Dr. Z. , Solutions to Exam 2, 12:00noon-1:20pm , Thurs. Nov. 19, 2009, SEC 117
• AN EXPERIMENTAL MATHEMATICS PERSPECTIVE ON THE OLD, AND STILL OPEN, QUESTION OF WHEN TO STOP?
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• How Adam Marcus and Gabor Tardos Divided and Conquered the Stanley-Wilf Conjecture
• Solution to the "QUIZ" for Nov. 23, 2009 Evaluate the surface integral S
• Dr. Z's Math151 Handout #4.9 [Antiderivatives] By Doron Zeilberger
• DETERMINANTS THROUGH THE LOOKING GLASS Tewodros Amdeberhan 1 and Doron Zeilberger 2
• \TRIVIALIZING" GENERALIZATIONS OF SOME IZERGIN-KOREPIN-TYPE DETERMINANTS
• THE COMPUTATIONAL CHALLENGE OF ENUMERATING HIGHDIMENSIONAL ROOK WALKS
• The GOULDEN-JACKSON CLUSTER Method For CYCLIC Words Anne E. EDLIN 1 and Doron ZEILBERGER 1
• How Adam Marcus and Gabor Tardos Divided and Conquered the Stanley-Wilf Conjecture
• Two EZ Proofs of sin 2 z + cos 2 z = 1 Leon EHRENPREIS 1 and Doron ZEILBERGER 1
• NSF Proposal: AUTOMATING COMBINATORICS: Project Description AUTOMATING COMBINATORICS: PROJECT DESCRIPTION
• Finite Analogs of Szemer edi's Theorem Paul RAFF 1 and Doron ZEILBERGER 1
• AN EXPERIMENTAL MATHEMATICS PERSPECTIVE ON THE OLD, AND STILL OPEN, QUESTION OF WHEN TO STOP?
• Proof of a Conjecture of Philippe Di Francesco and Paul Zinn-Justin related to the qKZ equation and to Dave Robbins' Two Favorite Combinatorial Objects
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Jan. 27, 2010
• NAME: Section: MATH 151(07-09, 20-22), Dr. Z. , First Practice Exam for the Second Midterm
• NAME: Section: MATH 151(07-09,20-22), Dr. Z. , Second Practice Exam for the Second Midterm
• Solutions to the "QUIZ" for Nov. 25, 2008 sin 2x dx .
• PROOF OF A q-ANALOG OF A CONSTANT TERM IDENTITY CONJECTURED BY FORRESTER
• Dr. Z's Math251 Handout #15.2 [Iterated Integrals] By Doron Zeilberger
• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER 1
• The Method of Undetermined Generalization and Specialization Illustrated with
• The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) And PROOF(!!) of Holonomic Determinant Evaluations
• THE UMBRAL TRANSFER-MATRIX METHOD: I. FOUNDATIONS Doron ZEILBERGER 1
• The Symbolic Goulden Jackson Cluster Method Xiangdong Wen
• NSF Proposal: Rigorous Experimental Combinatorics NSF PROPOSAL: RIGOROUS EXPERIMENTAL COMBINATORICS: Biographical Sketch
• How Likely Is P olya's Drunkard to Return to the Pub Without Getting Mugged? (In d-Dimensional Manhattan [d 2])
• Project Description Summary of Results from Previous NSF Support: DMS-8901610 and DMS-9123836
• An Inelegant (but Short(!)) Proof of a Major Index Theorem of Garsia and Gessel (Verbose Version) Doron ZEILBERGER 1
• PROOF OF A CONJECTURE OF CHAN, ROBBINS, AND YUEN Doron ZEILBERGER 1
• Proof of a Conjecture of Amitai Regev about Three-Rowed Young Tableaux (and much more!) Shalosh B. EKHAD and Doron ZEILBERGER 1
• How Many Singles, Doubles, Triples, Etc., Should The Coupon Collector Expect? Doron ZEILBERGER 1
• 2 # Proofs that # n k+1 # if k < n/2.
• Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms Sharpening of Wilf-Zeilberger Theory
• THE UMBRAL TRANSFER-MATRIX METHOD. III. Counting Animals Doron ZEILBERGER 1
• Solutions to the "QUIZ" for Oct. 2, 2008 1. Use the rules of differentiation to calculate f (x) (Do not simplify your answer).
• Dr. Z's Math251 Handout #12.2 [Vectors] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.3 [Double Integrals over General Regions] By Doron Zeilberger
• MATH 251 (1-3,10 ), Dr. Z. , Solutions to Exam 2, Thurs., Nov. 19, 2009, 10:20-11:40am, SEC 118
• Dr. Z.'s Math 250(2), (Fall 2010, RU) Solutions to REAL Quiz #4 (Oct. 7, 2010) 1. (4 pts.) Find an elemenary matrix E such that EA = B, where A and B are as follows
• Finite Analogs of Szemeredi's Theorem and Doron ZEILBERGER1
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Jan. 27, 2010
• A PROOF OF GEORGE ANDREWS' AND DAVID ROBBINS' q-TSPP CONJECTURE
• Dr. Z's Math151 Handout #4.3 [How Derivatives Affect the Shape of a Graph] By Doron Zeilberger
• Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms Sharpening of Wilf-Zeilberger Theory
• Solving di#erential equations by means of Hermite Helena Zakrajsek
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 16, 2007
• The Gift Exchange Problem, Part II By Moa Apagodu, David Applegate, Neil Sloane, and Doron Zeilberger
• HOW JOE GILLIS DISCOVERED COMBINATORIAL SPECIAL FUNCTION THE-Doron Zeilberger
• NSF Proposal: RIGOROUS EXPERIMENTAL COMBINATORICS RIGOROUS EXPERIMENTAL COMBINATORICS: References Cited
• PROOF OF IRA GESSEL'S LATTICE PATH CONJECTURE MANUEL KAUERS AND CHRISTOPH KOUTSCHAN AND DORON ZEILBERGER
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• THE COMPUTATIONAL CHALLENGE OF ENUMERATING HIGH-DIMENSIONAL ROOK WALKS
• RANDOM WALK IN A WEYL CHAMBER 1 Ira M. Gessel 2 and Doron Zeilberger 3
• Advances in Applied Mathematics 37 (2006) 139152 www.elsevier.com/locate/yaama
• Dr. Paul Alexander Charlottenburg Kaiserdamm 51
• EFFICIENT COUNTING AND ASYMPTOTICS OF k-NONCROSSING TANGLED-DIAGRAMS
• MATH 152 (01-03), Dr. Z. , Solution to Second Midterm, Monday Nov. 28, 2005. 1. (10 points [5 each]) For each of the two series below, determine whether they converge
• NSF Proposal: RIGOROUS EXPERIMENTAL COMBINATORICS RIGOROUS EXPERIMENTAL COMBINATORICS: References Cited
• Experimental Number Theory Edinah K. Gnang
• Dr. Z's Math151 Handout #5.3 [The Fundamental Theorem of Calculus] By Doron Zeilberger
• HISTABRUT: A Maple Package for Symbol-Crunching in Probability theory Doron ZEILBERGER1
• The Number of Same-Sex Marriages in a Perfectly Bisexual Population is Asymptotically Normal Shalosh B. EKHAD1
• Dr. Z's Math151 Handout #3.9 [Derivatives of Inverse Functions] By Doron Zeilberger
• IS DREIDEL EXPECTED TO LAST O(NUTS 2 ) SPINS? Doron ZEILBERGER 1
• KATHY O'HARA'S CONSTRUCTIVE PROOF OF THE UNIMODALITY OF THE GAUSSIAN POLYNOMIALS
• A HIGH-SCHOOL ALGEBRA 1 , WALLET-SIZED PROOF, OF THE BIEBERBACH CONJECTURE [After L. Weinstein]
• TOWARDS A WZ EVALUATION OF THE MEHTA INTEGRAL Doron Zeilberger *
• An Explicit Formula for the Number of Solutions of X 2 = 0 in Triangular Matrices Over a Finite Field Shalosh B. EKHAD 1 and Doron ZEILBERGER 1
• DIFFERENCE EQUATION AND PERMUTATION GROUP FOR (4) 1
• RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION Doron Zeilberger
• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER1
• SIAM J. MATH. ANAL. Vol. 11, No. 6, November 1980
• A NEW PROOF OF THE REFINED ALTERNATING SIGN MATRIX Ilse Fischer
• Experimental Number Theory Part I : Tower Arithmetic
• NAME: Section: MATH 151 (Fall 2008) Dr. Z. , Second Practice Exam for First Midterm.
• Journal of Combinatorial Theory, Series A 91, 451 463 (2000) The Umbral Transfer-Matrix Method. I. Foundations
• NAME: Section: MATH 251 (1-6,10-11), Dr. Z. , Fourth Practice Test for Exam #2
• FORTY "STRANGE" COMPUTER-DISCOVERED [and COMPUTER-PROVED (of course!)]
• REPORT ON THE PAPER "THE NUMBER OF INVERSIONS AND THE MAJOR INDEX
• JOURNAL OFMATHEMATICALANALYSIS AND APPLICATIONS 74, l%!-199(1!%0) A Lattice Walk Approach to the
• Finite Analogs of Szemeredi's Theorem Doron ZEILBERGER1
• J. Math. Biology (1982) 15:351-357 Mathematical
• Dr. Z.'s Math 250(1), (Fall 2010, RU). Solutions to the REAL Quiz for Sept. 16, 2010 1. (4 pts.) Compute the matrix-vector product
• AUTOMATED DISCOVERY AND PROOF IN THREE COMBINATORIAL PROBLEMS
• Dr. Z's Math251 Handout #14.6 (2nd ed.) [The Chain Rule] By Doron Zeilberger
• Solutions to the "QUIZ" for Oct. 29, 2009 1. Compute the Jacobian of the transfomation
• SOME NICE SUMS ARE ALMOST AS NICE IF YOU TURN THEM UPSIDE DOWN
• The Gift Exchange Problem, Part II By Moa Apagodu, David Applegate, Neil Sloane, and Doron Zeilberger
• Dr. Z's Math151 Handout #5.1 [The Definite Integral] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.5 [The Chain Rule] By Doron Zeilberger
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Sept. 21, 2008
• Two Dimensional Directed Lattice Walks with Arvind Ayyer
• A Comparison Of Two Methods For Random Labelling of Balls by Vectors of Integers Doron ZEILBERGER 1
• A SYMBOLIC FINITE-STATE APPROACH FOR AUTOMATED PROVING OF THEOREMS IN COMBINATORIAL GAME
• CHU'S 1303 IDENTITY IMPLIES BOMBIERI'S 1990 NORM-INEQUALITY [Via An Identity of Beauzamy and D egot]
• Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms Sharpening of Wilf-Zeilberger Theory
• Finite Analogs of Szemer edi's Theorem Doron ZEILBERGER 1 and Paul RAFF 1
• Advances in Applied Mathematics 25, 228232 (2000) doi:10.1006/aama.2000.0696, available online at http://www.idealibrary.com on
• Dr. Z's Math251 LAST Handout [The Meaning of It All] By Doron Zeilberger
• PROOF OF IRA GESSEL'S LATTICE PATH CONJECTURE MANUEL KAUERS AND CHRISTOPH KOUTSCHAN AND DORON ZEILBERGER
• NSF Proposal: Symbolic Computation and Combinatorics NSF PROPOSAL: SYMBOLIC COMPUTATION and COMBINATORICS
• Commutation relations and Vandermonde determinants Yuri Bahturin
• Searching for Strange Hypergeometric Identities By Sheer Brute Force Moa APAGODU and Doron ZEILBERGER 1
• The J.C.P. Miller Recurrence for Exponentiating a Polynomial, and its q-Analog Doron ZEILBERGER 1
• NSF Proposal: RIGOROUS EXPERIMENTAL COMBINATORICS RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION
• THE UMBRAL TRANSFER-MATRIX METHOD: II. Counting Plane Partitions Doron ZEILBERGER 1
• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER 1
• GAUSS'S 2 F 1 (1) CANNOT BE GENERALIZED TO 2 F 1 (x) Doron Zeilberger *
• The Generalized U2-Flashlight Microsoft 5-Minute Puzzle Shalosh B. EKHAD 1 and Doron ZEILBERGER 1
• A Generalization of Odlyzko's Conjecture: The Coecients of (1 q) j =((1 q 2n )
• Rutgers University (New Brunswick) Piscataway New Jersey 08854-8019 Department of Mathematics-Hill Center e-mail: zeilberg@math.rutgers.edu
• A WZ PROOF OF A \CURIOUS" IDENTITY Shalosh B. Ekhad and Mohamud Mohammed 1
• Dr. Z's Math151 Handout #4.1 Problem Type 4.1.1: Use the Linear Approximation to estimate f = f(a + h) -f(a) for the
• Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms Sharpening of Wilf-Zeilberger Theory
• SIAM J. MATH. ANAL. Vol. 19, No. 4, July 1988
• Dr. Z's Math151 Handout #2.7 [Tangents, Velocities, and Other Rates of Change] By Doron Zeilberger
• The Collector's Brotherhood Problem Using the Newman-Shepp Symbolic Method
• THE METHOD OF DIFFERENTIATING UNDER THE INTEGRAL SIGN Gert Almkvist * and Doron Zeilberger**
• The Number of Inversions and the Major Index of Permutations are Asymptotically JointIndependentlyNormal (Second Edition)
• Babson-Steingr msson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian)
• Towards a SymbolicComputational Philosophy (and Methodology!) for Mathematics Doron ZEILBERGER 1
• The Sum of Two and Seven and The Product of Three by Three Semaj Srelles
• Automatic CounTilings Doron ZEILBERGER 1
• TEST YOUR C.Q. [Conjecture-Quotient] Doron ZEILBERGER 1
• Dodgson's Determinant-Evaluation Rule Proved by TWO-TIMING MEN and WOMEN
• IDENTITIES IN SEARCH OF IDENTITY 1 Doron Zeilberger 2
• A Heterosexual Mehler Formula for the Straight Hermite Polynomials ( A La Foata)
• CLOSED FORM (pun intended!) Doron Zeilberger *
• I Am Sorry, Richard Ehrenborg and Margie Readdy, About Your Two Conjectures, But One is FAMOUS, While The Other Is FALSE
• Positive and Negative (Automated!) Thinking in Enumerating Permutations Avoiding Consecutive Patterns (According to Andrew Baxter and Brian Nakamura [and implemented by S.B. Ekhad])
• Remarks On The PARRONDO PARADOX Shalosh B. EKHAD 1 and Doron ZEILBERGER 1
• The Goulden-Jackson Cluster Method: Extensions, Applications and Implementations John NOONAN 1 and Doron ZEILBERGER 1
• Dr. Z's Math251 Handout #14.4 [Tangent Planes and Linear Approximations] By Doron Zeilberger
• PCMAUPCM001 Enumerative and Algebraic Combinatorics
• Dr. Z.'s Math 250(1), (Fall 2010, RU) Solutions to the REAL Quiz #3 (Sept. 30, 2010) 1. (4 pts.) Find (i) the (2, 3) entry of AC ; (ii) the (3, 2) entry of CA ; if the matrices A and C
• Dr. Z's Math251 Handout #14.3 (2nd ed.) [Partial Derivatives] By Doron Zeilberger
• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 57, 350-367 (1977) A New Approach to the Theory of Discrete Analytic Functions
• The Automatic Central Limit Theorems Generator (and Much More!) Doron ZEILBERGER1
• Dr. Z's Math151 Handout #5.2 Problem Type 5.2.1: Draw a graph of the signed area represented by the integral
• Discrete Mathematics 56 (1985) 61-72 ~1 North-Holland
• Annals of Combinatorics 8 (2004) 369-378 0218-0006/04/030369-10
• SOLUTIONS to MATH 250 (2), Dr. Z. , Exam 1, Thurs., Oct. 14, 2010, 10:20-11:40am, 1. (10 pts. altogether)
• Dodgson's Determinant-Evaluation Rule Proved by TWO-TIMING MEN and WOMEN
• ADVANCES IN MATHEMATICS 78, 42-75 (1989) Generalized Rogers-Ramanujan Bijections
• EXPERIMENTAL METHODS APPLIED TO THE COMPUTATION OF INTEGER SEQUENCES
• Solutions to the "QUIZ" for Sept. 28, 2009 1. Find the directional derivative of the function f(x, y, z) = xy2
• Lagrange Inversion Without Tears (Analysis) (based on Henrici) Doron ZEILBERGER
• THE QUANTUM MACMAHON MASTER THEOREM STAVROS GAROUFALIDIS, THANG TQ L ^
• How Berger, Felzenbaum and Fraenkel Revolutionized COVERING SYSTEMS The Same Way that George Boole Revolutionized LOGIC
• Babson-Steingr msson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian)
• A COMBINATORIAL PROBLEM THAT AROSE IN BIOPHYSICS By Doron Zeilberger
• FORTY \STRANGE" COMPUTER-DISCOVERED [and COMPUTER-PROVED (of course!)]
• AsyRec: A Maple package for Computing the Asymptotics of Solutions of Linear Recurrence Equations with Polynomial Coecients
• On Vince Vatter's Brilliant Extension of Doron Zeilberger's Enumeration Schemes for Herb Wilf's Classes
• King Solomon and Rabbi Ben Ezra's Evaluations of Pi and Patriarch Abraham's Analysis of an Algorithm
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding Doron ZEILBERGER 1
• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER 1
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
• GERT ALMKVIST'S GENERALIZATION OF A MISTAKE OF BOURBAKI 1 Doron Zeilberger 2
• Two Dimensional Directed Lattice Walks with Arvind Ayyer
• SOME NICE SUMS ARE ALMOST AS NICE IF YOU TURN THEM UPSIDE DOWN
• Temple University Philadelphia, Pennsylvania 19122-2595 Department of Mathematics e-mail: zeilberg@math.temple.edu
• REVIEW PROBLEMS FOR FINAL EXAM MATH 151, FALL 2003
• THE UMBRAL TRANSFERMATRIX METHOD. V. The GouldenJackson Cluster Method for Infinitely Many Mistakes
• Automatic CounTilings Doron ZEILBERGER 1
• How Borwein and Bradley's Hypergeometric Ugly Duckling Turned Into a Beautiful `Eulerian' Swan, thanks to Almkvist and Granville's Magic
• Mathematical Genitalysis: A Powerful New Combinatorial Theory that Obviates Mathematical Analysis Doron ZEILBERGER 1
• The Capital by Karl Marx by Hadas Zeilberger
• The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal
• Seminaire Lotharingien de Combinatoire, B16a (1987), 14 pp. [Formerly : Publ. I.R.M.A. Strasbourg, 1987, 341/S16, p. 7386.]
• New York Journal of Mathematics New York J. Math. 3 (1997) 54102.
• Solutions to the "QUIZ" for SEPT. 17, 2009 1, Find the curvature for
• Dr. Z's Math251 Handout #14.7 (2nd ed.) [Optimization in Several Variables] By Doron Zeilberger
• Dr. Z's Math152 Handout #6.2 [Volumes] By Doron Zeilbegrer
• The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) And PROOF(!!) of Holonomic Determinant Evaluations
• Solutions to the "QUIZ" for Nov. 5, 2009 1. Let C be the line segment from (0, 1) to (2, 3), find C
• NAME: Section: MATH 151(07-09,20-22), Dr. Z., Third Practice Final, Due Dec. 15, 2008, 3:50pm.
• NAME: (print!) Section: E-Mail address
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 16, 2007
• NAME: Section: MATH 151(20-22), Dr. Z. , First Midterm, Mon., Oct. 13, 2008.
• Positive and Negative (Automated!) Thinking in Enumerating Permutations Avoiding Consecutive Patterns (According to Andrew Baxter and Brian Nakamura [and implemented by S.B. Ekhad])
• Dr. Z's Math251 Handout #17.1b (2nd ed.) [Curl and Divergence] By Doron Zeilberger
• Dr. Z's Math151 Handout #2.5 [Continuity] By Doron Zeilberger
• REVEREND CHARLES to the aid of MAJOR PERCY and FIELDS-MEDALIST ENRICO Doron ZEILBERGER 1
• A Sharp Upper Bound for the Order of The Recurrence Outputted by Zeilberger's Algorithm 1 Mohamud MOHAMMED 2 and Doron ZEILBERGER 3
• A Sharp Upper Bound for the Order of The Recurrence Outputted by Zeilberger's Algorithm 1 Mohamud MOHAMMED 2 and Doron ZEILBERGER 3
• Symbolic Moment Calculus I.: Foundations and Permutation Pattern Statistics Doron ZEILBERGER 1
• THE UMBRAL TRANSFER-MATRIX METHOD. III. Counting Animals Doron ZEILBERGER 1
• Rutgers University New Brunswick New Jersey 08903 Department of Mathematics e-mail: zeilberg@math.rutgers.edu
• The ABSTRACT LACE EXPANSION Doron ZEILBERGER 1
• Sipur and Mispar in Ibn Ezra's Sefer HaMispar Doron ZEILBERGER1
• "TRIVIALIZING" GENERALIZATIONS OF SOME IZERGIN-KOREPIN-TYPE DETERMINANTS
• NAME: (print!) Section: E-Mail address
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• Positive and Negative (Automated!) Thinking in Enumerating Permutations Avoiding Consecutive Patterns (According to Andrew Baxter and Brian Nakamura [and implemented by S.B. Ekhad])
• The Automatic Central Limit Theorems Generator (and Much More!) Doron ZEILBERGER 1
• AN EXPERIMENTAL MATHEMATICS PERSPECTIVE ON THE OLD, AND STILL OPEN, QUESTION OF WHEN TO STOP?
• PUBLICATIONS OF DORON ZEILBERGER Last Update: May 4, 2005
• TALMUDIC LATTICE PATH COUNTING Jane Friedman, Ira Gessel, and Doron Zeilberger
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• A Fibonacci-Counting Proof Begged by Benjamin and Quinn Doron ZEILBERGER 1
• DECONSTRUCTING the ZEILBERGER algorithm Doron ZEILBERGER 1
• Patterns and Fractions Aaron Robertson
• The Number of Ways of Walking in x 1 : : : x k 0 for n Days, Starting and Ending at the Origin, Where at each Day you may either Stay in Place or Move One Unit in any Direction,
• Proof of a Conjecture of Amitai Regev About Hook Multi-Sets Doron ZEILBERGER 1
• Symbol-Crunching With the Gambler's Ruin Problem Doron ZEILBERGER 1
• A PROOF OF GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE
• Complete to Solutions: MATH 251 (1-3), Dr. Z. , Mid-Term #1, 10:20-11:40 , Thu., Oct. 12, 2006
• The Gift Exchange Problem, Part II By Moa Apagodu, David Applegate, Neil Sloane, and Doron Zeilberger
• An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding Doron ZEILBERGER1
• Solutions to MATH 151(20-22), Dr. Z. , Second Midterm, Thursday, Nov. 20, 2008, and some suggested extra problems
• ON THE EVOLUTION OF RANDOM GRAPHS P. ERD& and A. RBNYI
• A Multi-set Identity for Partitions Amitai REGEV 1
• The Gift Exchange Problem, Part II By Moa Apagodu, David Applegate, Neil Sloane, and Doron Zeilberger
• Proof of the Riemann Hypothesis, and some other Hitherto Undemonstrated Propositions Shalosh B. Ekhad 1
• PROOF OF A CONJECTURE OF GESSEL MANUEL KAUERS AND CHRISTOPH KOUTSCHAN AND DORON ZEILBERGER y
• A BINOMIAL COEFFICIENT IDENTITY ASSOCIATED TO A CONJECTURE OF BEUKERS
• The Theory of Self-Avoiding Walks is Only %66.81 Mathematical (According to the Appel Test) Shalosh B. EKHAD 1
• NAME: (print!) Section: E-Mail address
• Dr. Z's Math151 Handout #4.6 [Applied Optimization] By Doron Zeilberger
• Solutions to the "QUIZ" for Dec. 14, 2009 (Marathon Review Session) Which of the following answers is nonsense. Explain!
• Dr. Z's Math251 Handout #12.3 [The Dot Product] By Doron Zeilberger
• HolonomicFunctions.m HolonomicFunctions package by Christoph Koutschan, RISC-Linz, Version 1.3 (25.01.2010)
• Solutions to the "QUIZ" for Nov. 9, 2009 1. Determine whether or not the vector field
• Solutions to Dr. Z.'s Math 250(2), (Fall 2010, RU) REAL Quiz #7 (Nov. 4, 2010) 1. (5 points) Find a basis for the null space of the matrix
• Advances in Applied Mathematics 30 (2003) 633654 www.elsevier.com/locate/yaama
• The umbral transfer-matrix method IV. Counting self-avoiding polygons and walks
• Discrete Mathematics 64 (1987) 313-315 North-Holland
• Avoiding Differences Spanning Trees in Grid Graphs
• Solutions to the "QUIZ" for Dec. 4, 2008 1. Find the area of the region enclosed between y = x2
• THE 1958 PEKERIS-ACCAD-WEIZAC GROUND-BREAKING COLLABORATION THAT COMPUTED GROUND STATES OF
• Solutions to the `QUIZ" for Sept. 15, 2008 1. Evaluate the limit if it exists
• COMBINATORIAL PROOFS OF CAPELLI'S AND TURNBULL'S IDENTITIES FROM
• Symbolic Moment Calculus II.: Why is Ramsey Theory Sooooo Eeeenormously Hard? Doron ZEILBERGER 1
• The Capital by Karl Marx Trade is a very important procedure that society cannot do without but before one gets there they
• THE UMBRAL TRANSFER-MATRIX METHOD. V. The Goulden-Jackson Cluster Method for In nitely Many Mistakes
• ON FRAENKEL'S NHEAP WYTHOFF'S CONJECTURES XINYU SUN AND DORON ZEILBERGER
• All the Moments of the Vertex Degrees of Randomly Generated Graphs Doron ZEILBERGER 1
• Sylvie Corteel's One-Line Proof of a Partition Theorem Discovered by Andrews-Paule-Riese's In the conference `Combinatorics and Physics' organized by Bill Chen and Jim Louck (Los Alamos, Aug.
• Request for an NSF supplement for the AY 2006-07 for Graduate Student Support Doron ZEILBERGER 1
• Sharp Upper Bounds for the Orders of The Recurrences Outputted by the Zeilberger and q-Zeilberger Algorithms
• A note on the paper : Closed Form (pun in-tended),1993 by Doron Zeilberger
• A PROOF OF GEORGE ANDREWS' AND DAVID ROBBINS' q-TSPP CONJECTURE
• JOURNALOFCOMBINATORIALTHEORY,Series A 66, 17-27 (1994) A Constant Term Identity
• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER1
• Discrete Mathematics 80 (1990) 207-211 North-Holland
• Discrete Mathematics 82 (1990) 89-92 North-Holland
• Solutions to the Attendance Quiz for Oct. 11, 2010 1. a) Find an LU decomposition of the following matrix
• Dr. Z's Math152 Handout #7.2 [Trigonometric Integrals] By Doron Zeilberger
• 2 Proofs that n k+1 if k < n/2.
• David M. BRr;lSSOWD Deparmenr of Mathematics, Pennsylvania State Unwrsity., University Park, PA 1VW!, liSA
• Complete SOLUTIONS to: MATH 251 (1-3), Dr. Z. , Mid-Term #2, 10:20-11:40 , Mon., Nov. 20, 2006
• Complete Solutions to : MATH 251 (4-6), Dr. Z. , Mid-Term #1, 12:0-1:20 , Thu., Oct. 12, 2006
• DiscreteMathematics51 (1984) lOI-lG'8 North-Holland
• Journal of Combinatorial Theory, Series A 82, 186 192 (1998) A Pentagonal Number Sieve
• J. Symbolic Computation (1991) 11, 195-204 The Method of Creative Telescoping
• RESEARCH ANNOUNCEMENTS BULLETIN (New Series) OF THE
• SIAM J. MATH. ANAL. Vol. 18, No. 3, May 1987
• One-Line Proofs of the Unimodality of Doron Zeilberger
• Discrete Mathematics 44 (1983) 325-326 North-Holland Publishing Company
• SIAM J. MATH. ANAL. Vol. 14, No. 2, March 1983
• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 85, 114-145 (1982) Sister Celine's Technique
• Proc. Natl. Acad. Sci. USA Vol. 75, No. 8, pp. 3555-3556, August 1978
• Advances in Applied Mathematics 28, 279 (2002) doi:10.1006/aama.2001.0782, available online at http://www.idealibrary.com on
• Toward a Crlmbinatorial Proof of t h e Jacobian Conjecture?
• A ONE-LINE HIGH SCHOOL ALGEBRA PROOF OF THE UNIMODALITY OF THE GAUSSIAN
• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 147, 610611 (1990) A 21st Century Proof of Dougall's
• Invent.math. 108:575-633 (1992) mathematicae
• Discrete Mathematics 102 (1992) 85-93 North-Holland
• Theoretical Computer Science 117 (1993) 23-38 Identities in search of identity*
• JOURNAL OF COMBINATORIALTHEORY, Series A 68, 215-217 (1994) Talmudic Lattice Path Counting
• JOURNALOFCOMBINATORIALTHEORY,SeriesA 66, 311-312 (1994) Proof of a q-Analog of a Constant Term Identity
• SIAM J. MATH. ANAL. Vol. 25, No. 2, pp. 812-814, March 1994
• The Number of Solutions of X2 = 0 in Triangular Matrices Over GF(q) Shalosh B. EKHAD1
• New York Journal of Mathematics New York J. Math. 2 (1996) 5968.
• COMPUTATIONAL AND APPUED MATHEMATICS
• HYPERGEOMETRIC SERIES ACCELERATION VIA THE WZ METHOD Tewodros Amdeberhan and Doron Zeilberger
• journal of combinatorial theory, Series A 80, 380 384 (1997) A Classic Proof of a Recurrence
• ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY
• A BINOMIAL COEFFICIENT IDENTITY ASSOCIATED TO A CONJECTURE OF BEUKERS
• A 2-COLORING OF [1, N] CAN HAVE (1/22)N2 + O(N) MONOCHROMATIC
• Annals of Combinatorics 2 (1998) 185-195 Combinatorics
• Z .ADVANCES IN APPLIED MATHEMATICS 20, 275 283 1998 ARTICLE NO. AM970565
• Permutation Patterns and Continued Fractions Aaron Robertson
• SYMBOL-CRUNCHING WITH THE TRANSFER-MATRIX METHOD IN ORDER TO COUNT SKINNY PHYSICAL CREATURES
• Advances in Applied Mathematics 26, 168179 (2001) doi:10.1006/aama.2000.0714, available online at http://www.idealibrary.com on
• Z .Advances in Applied Mathematics 27, 207 209 2001 doi:10.1006raama.2001.0756, available online at http:rrwww.idealibrary.com on
• New York Journal of Mathematics New York J. Math. 7 (2001) 223231.
• Advances in Applied Mathematics 27, 390404 (2001) doi:10.1006/aama.2001.0741, available online at http://www.idealibrary.com on
• Algebra univers. 49 (2003) 387395 0002-5240/03/040387 09
• The Markov-WZ Method Mohamud MOHAMMED and Doron ZEILBERGER*
• Chomp, Recurrences and Chaos(?) DORON ZEILBERGER*,
• Annals of Combinatorics 8 (2004) 225-238 0218-0006/04/020225-14
• Journal of Symbolic Computation 39 (2005) 201207 www.elsevier.com/locate/jsc
• Advances in Applied Mathematics 34 (2005) 939954 www.elsevier.com/locate/yaama
• Ekhad and the Master Shalosh B. Ekhad is known to be
• The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal (Second Edition)
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
• Efficient Counting And Asymptotics Of k-noncrossing Tangled Diagrams
• A PROOF OF GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE @wyhvy e psxsi ewyx yp ysxi gevgvesyxA
• EXPERIMENTS WITH A POSITIVITY PRESERVING OPERATOR MANUEL KAUERS AND DORON ZEILBERGER
• Princeton Companion to Mathematics Proof 1 Enumerative and Algebraic
• FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Probability 1 Moa APAGODU and Doron ZEILBERGER
• The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Path Counting
• "TRIVIALIZING" GENERALIZATIONS OF SOME IZERGIN-KOREPIN-TYPE DETERMINANTS
• Symbolic Moment Calculus II.: Why is Ramsey Theory Sooooo Eeeenormously Hard? Doron ZEILBERGER 1
• THE QUANTUM MACMAHON MASTER THEOREM STAVROS GAROUFALIDIS, THANG TQ L^E, AND DORON ZEILBERGER
• Pythagorean Primes and Palindromic Continued Fractions Arthur T. Benjamin and Doron Zeilberger
• ON FRAENKEL'S N-HEAP WYTHOFF'S CONJECTURE XINYU SUN AND DORON ZEILBERGER
• "REAL" ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS Doron ZEILBERGER 1
• THE UMBRAL TRANSFER-MATRIX METHOD. V. The Goulden-Jackson Cluster Method for Infinitely Many Mistakes
• !#"$%'&()0 2143560 87@9BA 1DCBAFEHGPIRQTSVUWQYX`a%b"c&(dCe7'149e148fhg7'Tipfp7'!qQsrut62bv!
• &('0)214365187@9A)CBEDF143 GIHQPSRUTVHXW`YUacb$HQdfefacgih$prqtsUauTuvxwUHQTuRUsUauvypAq0CyFx
• Dodgson's Determinant-Evaluation Rule Proved by TWO-TIMING MEN and WOMEN
• "!#$&% ')(0123546&37" 8@9BAC308EDGFF H IQPSRUTVTWRUTYXQ`3Ia)Ib`0cedgfhcid Pgcipqcidgcirs`&XtfvuwfxIbTyrf
• Combinatorial Proofs of Capelli's and Turnbull's Identities from Classical Invariant Theory
• THE METHOD OF DIFFERENTIATING UNDER THE INTEGRAL SIGN Gert Almkvist * and Doron Zeilberger**
• April 3, 2007 9:42 WSPC -Proceedings Trim Size: 9in x 6in WWCA06 FIVE APPLICATIONS OF WILF-ZEILBERGER THEORY
• Combinatorial Proofs of Capelli's and Turnbull's Identities from Classical Invariant Theory
• Dr. Z's March 10 Colloquium Handout Problem Type: A function is given by some rule. First conjecture, and then rigorously prove, an
• Referee Report for "On Vince Vatter's Brilliant Extension of Doron Zeilberger's Enu-meration Schemes for Herb Wilf's Classes"
• A bijective proof of fn+4 + f1 + 2f2 + + nfn = (n + 1)fn+2 + 3
• D'var Torah on Parshat D'varim Jane LeGrange
• RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION Doron Zeilberger
• Project Description Summary of Results from Previous NSF Support: DMS-8901610 and DMS-9123836
• COMPUTER-ASSISTED AND COMPUTER-GENERATED RESEARCH IN COMBINATORIAL GAMES AND
• ENUMERATION SCHEMES FOR PATTERN-AVOIDING WORDS AND
• Dr. Z's Math151 Handout #2.1 [The Tangent and Velocity Problems] By Doron Zeilberger
• Dr. Z's Math151 Handout # 2.3 [Calculating Limits Using the Limit Laws] By Doron Zeilberger
• Dr. Z's Math151 Handout #2.6 [Limits at Infinity: Horizontal Asymptotes] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.1 [Derivatives of Polynomials and Exponential Functions] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.3 [Rates of Change in the Natural and Social Sciences] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.6 [Implicit Differentiation] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.7 [Higher Derivatives] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.1 [Maximum and Minimum Values] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.2 [The Mean Value Theorem] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.4 [Indeterminate Forms and L'H^ospital's Rule] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.7 [Optimization Problems] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.9 [Newton's Method] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.10 [Antiderivatives] By Doron Zeilberger
• Dr. Z's Math151 Handout #5.4 [Indefinite Integrals and the Net Change Theorem] By Doron Zeilberger
• Dr. Z's Math151 Handout #5.5 [The Substitution Rule] By Doron Zeilberger
• Dr. Z's Math152 Handout #6.4 [Work] By Doron Zeilberger
• Dr. Z's Math152 Handout #7.1 [Integration by Parts] By Doron Zeilberger
• Dr. Z's Math152 Handout #7.3 [Trigonometric Substitution] By Doron Zeilberger
• Dr. Z's Math152 Handout #7.7 [Approximate Integration] By Doron Zeilberger
• Dr. Z's Math152 Handout #8.2 [Area of a Surface of Revolution] By Doron Zeilberger
• Dr. Z's Math152 Handout #9.3 [Separable Equations] By Doron Zeilberger
• Dr. Z's Math152 Handout #9.4 [Exponential Growth and Decay] By Doron Zeilberger
• Dr. Z's Math152 Handout #10.2 [Calculus with Parametric Curves] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.1 [Sequences] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.3 [The Integral Test and Estimation of Sums] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.5 [Alternating Series] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.8 [Power Series] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.9 [Representations of Functions as Power Series] By Doron Zeilberger
• Dr. Z's Math251 Handout #12.4 [The Cross Product] By Doron Zeilberger
• Dr. Z's Math251 Handout #13.2 [Derivates and Integrals of Vector Functions] By Doron Zeilberger
• Dr. Z's Math251 Handout #13.3 [Arc Length and Curvature] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.6 [Directional Derivatives and the Gradient Vector] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.6 [Surface Area] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.7 [Triple Integrals] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.8 [Triple Integrals in Cylindrical and Spherical Coordinates] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.2 [Line Integrals] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.3 [The Fundamental Theorem for Line Integrals] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.8 [Stokes' Theorem] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.9 [The Divergence Theorem] By Doron Zeilberger
• Dr. Z's Math151 Handout # 2.2 [Limits: A Numerical and Graphical Approach] By Doron Zeilberger
• Dr. Z's Math151 Handout # 2.6 [Trigonometric Limits] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.1 Problem Type 3.1.1: Compute the derivative at the fiven point x = a, of a given function f(x),
• Dr. Z's Math151 Handout #3.2 Problem Type 3.2.1: Compute f (x) from the limit definition (no credit for other methods!),
• Dr. Z's Math151 Handout #3.4 [Rates of Change] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.5 [Higher Derivatives] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.6 [Trigonometric Functions] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.7 [The Chain Rule] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.8 [Implicit Differentiation] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.2 [Extreme Values] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.3 [The Mean Value Theorem and Monotinicity] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.5 [Graph Sketching and Asymptotes] By Doron Zeilberger
• Dr. Z's Math151 Handout #4.7 [L'H^ospital's Rule] By Doron Zeilberger
• Dr. Z's Math151 Handout #5.6 [The Substitution Rule] By Doron Zeilberger
• Solutions to "QUIZ" for Sept. 4, 2008 1. What are: (a) sin 0 (b) cos 0 (c) ln 1 .
• Solution to the "QUIZ" for Monday, Sept. 8, 2008 1. : (a) Draw the function
• Solutions to the "QUIZ" for Oct. 27, 2008 1. Suppose that f(x) is differentiable everywhere and we know that f(2) = 1 and f (x) -2 for
• Solutions to the "QUIZ" for Nov. 3, 2008 1. A farmer has 3000 meters of fence, and needs to make a rectangular animal-shed, with a partition
• Solutions to the "QUIZ" for Nov. 13, 2008 100 -x2 dx .
• Dr. Z's Math251 Handout (2nd ed.) #12.1 [Vectors in the Plane] By Doron Zeilberger
• Dr. Z's Math251 Handout (2nd ed.) #12.2 [Vectors in three dimensions] By Doron Zeilberger
• Dr. Z's Math251 Handout (2nd ed.) #12.3 [Dot Product and the Angle Between Two Vectors] By Doron Zeilberger
• Dr. Z's Math251 Handout #12.4 (2nd ed.) [The Cross Product] By Doron Zeilberger
• Dr. Z's Math251 Handout #12.5 (2nd ed.) [Planes in Three Space] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.2 (2nd ed.) [Limits and Continuity in Several Variables] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.1 (2nd ed.) [Integration in Several Variables] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.2 (2nd ed.) [Double Integrals over General Regions] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.3 (2nd ed.) [Triple Integrals] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.2 (2nd ed.) [Line Integrals] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.3 (2nd ed.) [Conservative Vector Fields] By Doron Zeilberger
• Dr. Z's Math251 Handout #17.2 (2nd ed.) [Stokes' Theorem] By Doron Zeilberger
• Dr. Z's Math251 Handout #17.3 (2nd ed.) [The Divergence Theorem] By Doron Zeilberger
• Solutions to the "QUIZ" for SEPT. 3, 2009 1. Show that the triangle with vertices P = (1, 0, 0), Q = (0, 1, 0), and R = (0, 0, 1) is an equilateral
• Solutions to the "QUIZ" for Sept. 10, 2009 1. Find an equation of the plane that passes through the points (0, 1, 1), (1, 0, 1), (1, 1, 0).
• Solutions to the "QUIZ" of SEPT. 14, 2009 1. Find a parametric equation for the tangent line to the curve with the given parametric equation
• Solutions to the "QUIZ" for Sept. 21, 2009 1. Find the limit if it exists, or show that the limit does not exist.
• Solutions to the "QUIZ" for Sept. 24, 2009 1. Compute the partial derivatives with respect to x and y.
• Solutions to the "QUIZ" for Oct. 5, 2009 1. Find the local maximum and minimum point(s), the local maximum and minimum values, and
• Solutions to the "QUIZ" for Nov. 2, 2009 1. Sketch the planar vector field
• Solutions to the `QUIZ" for Nov. 12, 2009 1. Find an equation for the tangent plane to the parametric surface
• Solutions to the "QUIZ" for Nov. 30, 2009 1. Determine whether or not the vector field is conservative. If it is, find a function f such that
• Solution to the "QUIZ" for Dec. 3, 2009 By using Stokes' Theorem, or otherwise, evaluate C
• Solutions to the Attendance Quiz for Sept. 16, 2010 1. Determine the value of r for which
• Solutions to the Attendance Quiz for Nov. 1, 2010 1. Determine the dimension of the following subspace. Explain what you are doing!
• Solutions to the Attendance Quiz for Nov. 4, 2010 1. A matrix and a vector are given. Show that the vector is an eigenvector of the matrix, and
• Solutions to the Attendance Quiz for Nov. 8, 2010 1. Find the eigenvues of the following matrix, and determine a basis for each eigenspace.
• Solutions to the Attendance Quiz for Nov. 11, 2010 1. Let v be a non-zero vector in R2
• Solutions to the Attendance Quiz for Nov. 18, 2010 Version of Nov. 29., 2010 (Correcting the final answer, thanks to Charlie Cawczynski who won $2)
• Solutions to the Attendance Quiz for Dec. 2, 2010 1. (a) Apply the Gram-Schmidt process to replace the given linearly independent set S by an
• Solution to Attendance Quiz for Dec. 13, 2010 1. Obtain the solution of least norm to the equation
• Dr. Z.'s Math 250(1), (Fall 2010, RU) SOLUTIONS to the REAL Quiz #2 (Sept. 23, 2010) 1. (4 pts.) Determine whether the given system is consistent, and if so, find its general solution.
• Dr. Z.'s Math 250(2), (Fall 2010, RU) Solutions to REAL Quiz #3 (Sept. 30, 2010) 1. (4 pts.) Find A4
• Solutions to Dr. Z.'s Math 250(1), (Fall 2010, RU) REAL Quiz #5 (Oct. 21, 2010) 1. a) Find an LU decomposition of the following matrix
• Solutions to Dr. Z.'s Math 250(1), (Fall 2010, RU) REAL Quiz #7 (Nov. 4, 2010) 1. (5 points) Find a basis for the following subspace
• Solutions to Dr. Z.'s Math 250(1), (Fall 2010, RU) REAL Quiz #9 (Dec. 2, 2010) 1. (4 points) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix
• Answers (and some hints) for the Exam 1 Review Problems (version of Oct. 13, 2010, 2:15pm, thanks to Devon Peticolas
• MATH 250, Fall 2010, Sections 1 and 2 (Dr. Z.) , Answers (and some hints and sketches) for Practice Problems for Exam 2
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• Automatic Generation of Generating Functions for Enumerating Matchings By Shalosh B. EKHAD and Doron ZEILBERGER
• The Sum of Two and Seven and The Product of Three by Three Semaj Srelles
• Automatic Generation of Generating Functions for the Number of Spanning Trees for Grid Graphs (and Much More General Creatures) of Fixed (but arbitrary!) Width
• Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
• The Sagan-Savage Lucas-Catalan Polynomials Have Positive Coefficients Shalosh B. EKHAD1
• A Note on the Stanley Distribution Shalosh B. EKHAD1
• A Eulogy for Jack Good Doron ZEILBERGER1
• You Don't Have To Be an Einstein to Figure Out that Sara Should (Asymptotically) Eat 27 + O(1/n) Dove Bars,
• Research Announcement: A Computer-Generated Proof that P=NP Doron ZEILBERGER1
• An Inelegant (but Short(!)) Proof of a Major Index Theorem of Garsia and Gessel Doron ZEILBERGER1
• An Inelegant (but Short(!)) Proof of a Major Index Theorem of Garsia and Gessel (Verbose Version) Doron ZEILBERGER1
• ON THE NUMBER OF WALKS ON A REGULAR CAYLEY ERIC ROWLAND AND DORON ZEILBERGER
• AsyRec: A Maple package for Computing the Asymptotics of Solutions of Linear Recurrence Equations with Polynomial Coefficients
• How Likely Is Polya's Drunkard to Return to the Pub Without Getting Mugged? (In d-Dimensional Manhattan [d 2])
• Proof of a Conjecture of Philippe Di Francesco and Paul Zinn-Justin related to the qKZ equation and to Dave Robbins' Two Favorite Combinatorial Objects
• In How Many Ways Can n (Straight) Men and n (Straight) Women Get Married, if Each Person Has Exactly k Spouses?
• Fully AUTOMATED Computerized Redux of Feller's (v.1) Ch. III (and Much More!) Doron ZEILBERGER1
• What Is Experimental Mathematics? Doron ZEILBERGER1
• An Umbral Approach to the Hankel Transform for Sequences Doron ZEILBERGER1
• Another Proof that Euler Missed: Jonas Sjostrand's Amazingly Simple (and Lovely!) Proof of the No-Longer-So-Amazing Loehr-Warrington Lattice Paths Conjecture
• Dr. Paul Alexander Berlin-Charlottenburg 4, May 23, 1942 Mommsen Street 47 III
• The Gift Exchange Problem Moa Apagodu
• A Heterosexual Mehler Formula for the Straight Hermite Polynomials (`A La Foata) Doron ZEILBERGER1
• Optimizing a losing game December 15, 2009
• Solution to Monthly Problem 11567 Andrew M. Baxter
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• NAME: Section: MATH 251 (4-6,11), Dr. Z. , Exam 2, 12:00noon-1:20pm , Thurs. Nov. 19, 2009, SEC
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• NAME: Section: MATH 251 (1-6,10-11), Dr. Z. , Third Practice Test for Exam #2
• MATH 251 (1-3,10 ), Dr. Z. , Solutions to Exam 1 , Thurs., Oct. 8, 2009, SEC 118 1. (10 pts.) Find the curvature of the curve
• There is a series of Erdos-Renyi papers on the subject, but the most concise formulation I found was in the 1961 paper (attached, page 3 bottom). Here the
• Fractals, Vol. 14, No. 2 (2006) 133142 c World Scientific Publishing Company
• NAME: Section: MATH 151(07-09,20-22), Dr. Z., First Practice Final, Due Dec. 15, 2008, 3:50pm.
• Solutions For MATH 151(07-09), Dr. Z. , Second Midterm, Thursday, Nov. 20, 2008. Remember: 1. Show all your work. 2. Make sure that the answer(s) is (are) of the right type.
• NAME: Section: MATH 151(20-22), Dr. Z. , Second Midterm, Thursday, Nov. 20, 2008.
• Formula Sheet for Math 151, Exam 2 Lines: If (x1, y1), (x2, y2) lie on a line L, the slope of L is m = y2-y1
• Solutions to MATH 151(07-09), Dr. Z. , First Midterm, Mon., Oct. 13, 2008. 1. (12 points) Find f (4), if
• NAME: Section: MATH 151 (Fall 2008) Dr. Z. , First Practice For First Midterm Exam
• NAME: Section: MATH 151 (Fall 2008) Dr. Z. , Third Practice For First Midterm Exam
• Discrete Mathematics 64 (1987) 313-315 North-Holland
• Bijecting Euler's Partitions-Recurrence David M. Bressoud; Doron Zeilberger
• Investigating Young Tableaux in a Box Emilie Hogan
• Experimental Math Project Emilie Hogan
• ON THE MONOCHROMATIC SCHUR TRIPLES TYPE THOTSAPORN "AEK" THANATIPANONDA
• NAME: Section: MATH 251 (1-3), Dr. Z. , Mid-Term #2, 10:20-11:40 , Mon., Nov. 20, 2006
• NAME: Section: MATH 251 (4-6), Dr. Z. , Mid-Term #2, 12:00-1:20 , Mon., Nov. 20, 2006
• Complete Solutions to MATH 251 (4-6), Dr. Z. , Mid-Term #2, 12:00-1:20 , Mon., Nov. 20, 2006
• INTRODUCTION TO MACAULAY 2 DIANE MACLAGAN
• MATH 152 (07-09), Dr. Z. , Solution to Second Midterm 1. (10 points) Use the integral test to determine whether the series is convergent or
• Dr. Z's Math 152 Review Problems for Final Exam, Fall 2005 Due: Fri. Dec. 16, 4:00pm, 2005
• ISRAEL MOISEEVITCH GELFAND I spent many years in close association with Gelfand. Let me try to recall a few moments.
• THE ANDREWS-STANLEY PARTITION FUNCTION AND p(n) HOLLY SWISHER
• TALES OF OUR PARENTS Lea Sachsendorfer
• Chemical Matters Found in the Bible Lecture for the Benefit of the Scholarship Fund
• In[1]:= HolonomicFunctions.m HolonomicFunctions package by Christoph Koutschan, RISC-Linz, Version 1.3 (25.01.2010)
• The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Walk Counting
• April 14, 2007 9:46 World Scientific Review Volume -9in x 6in enquiry An Enquiry Concerning Human (and Computer!)
• A Symbolic Computation Approach to a Problem involving Multivariate Poission Distributions (Draft, do not distribute!)
• The Automatic Central Limit Theorems Generator (and Much More!)
• The Maximal number of floors a Building can have where you can tell the highest floor from where you can throw a glass ball without breaking it,
• Doron ZEILBERGER1 In algebra we have symbols and numbers mixed up. The notation is confusing. ab means a times
• The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal
• Automatic CounTilings Doron ZEILBERGER1
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
• NSF Proposal: RIGOROUS EXPERIMENTAL COMBINATORICS RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION
• PROJECT SUMMARY RIGOROUS EXPERIMENTAL COMBINATORICS
• SOME NICE SUMS ARE ALMOST AS NICE IF YOU TURN THEM UPSIDE DOWN
• Proof of a Conjecture of Amitai Regev About Hook Multi-Sets Doron ZEILBERGER1
• The Symbolic Goulden Jackson Cluster Method Xiangdong Wen
• EFFICIENT COUNTING AND ASYMPTOTICS OF k-NONCROSSING TANGLED-DIAGRAMS
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
• Automatic CounTilings Doron ZEILBERGER1
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 11, 2006
• Dr. Z's Math151 Handout # 2.2 [The Limit of a Function] By Doron Zeilberger
• Dr. Z's Math251 Handout #12.1 [Three Dimensional Coordinate Systems] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.8 (2nd ed.) [Lagrange Multipliers: Optimizing with a Constraint] By Doron Zeilberger
• Solutions to Dr. Z.'s Math 250(2), (Fall 2010, RU) REAL Quiz #8 (Nov. 11, 2010) 1. (5 points) Determine the dimension of the following subspace. Explain what you are doing!
• A Combinatorial Proof of log(e z ) = z Doron ZEILBERGER 1
• NSF Proposal: Targeted Proof Machines NSF PROPOSAL: Targeted Proof Machines in Combinatorics
• A SHORT WZ-STYLE PROOF OF ABEL'S IDENTITY Shalosh B. Ekhad and John E. Majewicz
• Automatic CounTilings Doron ZEILBERGER 1
• The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Path Counting
• Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 16, 2007
• THE ENUMERATION OF PERMUTATIONS WITH A PRESCRIBED NUMBER OF \FORBIDDEN" PATTERNS
• FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Probability 1 Moa APAGODU and Doron ZEILBERGER
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• Doron Zeilberger*, Department of Mathematics, Drexel University, Philadelphia, PA 19104 Current Address (1990-): Department of Mathematics, Temple University, Philadelphia, PA 19122;
• HISTABRUT: A Maple Package for SymbolCrunching in Probability theory Doron ZEILBERGER 1
• The Collector's Brotherhood Dominique Foata, 1 Doron Zeilberger 2
• Dr. Z's Math151 Handout #3.10 [Related Rates] By Doron Zeilberger
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• HOW TO PROVE GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE
• Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture
• Dr. Z's Math152 Handout #7.4 [Integration of Rational Functions by Partial Fractions]
• SIAM J. MATH. ANAL. Vol. 19, No. 6, November 1988
• Electronic Transactions on Numerical Analysis. Volume 9, 1999, pp. 147-148.
• Solutions to the "QUIZ" for Nov. 10, 2008 1. Find y = y(x) if d2
• The Markov-WZ Method Mohamud MOHAMMED and Doron ZEILBERGER*
• Proof of an Identity Conjectured by Iossif Polterovitch that Came Up in the Agmon-Kannai Asymptotic Theory of the Heat Kernel
• REFINED RESTRICTED PERMUTATIONS Aaron Robertson 1
• AUTOMATIC GENERATION of THEOREMS and PROOFS On Enumerating Permutations that Avoid Consecutive Patterns Brian NAKAMURA and Doron ZEILBERGER 1
• HOW TO PROVE GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE
• A NEW PROOF OF THE REFINED ALTERNATING SIGN MATRIX Ilse Fischer
• ADVANCES IN APPLIED MATHEMATICS ?, 1 8(2002) ARTICLE NO. ???
• Dave ROBBINS's ART of GUESSING Doron ZEILBERGER 1
• The Joy of Brute Force: The Covariance of The number of Inversions and the Major Index
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 11, 2006
• NAME: Section: MATH 151(07-09,20-22), Dr. Z. , Third Practice Exam for the Second Midterm
• Journal of Computational and Applied Mathematics 32 (1990) 321-368 North-Holland
• Z .ADVANCES IN APPLIED MATHEMATICS 19, 355 359 1997 ARTICLE NO. AM970552
• Dr. Z's Math151 Handout #5.3 [The Fundamental Theorem of Calculus, Part I] By Doron Zeilberger
• SYMBOL-CRUNCHING with the TRANSFER-MATRIX Method In Order to Count
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: March 6, 2009
• A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture Shalosh B. EKHAD 1 , Vince VATTER 1 , and Doron ZEILBERGER 1
• REFINED ASYMPTOTICS AND EXPLICIT RECURRENCES FOR THE NUMBERS OF YOUNG TABLEAUX IN THE (k; l) HOOK FOR k + l 5
• Proof of a Conjecture of Philippe di Francesco and Paul Zinn-Justin related to the qKZ equations and to Dave Robbins' Two Favorite Combinatorial Objects
• Akalu Tefera One of the most exciting mathematical dis-
• Self Avoiding Walks, The Language 1 of Science, and Fibonacci Numbers Doron ZEILBERGER 2
• How Much Should a 19th-Century French Bastard Inherit Doron ZEILBERGER 1
• GRAPHICAL MAJOR INDICES Dominique FOATA 1 and Doron ZEILBERGER 2
• Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(!!!)) Analogs of Collatz's Notorious 3x+1 Conjecture
• The MARKOV-WZ METHOD 1 Mohamud MOHAMMED 2 and Doron ZEILBERGER 3
• The Number of Inversions and the Major Index of Permutations are Asymptotically JointIndependentlyNormal (First Edition)
• Doron ZEILBERGER 1 In algebra we have symbols and numbers mixed up. The notation is confusing. ab means a times
• S eminaire Lotharingien de Combinatoire, B24a, 1990 THREE RECITATIONS ON HOLONOMIC SYSTEMS
• A Computational Approach To Finding Exact Solutions Of Ising-Type Problems Doron Zeilberger *
• Journal ?/ Sfu~i.s:ic-illPhj~siis.Cid. -5 7, Nos.; / 6 ,19SY How Likely Is Polya's Drunkard to Stay in x 3y 39
• THE UMBRAL TRANSFER-MATRIX METHOD V. The Goulden-Jackson Cluster Method for Infinitely Many Mistakes
• Discrete Mathematics 31 (1980) 65-T @ North-Holland Publishing Cornpar.,
• Discrete Mathematics 58 (1986) 109 North-Holland
• How Berger, Felzenbaum and Fraenkel Revolutionized COVERING SYSTEMS The Same Way that George Boole Revolutionized LOGIC
• In How Many Ways Can a King Return Home After n Steps? Shalosh B. EKHAD 1
• TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• The average number of i-dimensional Author: C.K.Lee
• NAME: (print!) Section: E-Mail address
• Dr. Z's Math251 Handout #15.9 [Change of Variables in Multiple Integrals] By Doron Zeilberger
• Solutions to the "QUIZ" for Oct. 12, 2009 1. Use Lagrange multipliers (no credit for other methods) to find the largest value that x + y + z
• Journal of Computational and Applied Mathematics 39 (1992) 379-382 North-Holland
• Solutions to the"QUIZ" for Oct. 30, 2008 1. Sketch the curve y = 2x3
• How to Play Backgammon (if you must) and how to Research it (if you have time) Shalosh B. EKHAD 1
• Dr. Z's Math251 Handout #15.5 (2nd ed.) [Change of Variables in Multiple Integrals] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.6 [Absolute Convergence and the Ratio and Root Tests] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.8 [Lagrange Multipliers] By Doron Zeilberger
• STATISTICAL MECHANICS AND COMBINATORICS OF SOME DISCRETE LATTICE MODELS
• Solutions to Dr. Z.'s Math 250(2), (Fall 2010, RU) REAL Quiz #5 (Oct. 21, 2010) 1. Find an LU decomposition of the following matrix
• Dr. Z's Math151 Handout #2.4 [The Precise Definition of a Limit] By Doron Zeilberger
• Seminaire Lotharingien de Combinatoire, B08c (1984) 9 pp. [Formerly : Publ. I.R.M.A. Strasbourg, 1984, 229/S08, p. 1725.]
• NAME: (print!) Section: E-Mail address
• Solutions to the "QUIZ" for Oct. 15, 2009 1. Calculate the iterated integral
• THE COMPUTATIONAL CHALLENGE OF ENUMERATING HIGH-DIMENSIONAL ROOK WALKS
• Solutions to the "QUIZ" for Dec. 1, 2008 1. Compute
• Dr. Z.'s Math 250(2), (Fall 2010, RU) Solutions to REAL Quiz #2 (Sept. 23, 2010) 1. (4 pts.) Determine the value of r, if any, for which the given system of linear equations is
• Solutions to MATH 250 (2), Dr. Z. , Exam 2, Mon., Nov. 15, 2010, 10:20-11:40am, ARC For both parts we need to do Gaussian elimination, and because of the second part we
• Dr. Z's Solutions to Dr. Scheffer's Math 152 Review Problems for Final Exam, Fall 2005
• Discrete Mathematics 54 (1985) 201-224 North-Holland
• Discrete Mathematics 79 (1989/90) 313-322 North-Holland
• Z .ADVANCES IN APPLIED MATHEMATICS 17, 381 407 1996 ARTICLE NO. 0016
• Report on the paper "The number of inversions and the major in-dex of permutations are asymptotically joint-independently-normal",
• Dr. Z's Math151 Handout #5.4 [The Fundamental Theorem of Calculus, Part II] By Doron Zeilberger
• A PROOF OF GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE
• AUTOMATIC GENERATION of THEOREMS and PROOFS On Enumerating Permutations that Avoid Consecutive Patterns Brian NAKAMURA and Doron ZEILBERGER1
• Dr. Z's Math251 Handout #15.4 [Double Integrals in Polar Coordinates] By Doron Zeilberger
• THE 1958 PEKERIS-ACCAD-WEIZAC GROUND-BREAKING COLLABORATION THAT COMPUTED GROUND STATES OF
• A CONDENSED CONDENSATION PROOF OF A DETERMINANT EVALUATION CONJECTURED BY Greg KUPERBERG AND Jim PROPP
• All the Hypergeometric Series Evaluations that are Fit to Print (By Looking Under the Hood of Zeilberger's Algorithm)
• Research Announcement: A ComputerGenerated Proof that P=NP Doron ZEILBERGER 1
• PROOF of CONWAY'S LOST COSMOLOGICAL THEOREM Shalosh B. Ekhad 1 and Doron Zeilberger 1
• A STEMBRIDGE-STANTON STYLE PROOF OF THE HABSIEGER-KADELL q-MORRIS IDENTITY
• A Eulogy for Jack Good Doron ZEILBERGER 1
• A FAST ALGORITHM FOR PROVING TERMINATING HYPERGEOMETRIC IDENTITIES *
• The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Walk Counting
• How Adam Marcus and Gabor Tardos Divided and Conquered the Stanley-Wilf Conjecture
• ``REAL'' ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS Doron ZEILBERGER 1
• A Constant Term Identity Featuring The Ubiquitous (And Mysterious) Andrews-Mills-Robbins-Rumsey Numbers 1,2,7,42,429, ...
• A New Algorithm for Proving Global Asymptotic Stability of Rational Difference Equations
• Dr. Z's Math151 Handout #4.4 [The Shape of a Graph] By Doron Zeilberger
• Dr. Z's Math251 Handout #13.5 (2nd ed.) [Motion in Three-Space] By Doron Zeilberger
• A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a finite amount of routine calculations) 1
• Solutions to MATH 251 (4-6,11 ), Dr. Z.'s , Exam 1 1. (10 points) Use the chain rule to find fu and fv if
• Pythagorean Primes and Palindromic Continued Fractions Arthur T. Benjamin and Doron Zeilberger
• Q-AP ERY IRRATIONALITY PROOFS BY Q-WZ PAIRS Tewodros Amdeberhan and Doron Zeilberger
• A HOLONOMIC SYSTEMS APPROACH TO SPECIAL FUNCTIONS IDENTITIES Doron Zeilberger
• Combinatorial Games (Handout for Math428) An impartial combinatorial game is given by a set of positions, V , and a function f : V ! 2 V
• A WORDY PROOF OF A COMBINATORIAL LEMMA THAT AROSE IN OPERATOR THEORY Doron ZEILBERGER 1
• Book Review of \Mathematics by Experiments" by J. Borwein and D. Bailey and \Experimentation in Mathematics" by J. Borwein, D. Bailey and R. Girgensohn
• The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal
• Letter to the Editor of the Monthly about v. 102, issue 10 (Dec. 1995) Doron ZEILBERGER 1
• A 2COLORING OF [1, N ] CAN HAVE (1/22)N 2 +O(N) MONOCHROMATIC SCHUR TRIPLES, BUT NOT LESS!
• Automatic Generation of Theorems and Proofs on Enumerating ConsecutiveWilf Classes By Andrew BAXTER 1 , Brian NAKAMURA 1 , and Doron ZEILBERGER 1
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team
• NAME: (print!) Section: E-Mail address
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• MATH 151(20-22), Dr. Z. , Solutions to First Midterm, Mon., Oct. 13, 2008. 1. (12 points) Find f (1), if
• Dr. Z's Math152 Handout #6.1 [Areas Between Curves] By Doron Zeilberger
• NAME: (print!) Section: E-Mail address
• Dr. Z's Math151 Handout # 2.5 [Evaluating Limits Algebraically] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.2 [Limits and Continuity] By Doron Zeilberger
• A proof of George Andrews' and David Robbins' q-TSPP conjecture
• NAME: (print!) Section: E-Mail address
• NAME: Section: MATH 151(07-09), Dr. Z. , First Midterm, Mon., Oct. 13, 2008.
• AN EXPERIMENTAL MATHEMATICS PERSPECTIVE ON THE OLD, AND STILL OPEN, QUESTION OF WHEN TO STOP?
• A bijectional attack on the Razumov-Stroganov conjecture
• NSF Proposal: Rigorous Experimental Combinatorics NSF PROPOSAL: RIGOROUS EXPERIMENTAL COMBINATORICS: Biographical Sketch
• NAME: Section: MATH 151(07-09), Dr. Z. , Second Midterm, Thursday, Nov. 20, 2008.
• A Multi-set Identity for Partitions Amitai REGEV 1 and Doron ZEILBERGER 2
• PALEYWIENER AND BOAS THEOREMS FOR SINGULAR STURMLIOUVILLE INTEGRAL TRANSFORMS
• Three-Rowed CHOMP Doron ZEILBERGER 1
• An Umbral Approach to the Hankel Transform for Sequences Doron ZEILBERGER 1
• Dr. Z's Math251 Handout #13.4 [Motion in Space: Velocity and Acceleration] By Doron Zeilberger
• Dr. Z's Math251 Handout #15.4b [Integrations in Cylindrical and Spherical Coordinates] By Doron Zeilberger
• Proof of a Conjecture of Philippe di Francesco and Paul Zinn-Justin related to the qKZ equations and to Dave Robbins' Two Favorite Combinatorial Objects
• The Quasi-Holonomic Ansatz and Restricted Lattice Walks Manuel KAUERS1
• The Number of Ways of Walking in x1 . . . xk 0 for n Days, Starting and Ending at the Origin, Where at each Day you may either Stay in Place or Move One Unit in any Direction,
• Solutions to the "QUIZ" for Oct. 22, 2009 1. Evaluate the iterated integral
• Dr. Z.'s Math 250(1), (Fall 2010, RU) Solutons to the REAL Quiz #4 (Oct. 7, 2010) 1. (4 pts.) Find an elemenary matrix E such that EA = B, where A and B are as follows
• PROOF OF A CONJECTURE OF GESSEL MANUEL KAUERS AND CHRISTOPH KOUTSCHAN AND DORON ZEILBERGER
• COMBINATORIAL PROOFS OF CAPELLI'S AND TURNBULL'S IDENTITIES FROM
• RATIONAL FUNCTIONS CERTIFY COMBINATORIAL IDENTITIES Herbert S. Wilf and Doron Zeilberger
• A 2-COLORING OF [1, N] CAN HAVE (1/22)N2 + O(N) MONOCHROMATIC
• Solutions to the "QUIZ" for Nov. 17, 2008 1. Use the Linear Approximation to approximate
• We consider an identity on directed trees, where all edges are oriented towards the root. Define the weight of a directed tree T to be
• NAME: (print!) Section: E-Mail address
• Advances in Applied Mathematics 27, 225230 (2001) doi:10.1006/aama.2001.0732, available online at http://www.idealibrary.com on
• Dr. Z's Math251 Handout #14.3 [Partial Derivatives] By Doron Zeilberger
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: March 6, 2009
• Dr. Z's Math251 Handout #15.4a (2nd ed.) [Double Integrals in Polar Coordinates] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.11 [Linear Approximation] Problem Type 3.11.1: Use the Linear Approximation to estimate f = f(a + h) -f(a) for the
• The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) And PROOF(!!) of Holonomic Determinant Evaluations
• Answers [And Some Hints] to Dr. Z.'s Four Practice Finals for Fall 2010 Fifth Version (Dec. 17, 2010, 7:30am): Thanks to Qin (Chane) Lou, for correcting the
• The Automatic Central Limit Theorems Generator (and Much More!) Doron ZEILBERGER1
• Dr. Z's Math152 Handout #11.2 [Series] By Doron Zeilberger
• Solutions to Dr. Z.'s Math 250(2), (Fall 2010, RU) REAL Quiz #9 (Dec. 2, 2010) 1. (4 points) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix
• Annals of Combinatorics 6 (2002) 427-444 0218-0006/02/040427-18
• By Doron ZEILBERGER1 [Silence for 30 seconds]. I always dreamed about giving a talk about nothing. First, I thought of
• Dr. Z's Math151 Handout #3.3 [The Product and Quotient Rule] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.11 [The Binomial Series] By Doron Zeilberger
• Solutions to the "QUIZ" of Sept. 11, 2008 1. Assuming that
• Solution to the Attendance Quiz for Sept. 2, 2010 1. Compute the matrix-vector product
• Dr. Z's Math151 Handout #3.11 [Related Rates] By Doron Zeilberger
• JOURNALOFDIFFERENTIALEQUATIONS31, 287--295(1979) Solutions of Exponential Growth to Systems of Partial
• Solutions to "QUIZ" for Oct. 6, 2008 1. Use rules of differentiation to calculate f (x) (Do not simplify your answer).
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 9, 2005
• PLAY TIME WITH DETERMINANTS Tewodros Amdeberhan and Shalosh B. Ekhad
• Formula Sheet for Math 151, Exam 1 Lines: If (x1, y1), (x2, y2) lie on a line L, the slope of L is m = y2-y1
• WZ THEORY, CHAPTER II Doron ZEILBERGER 1
• PROJECT SUMMARY RIGOROUS EXPERIMENTAL COMBINATORICS
• The n n 2 th Proof Of The Formula For The Number Of Labelled Trees
• THEOREMS FOR A PRICE: Tomorrow's Semi-Rigorous Mathematical Culture Doron Zeilberger 1
• THE UMBRAL TRANSFER-MATRIX METHOD. IV. Counting SELF-AVOIDING POLYGONS And WALKS
• HYPERGEOMETRIC SERIES ACCELERATION VIA THE WZ METHOD Tewodros Amdeberhan and Doron Zeilberger
• How to Play Backgammon (if you must) and how to Research it (if you have time) Shalosh B. EKHAD 1 and Doron ZEILBERGER 1
• Rutgers University (New Brunswick) Piscataway New Jersey 08854-8019 Department of Mathematics-Hill Center e-mail: zeilberg@math.rutgers.edu
• The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team
• Dave ROBBINS's ART of GUESSING Doron ZEILBERGER 1
• A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a nite amount of routine calculations) 1
• arXiv:math.CO/9207218v11Jul1992 APPEARED IN BULLETIN OF THE
• PROOF OF THE ALTERNATING SIGN MATRIX CONJECTURE 1 Doron ZEILBERGER2
• Proof of a Conjecture of Amitai Regev about Three-Rowed Young Tableaux (and much more!) Shalosh B. EKHAD and Doron ZEILBERGER1
• Akalu Tefera One of the most exciting mathematical dis-
• NAME: (print!) Section: E-Mail address
• NAME: Section: MATH 151(07-09,20-22), Dr. Z., Second Practice Final, Due Dec. 15, 2008, 3:50pm.
• Searching for Strange Hypergeometric Identities By Sheer Brute Force Moa APAGODU and Doron ZEILBERGER1
• Dr. Z's Math251 Handout #16.4 (2nd ed.) [Parametrized Surfaces and Surface Integrals] By Doron Zeilberger
• Dr. Z's Math152 Handout #11.10 [Taylor and Maclaurin Series] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.6 [Parametric Surfaces and Their Areas] By Doron Zeilberger
• Dr. Z's Math151 Handout #3.5 [The Chain Rule] By Doron Zeilberger
• iscrete Mathem:ntics 41 (1982) 317-321 Forth-Holland PI:blishing Company
• Automatic Generation of Theorems and Proofs on Enumerating Consecutive-Wilf Classes By Andrew BAXTER1
• RANDOM WALK IN A WEYL CHAMBER 1 Ira M. Gessel 2
• EXPERIMENTAL MATHEMATICS APPLIED TO THE STUDY OF NON-LINEAR RECURRENCES
• CHOMP, RECURRENCES, and CHAOS(?) Doron ZEILBERGER 1
• How Likely Is P'olya's Drunkard to Return to the Pub Without Getting Mugged? (In d-Dimensional Manhattan [d 2])
• How Berger, Felzenbaum and Fraenkel Revolutionized COVERING SYSTEMS The Same Way that George Boole Revolutionized LOGIC
• A FAST ALGORITHM FOR PROVING TERMINATING HYPERGEOMETRIC IDENTITIES *
• AUTOMATED COUNTING of LEGO TOWERS Doron ZEILBERGER 1
• "TRIVIALIZING" GENERALIZATIONS OF SOME IZERGIN-KOREPIN-TYPE DETERMINANTS
• CATALAN STRIKES AGAIN (AND AGAIN)* Doron ZEILBERGER1
• The Gift Exchange Problem Moa Apagodu
• THE 1958 PEKERIS-ACCAD-WEIZAC GROUND-BREAKING COLLABORATION THAT COMPUTED GROUND STATES OF
• HISTABRUT: A Maple Package for Symbol-Crunching in Probability theory Doron ZEILBERGER1
• Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
• AN EXPERIMENTAL MATHEMATICS PERSPECTIVE ON THE OLD, AND STILL OPEN, QUESTION OF WHEN TO STOP?
• Doron Zeilberger*, Department of Mathematics, Drexel University, Philadelphia, * Current Address (1990-): Department of Mathematics, Temple University, Philadel*
• A WZ PROOF OF RAMANUJAN'S FORMULA FOR ss Shalosh B. EKHAD1 and Doron ZEILBERGER1
• How Borwein and Bradley's Hypergeometric Ugly Duckling Turned Into a Beautif* `Eulerian' Swan, thanks to Almkvist and Granville's Magic
• AUTOMATIC GENERATION of THEOREMS and PROOFS On Enumerating Permutations that Av* *oid Consecutive Patterns
• The MARKOV-WZ METHOD 1 Mohamud MOHAMMED 2and Doron ZEILBERGER3
• Project Description Summary of Results from Previous NSF Support: DMS-8901610 and DMS-9123836
• PROOF OF THE ALTERNATING SIGN MATRIX CONJECTURE 1 Doron ZEILBERGER2
• THE QUANTUM MACMAHON MASTER THEOREM STAVROS GAROUFALIDIS, THANG TQ L^E, AND DORON ZEILBERGER
• Research Announcement: A Computer-Generated Proof that P=NP Doron ZEILBERGER1
• A SYMBOLIC FINITE-STATE APPROACH FOR AUTOMATED PROVING OF THEOREMS IN COMBINATORIAL GAME
• A Snappy Proof That 123-Avoiding Words are Equinumerous with 132-Avoiding Words Doron ZEILBERGER 1
• A WORDY PROOF OF A COMBINATORIAL LEMMA THAT AROSE IN OPERATOR THEORY Doron ZEILBERGER1
• The J.C.P. Miller Recurrence for Exponentiating a Polynomial, and its q-Analog Doron ZEILBERGER 1
• THE UMBRAL TRANSFER-MATRIX METHOD. III. Counting Animals Doron ZEILBERGER 1
• The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal (Second Edition)
• Supplementary Information for PEC for Doron ZEILBERGER Last Update: Jan. 27, 2010
• PROOF OF A CONJECTURE OF CHAN, ROBBINS, AND YUEN Doron ZEILBERGER 1
• Dodgson's Determinant-Evaluation Rule Proved by TWO-TIMING MEN and WOMEN
• All the Hypergeometric Series Evaluations that are Fit to Print (By Looking Under the Hood of Zeilberger's Algorithm)
• Proof of a Conjecture of Philippe di Francesco and Paul Zinn-Justin related to * *the qKZ equations
• A Fibonacci-Counting Proof Begged by Benjamin and Quinn Doron ZEILBERGER 1
• A STEMBRIDGE-STANTON STYLE PROOF OF THE HABSIEGER-KADELL q-MORRIS IDENTITY
• Proof of a Conjecture of Amitai Regev about Three-Rowed Young Tableaux (and muc* Shalosh B. EKHAD and Doron ZEILBERGER1
• A Sharp Upper Bound for the Order of The Recurrence Outputted by Zeilberger's A* *lgorithm 1
• A BIJECTION FROM ORDERED TREES TO BINARY TREES THAT SENDS THE PRUNING ORDER TO THE STRAHLER NUMBER
• If An Has 6n Dyes in a Box, With Which He Has To Fling [at least] n Sixes, Then An Has An Easier Task Than An+1, at Eaven Luck
• AsyRec: A Maple package for Computing the Asymptotics of Solutions of Linear Recurrence Equations with Polynomial Coeffi*
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• Babson-Steingr'imsson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian)
• The COMBINATORIAL ASTROLOGY of Rabbi ABRAHAM IBN EZRA Doron ZEILBERGER 1
• "Book Review of "Kepler's Conjecture" by George G. Szpiro" Doron ZEILBERGER 1
• In How Many Ways Can a King Walk n Steps? Shalosh B. EKHAD 1
• GAUSS'S 2F1(1)CANNOT BE GENERALIZED TO 2F1(x) Doron Zeilberger *
• PROOF OF A DETERMINANT EVALUATION CONJECTURED BY BOMBIERI, HUNT AND VAN DER POORTEN
• CLOSED FORM (pun intended!) Doron Zeilberger *
• The Capital by Karl Marx by Hadas Zeilberger
• An Umbral Approach to the Hankel Transform for Sequences Doron ZEILBERGER1
• THE UMBRAL TRANSFER-MATRIX METHOD: I. FOUNDATIONS Doron ZEILBERGER 1
• Babson-Steingr'imsson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian)
• TOWARDS A WZ EVALUATION OF THE MEHTA INTEGRAL Doron Zeilberger *
• Letter to the Editor of the Monthly about v. 102, issue 10 (Dec. 1995) Doron ZEILBERGER1
• Request for an NSF supplement for the AY 2006-07 for Graduate Student Support Doron ZEILBERGER1
• ON THE NUMBER OF WALKS ON A REGULAR CAYLEY TREE
• Fully AUTOMATED Computerized Redux of Feller's (v.1) Ch. III (and Much More!) Doron ZEILBERGER1
• A HOLONOMIC SYSTEMS APPROACH TO SPECIAL FUNCTIONS IDENTITIES Doron Zeilberger
• Sylvie Corteel's One-Line Proof of a Partition Theorem Discovered by Andrews-Pa* *ule-Riese's
• The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team
• A WZ PROOF OF A "CURIOUS" IDENTITY Shalosh B. Ekhad and Mohamud Mohammed 1
• Sharp Upper Bounds for the Orders of The Recurrences Outputted by the Zeilberger and q-Zeilberger Algorithms
• PUBLICATIONS OF DORON ZEILBERGER Last Update: May 4, 2005
• TEST YOUR C.Q. [Conjecture-Quotient] Doron ZEILBERGER1
• A note on the paper : Closed Form (pun in-tended),1993 by Doron Zeilberger
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• RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION Doron Zeilberger
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• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: March 6, 2009
• The Gift Exchange Problem David Applegate and N. J. A. Sloane(a),
• The Method of Undetermined Generalization and Specialization Illustrated with
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• PROOF OF THE REFINED ALTERNATING SIGN MATRIX CONJECTURE Doron ZEILBERGER1
• Proof of an Identity Conjectured by Iossif Polterovitch that Came Up in the Agmon-Kannai Asymptotic Theory of the Heat Kernel
• The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Path Counting
• Three-Rowed CHOMP Doron ZEILBERGER 1
• A Heterosexual Mehler Formula for the Straight Hermite Polynomials (A`La Foa* Doron ZEILBERGER1
• A SHORT PROOF OF JACOBI'S FORMULA FOR THE NUMBER OF REPRE-SENTATIONS OF AN INTEGER AS A SUM OF FOUR SQUARES
• By Doron ZEILBERGER1 [Silence for 30 seconds]. I always dreamed about giving a talk about nothing.*
• The Right Answers to The Rong Questions: Solutions to the Review Questions for Final Exam Math 151, Fall 2003, Rutgers U*
• Efficient Counting and Asymptotics of k-noncrossing tangled diagrams William Y.C. CHEN 1, Jing QIN1, Christian M. REIDYS1, and Doron ZEILBERGE*
• THEOREMS FOR A PRICE: Tomorrow's Semi-Rigorous Mathematical Culture Doron Zeilberger1
• PROOF OF IRA GESSEL'S LATTICE PATH CONJECTURE MANUEL KAUERS *AND CHRISTOPH KOUTSCHAN *AND DORON ZEILBERGER y
• Pythagorean Primes and Palindromic Continued Fractions Arthur T. Benjamin and Doron Zeilberger
• A PROOF OF GEORGE ANDREWS' AND DAVID ROBBINS' q-TSPP CONJECTURE
• AN EVEN SIMPLER PROOF OF PASCAL'S HEXAGON THEOREM Ren'e DESCARTES1 and Shalosh B. EKHAD2
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• A Symbolic Computation Approach to a Problem involving Multivariate Poission Distributions (Draft, do not distribute!)
• Research Announcement: The Transcendence of e + and e Doron Zeilberger 1
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• In How Many Ways Can a King Return Home After n Steps? Shalosh B. EKHAD 1
• The Automatic Central Limit Theorems Generator (and Much More!) Doron ZEILBERGER 1
• Automatic Generation of Generating Functions for Enumerating Matchings By Shalosh B. EKHAD and Doron ZEILBERGER
• A Fibonacci-Counting Proof Begged by Benjamin and Quinn Doron ZEILBERGER 1
• A SHORT PROOF OF JACOBI'S FORMULA FOR THE NUMBER OF REPRE-SENTATIONS OF AN INTEGER AS A SUM OF FOUR SQUARES
• A BIJECTION FROM ORDERED TREES TO BINARY TREES THAT SENDS THE PRUNING ORDER TO THE STRAHLER NUMBER
• The Gift Exchange Problem David Applegate and N. J. A. Sloane (a) ,
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• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions #
• ECO order theory I. Lattices of lattice paths \Lambda Luca Ferrari y Renzo Pinzani z
• The Right Answers to The Rong Questions: Solutions to the Review Questions for Final Exam Math 151, Fall 2003, Rutgers Univ
• Dr. Z's Math151 Handout # 2.3 [Basic Limit Laws] By Doron Zeilberger
• Journal of Statistical Planning and Inference 54 (1996) 135 138
• Solution to the"QUIZ" for Oct. 16, 2008 Question: If three resistors with resistence R1 and R2 and R3 are connected in parallel, then the
• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 58, 405-418 (1977) Further Properties of Discrete Analytic Functions
• JOURNAL OF ALGORITHMS 3, 317-343 (1982) A Bijective Proof of the Hook-Length Formula
• The Maximal number of floors a Building can have where you can tell the highest floor from where you can throw a glass ball without breaking it,
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• MATH 151 (17-19), Dr. Z. , Answers for the Practice For Midterm II, These posted answers refer to the Nov. 20, 7:30pm version. If you have an earlier version,
• All the Hypergeometric Series Evaluations that are Fit to Print (By Looking Under the Hood of Zeilberger's Algorithm)
• Patterns and Fractions Aaron Robertson
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 9, 2005
• Math Bite: Constructing Ecient Particle Accelerators is as Easy as 1+1=2 (Thanks to Vladimir Visnjic)
• A Note on the Stanley Distribution Shalosh B. EKHAD 1
• Experiments with a cubic polynomial equation Consider the cubic polynomial equation
• Solutions to the Attendance Quiz of Sept. 13, 2010 1. Determine whether the given system is consistent, and if so, find its general solution.
• Discrete Mathematics 34 (1981) 8+-91 North-Holland P&iishing Campany
• Deconstructing the Zeilberger algorithm DORON ZEILBERGER*
• In How Many Ways Can a King Walk n Steps? Shalosh B. EKHAD 1
• Answers to Dr. Z's Three Practice Tests For The Second Midterm Exam (First Posted Nov. 16, 2008. Version of Nov. 17, 2008 (one mistake corrected, thanks to
• Commutation relations and Vandermonde determinants Yuri Bahturin
• Finite Analogs of Szemeredi's Theorem and Doron ZEILBERGER1
• The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently-Normal (First Edition)
• A Computer Algebra Approach to the Discrete Dirichlet Problem]A Computer Algebra Approach to the Discrete Dirichlet Problem Craig R. Orr and Doron Zeilberger]CRAIG R. ORR AND DORON ZEILBERGER Department of Mathematics, Temple University, Philadelphia, PA
• ON THE NUMBER OF WALKS ON A REGULAR CAYLEY ERIC ROWLAND AND DORON ZEILBERGER
• ON A CONJECTURE OF R.J.SIMPSON ABOUT EXACT COVERING CONGRUENCES Doron ZEILBERGER
• In How Many Ways Can a King Walk n Steps? Shalosh B. EKHAD 1
• SOME NICE SUMS ARE ALMOST AS NICE IF YOU TURN THEM UPSIDE DOWN
• TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• A PROOF OF GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE (MODULO A FINITE AMOUNT OF ROUTINE CALCULATIONS)
• A 21st-Century Proof Of Dougall's Hypergeometric Sum Identity Shalosh B. Ekhad and Doron Zeilberger* *
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• Yet Another Proof for the Enumeration of Labelled Trees Based on a comment of Herb Wilf (spelled out by D. Zeilberger)
• Sharp Upper Bounds for the Orders of The Recurrences Outputted by the Zeilberger and q-Zeilberger Algorithms
• A New Proof that there are 2 n Possible Outcomes on Tossing a Coin n Times Doron ZEILBERGER 1
• CURING The ANDREWS SYNDROME Shalosh B. EKHAD 1 and Doron ZEILBERGER 2
• Finite Versions of Szemer edi's Theorem on Arithmetical Progressions Paul RAFF 1 and Doron ZEILBERGER 1
• The Revenge of the Plain Mathematician: How I Answered Two Questions by Two Fancy Jerusalem Mathematicians In One Day
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• A Proof of the Celebrated Goldbach's Theorem Doron ZEILBERGER 1
• If A n Has 6n Dyes in a Box, With Which He Has To Fling [at least] n Sixes, Then A n Has An Easier Task Than A n+1 , at Eaven Luck
• Lieber Opa Paul, Ich Bin Auch Ein Experimental Scientist! Doron ZEILBERGER 1
• The Gift Exchange Problem Moa Apagodu
• Finite Analogs of Szemer edi's Theorem Paul RAFF 1 and Doron ZEILBERGER 1
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• A WZ PROOF OF RAMANUJAN'S FORMULA FOR Shalosh B. EKHAD 1 and Doron ZEILBERGER 1
• A PROOF OF GEORGE ANDREWS' AND DAVID ROBBINS' q-TSPP CONJECTURE
• Report on "Finite Analogs of Szemeredi's Theorem" by Paul Raff and Doron Zeilberger
• JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 111, 162-176 (1985) Resurrecting the Asymptotics
• On K. F. Roth's `On Certain Sets of Integers' David J. Wilson
• Answers to Dr. Z's Three Practice Tests For The First Midterm Exam (Version of Oct. 12, 2008, three corrections and I5(b) added (thanks to Ashwin for pointing
• Solutions to the Attendance Quiz for Sept. 30, 2010 1. Determine whether the matrix is invertible. If so find, its inverse.
• On Vince Vatter's Brilliant Extension of Doron Zeilberger's Enumeration Schemes for Herb Wilf's Classes
• SIAM J. DISC. MATH. Vol. 1, No. 4, November 1988
• Dr. Z's Math151 Handout #3.10 [Derivatives of General Exponential and Logarithmic Functions] By Doron Zeilberger
• Dr. Z's Math251 Handout #14.5 (2nd ed.) [The Gradient and Directional Derivatives] By Doron Zeilberger
• Nonlinear dynamics in combinatorial games: Renormalizing Chomp Eric J. Friedman
• Our reference: YAAMA 1412 P-authorquery-v7 AUTHOR QUERY FORM
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• JOURNAL OF COMBINATORIAL THEORY, Series A 38,9698 (1985) Some Asymptotic Bijections
• Dr. Z's Math151 Handout #2.8 [The Formal Definition of a Limit] By Doron Zeilberger
• Dr. Z's Math251 Handout #16.5 [Curl and Divergence] By Doron Zeilberger
• Discrete Matheml tics 51 (1984) 109-110 North-Holland
• NSF Proposal: Targeted Proof Machines NSF PROPOSAL: Targeted Proof Machines in Combinatorics
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• Review Sheet for the Final Exam for Math 151 This review sheet emphasizes the material covered after Exam 2. You should also study
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• THE QUANTUM MACMAHON MASTER THEOREM STAVROS GAROUFALIDIS, THANG TQ L^E, AND DORON ZEILBERGER
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• Project Description Summary of Results from Previous NSF Support: DMS-8901610 and DMS-9123836
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• The HOLONOMIC ANSATZ I. FOUNDATIONS and Applications to Lattice Walk Counting
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• A Generalization of Odlyzko's Conjecture: The Coefficients of (1 -q)j=((1 -q2* *n)...(1 -q2n+2j))
• NSF Proposal: RIGOROUS EXPERIMENTAL COMBINATORICS RIGOROUS EXPERIMENTAL COMBINATORICS: References Cited
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• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
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• The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) And PROOF(!!) of Holonomic Determinant Evaluations
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• An Inelegant (but Short(!)) Proof of a Major Index Theorem of Garsia and Gessel* * (Verbose Version)
• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER1
• Proof of an Identity of Don Knuth Doron ZEILBERGER1
• NSF Proposal: Symbolic Computation and Combinatorics NSF PROPOSAL: SYMBOLIC COMPUTATION and COMBINATORICS
• Proof of a Conjecture of Philippe Di Francesco and Paul Zinn-Justin related to * *the qKZ equation
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• TALMUDIC LATTICE PATH COUNTING Jane Friedman, Ira Gessel, and Doron Zeilberger
• Rutgers_University_____________________New_Brunswick_New_Jersey_08903__________* Department of Mathematics e-mail: zeilberg@math.rutgers.edu
• FORTY "STRANGE" COMPUTER-DISCOVERED [and COMPUTER-PROVED (of course!)]
• A 21st-Century Proof Of Dougall's Hypergeometric Sum Identity Shalosh B. Ekhad and Doron Zeilberger* *
• Lieber Opa Paul, Ich Bin Auch Ein Experimental Scientist! Doron ZEILBERGER 1
• THE COMPUTATIONAL CHALLENGE OF ENUMERATING HIGH-DIMENSIONAL ROOK WALKS
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• Symbol-Crunching With the Gambler's Ruin Problem Doron ZEILBERGER1
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• A Comparison Of Two Methods For Random Labelling of Balls by Vectors of Intege* Doron ZEILBERGER1
• A BINOMIAL COEFFICIENT IDENTITY ASSOCIATED TO A CONJECTURE OF BEUKERS
• Teaching the Computer how to Discover(!) and then Prove(!!) (all by Itself(* Analogs of Collatz's Notorious 3x+1 Conjecture
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Jan. 27, 2010
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• Finite Analogs of Szemer'edi's Theorem Paul RAFF1 and Doron ZEILBERGER1
• All the Moments of the Vertex Degrees of Randomly Generated Graphs Doron ZEILBERGER 1
• MATH 151 (17-19), Dr. Z. , Practice For Midterm II, First Posted: Nov. 14, 2004. This version: Nov. 20, 7:30pm. Some typos have been corrected. The posted answe*
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• Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions Shalosh B. EKHAD and Doron ZEILBERGER1
• NSF Proposal: RIGOROUS EXPERIMENTAL COMBINATORICS RIGOROUS EXPERIMENTAL COMBINATORICS: PROJECT DESCRIPTION
• Research Announcement: The Transcendence of e + ss and ess Doron Zeilberger1
• Math Bite: Constructing Efficient Particle Accelerators is as Easy as 1+1=2 (Thanks to Vladimir Visnjic)
• A PROOF OF GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
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• Automatic Generation of Generating Functions for the Number of Spanning Trees for Grid Graphs (and Much More General Creatures) of Fixed (but arbitrary!) Wid*
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• The Number of Same-Sex Marriages in a Perfectly Bisexual Population is Asymptot* *ically Normal
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• Mathematical Genitalysis: A Powerful New Combinatorial Theory that Obviates Mat* *hematical Analysis
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• The Number of Ways of Walking in x1 . . .xk 0 for n Days, Starting and Endi* *ng at the Origin,
• PROOF OF IRA GESSEL'S LATTICE PATH CONJECTURE MANUEL KAUERS *AND CHRISTOPH KOUTSCHAN *AND DORON ZEILBERGER **
• PROOF OF A CONJECTURE OF GESSEL MANUEL KAUERS *AND CHRISTOPH KOUTSCHAN *AND DORON ZEILBERGER y
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• A Symbolic Computation Approach to a Problem involving Multivariate Poission Di* *stributions
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• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions*
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• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 16, 2007
• PROOF OF IRA GESSEL'S LATTICE PATH CONJECTURE MANUEL KAUERS AND CHRISTOPH KOUTSCHAN AND DORON ZEILBERGER
• THE COMPUTATIONAL CHALLENGE OF ENUMERATING HIGH-DIMENSIONAL ROOK WALKS
• Dr. Z's Math251 Handout #13.2 (2nd ed.) [Calculus of Vector-Valued Functions] By Doron Zeilberger
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• Dr. Z's Math152 Handout #7.8 [Improper Integrals] By Doron Zeilberger
• Report on "Proof of a conjecture of Philippe Di Francesco and Paul Zinn-Justin related to the qKZ equation and to
• Enumerative and Algebraic Combinatorics
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• In How Many Ways Can You Reassemble Several Russian Dolls? Doron ZEILBERGER 1
• PROOF OF IRA GESSEL'S LATTICE PATH CONJECTURE MANUEL KAUERS AND CHRISTOPH KOUTSCHAN AND DORON ZEILBERGER y
• How Sister Celine Fasenmyer and Dick Dun Shaped my Mathematical Personality Doron ZEILBERGER 1
• The Right Answers to The Rong Questions: Solutions to the Review Questions for Final Exam Math 151, Fall 2003, Rutgers Univ
• Supplementary Information for PEC for Doron ZEILBERGER Last Update: Jan. 27, 2010
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• SYMBOL-CRUNCHING with the TRANSFER-MATRIX Method In Order to Count
• THE QUANTUM MACMAHON MASTER THEOREM STAVROS GAROUFALIDIS, THANG TQ L ^
• PROOF OF A CONJECTURE ON MULTISETS OF HOOK NUMBERS Amitai REGEV 1 and Doron ZEILBERGER 2
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• CATALAN STRIKES AGAIN (AND AGAIN) Doron ZEILBERGER 1
• COMPUTERIZED DECONSTRUCTION Doron ZEILBERGER 1
• 1. \Real" Analysis is a Degenerate Case of Discrete Analysis, Appeared in: "New Progress in Di erence Equations"(Proc. ICDEA 2001), edited by Bernd Aulbach, Saber Elaydi, and Gerry
• Another Proof that Euler Missed: Jonas Sjostrand's Amazingly Simple (and Lovely!) Proof of the No-Longer-So-Amazing Loehr-Warrington Lattice Paths Conjecture
• Dr. Z's Math251 Handout #14.7 [Maximum and Minimum Values] By Doron Zeilberger
• Solutions to MATH 250 (1), Dr. Z. , Exam 2, Mon., Nov. 15, 2010, 8:40-10:00am, SEC 1. (a) (6 points) Find an LU decomposition of the matrix
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• March 20, 2007 9:39 WSPC -Proceedings Trim Size: 9in x 6in ApaZeil FIVE Applications of Wilf-Zeilberger Theory to Enumeration
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• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Sept. 21, 2008
• 640:250 Linear Algebra EXAM 1: REVIEW PROBLEMS SPRING 2010 1. (a) What does it mean to say that the vectors u1, . . ., uk in Rn
• THE ENUMERATION AND STRUCTURE OF PERMUTATION CLASSES
• Solutions to the "QUIZ" for Oct. 19, 2009 1. Change the order of integration in
• Dr. Z's Math251 Handout #13.3 (2nd ed.) [Arc Length and Speed] By Doron Zeilberger
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• Europ. J. Comhinurrrric~(1987)8. 461-463 A q-Foata Proof of the q-Saalschiitz Identity
• Dr. Z's Math251 Handout #16.4 [Green's Theorem] By Doron Zeilberger
• Formula Sheet for Math 151, Final Exam Lines: If (x1, y1), (x2, y2) lie on a line L, the slope of L is m = y2-y1
• Answers to Dr. Z's Three Practice Final Exams Disclaimer: Not repsponsible for any typos or other erros. Award of $1 for any mistake
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• Solutions to the "QUIZ" for Sept. 25, 2008 1. Differentiate
• JOURNAL OF ~IA'I'IIE~IATICAI. ANALYSIS ASD APPI.ICATIOXS 74, 456-463 (1980) Some Comments on Rota's Umbra1 Calculus
• Solutions to Dr. Z.'s Math 250(1), (Fall 2010, RU) REAL Quiz #8 (Nov. 11, 2010) 1. (5 points) Determine the dimension of the following subspace. Explain what you are doing!
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• Sipur and Mispar in Ibn Ezra's Sefer HaMispar Doron ZEILBERGER 1
• MATH 151 (17-19), Dr. Z. , Practice For Midterm II, First Posted: Nov. 14, 2004. This version: Nov. 20, 7:30pm. Some typos have been corrected. The posted answers refer
• Review of Dave Bressoud's \Proofs and Con rmations" Doron ZEILBERGER 1
• The SaganSavage LucasCatalan Polynomials Have Positive Coe#cients Shalosh B. EKHAD 1
• The Quasi-Holonomic Ansatz and Restricted Lattice Walks Manuel KAUERS 1 and Doron ZEILBERGER 2
• A Proof of Morley's Theorem (From The (Devil's) Book) Shalosh B. Ekhad 1
• An In nite Sequence of Trite but True Sentences Doron Zeilberger 1
• Solutions to the "QUIZ" of Sept. 18, 2008 1. Explain why x4
• Solutions to the Attendance Quiz for Sept. 20, 2010 1. Determine whether the given set is linearly independent
• Advances in Applied Mathematics 31 (2003) 532543 www.elsevier.com/locate/yaama
• Contemporary Mathemafica Volume 178,1991
• This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research
• Sige social et bureaux : 111, Faubourg Saint Honor, 75008 Paris. Tel. : 01 42 89 10 89. Fax : 01 42 89 10 69 Socit Anonyme au capital de 46 200 Euros. RCS : Paris B 399 991 041. SIRET : 399 991 041 00035. APE : 731Z
• Supplementary Information for PEC for Doron ZEILBERGER Last Update: Jan. 27, 2010
• Solutions to the "QUIZ" of Oct. 26, 2009 1. Use polar coordinates to compute the double integral
• Dr. Z's Math152 Last Handout By Doron Zeilberger
• A SYMBOLIC FINITE-STATE APPROACH FOR AUTOMATED PROVING OF THEOREMS IN COMBINATORIAL GAME
• A PROOF OF JULIAN WEST'S CONJECTURE THAT THE NUMBER OF TWO-STACK-SORTABLE PERMUTATIONS OF LENGTH n IS 2(3n)!/((n+1)!(2n+1)!)
• THE UMBRAL TRANSFER-MATRIX METHOD. III. Counting Animals Doron ZEILBERGER 1
• The Collector's Brotherhood Dominique Foata,1 Doron Zeilberger2
• A Fibonacci-Counting Proof Begged by Benjamin and Quinn Doron ZEILBERGER 1
• The Symbolic Goulden Jackson Cluster Method Xiangdong Wen
• Towards a SymbolicComputational Philosophy (and Methodology!) for Mathematics Doron ZEILBERGER 1
• Rutgers_University_____(New_Brunswick)_Piscataway_New_Jersey_08854-8019________* Department of Mathematics-Hill Center e-mail: zeilberg@math.rutgers.e*
• NSF Proposal: Targeted Proof Machines NSF PROPOSAL: Targeted Proof Machines in Combinatorics
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Sept. 21, 2008
• Symbolic Moment Calculus I.: Foundations and Permutation Pattern Statistics Doron ZEILBERGER 1
• AN EXPERIMENTAL MATHEMATICS PERSPECTIVE ON THE OLD, AND STILL OPEN, QUESTION OF WHEN TO STOP?
• THE METHOD OF DIFFERENTIATING UNDER THE INTEGRAL SIGN Gert Almkvist * and Doron Zeilberger**
• The ABSTRACT LACE EXPANSION Doron ZEILBERGER 1
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 11, 2006
• Sipur and Mispar in Ibn Ezra's Sefer HaMispar Doron ZEILBERGER1
• SOME NICE SUMS ARE ALMOST AS NICE IF YOU TURN THEM UPSIDE DOWN
• KATHY O'HARA'S CONSTRUCTIVE PROOF OF THE UNIMODALITY OF THE GAUSSIAN POLYNOMIALS
• Finite Analogs of Szemer'edi's Theorem Doron ZEILBERGER1 and Paul RAFF1
• Self Avoiding Walks, The Language1 of Science, and Fibonacci Numbers Doron ZEILBERGER 2
• All the Hypergeometric Series Evaluations that are Fit to Print (By Looking Under the Hood of Zeilberger's Algorithm)
• In How Many Ways Can a King Walk n Steps? Shalosh B. EKHAD 1
• THE UMBRAL TRANSFER-MATRIX METHOD: II. Counting Plane Partitions Doron ZEILBERGER 1
• The Capital by Karl Marx Trade is a very important procedure that society cannot do without but before o*
• A PROOF OF GEORGE ANDREWS' AND DAVID ROBBINS' q-TSPP CONJECTURE
• DETERMINANTS THROUGH THE LOOKING GLASS Tewodros Amdeberhan1 and Doron Zeilberger2
• REVEREND CHARLES to the aid of MAJOR PERCY and FIELDS-MEDALIST ENRICO Doron ZEILBERGER1
• Exponents Doron ZEILBERGER1
• Enumerative and Algebraic fact has to incorporate infinitely many* * facts, and
• The GOULDEN-JACKSON CLUSTER Method For CYCLIC Words Anne E. EDLIN1 and Doron ZEILBERGER1
• The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) And PROOF(!!) of Holonomic Determinant Evaluations
• Dave ROBBINS's ART of GUESSING Doron ZEILBERGER 1
• A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a finite amount of routine calculations) 1
• The Maximal number of floors a Building can have where you can tell the highest* from where you can throw a glass ball without breaking it,
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 16, 2007
• Finite Analogs of Szemer'edi's Theorem Paul RAFF1 and Doron ZEILBERGER1
• "REAL" ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS Doron ZEILBERGER 1
• A CONDENSED CONDENSATION PROOF OF A DETERMINANT EVALUATION CONJECTURED BY Greg KUPERBERG AND Jim PROPP
• Remarks On The PARRONDO PARADOX Shalosh B. EKHAD 1and Doron ZEILBERGER 1
• CURING The ANDREWS SYNDROME Shalosh B. EKHAD1 and Doron ZEILBERGER2
• A Proof of the Celebrated Goldbach's Theorem Doron ZEILBERGER1
• Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
• An Infinite Sequence of Trite but True Sentences Doron Zeilberger1
• Commutation relations and Vandermonde determinants Yuri Bahturin
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• A Combinatorial Proof of log(ez) = z Doron ZEILBERGER 1
• GERT ALMKVIST'S GENERALIZATION OF A MISTAKE OF BOURBAKI 1 Doron Zeilberger 2
• The Sagan-Savage Lucas-Catalan Polynomials Have Positive Coefficients Shalosh B. EKHAD1
• PUBLICATIONS OF DORON ZEILBERGER Resulting from DMS -9123836 69. Closed Form (pun intended!), in: "Special volume in memory of Emil Grosswal*
• Disturbing the Dyson Conjecture (in a GOOD Way)
• COMPUTERIZED DECONSTRUCTION Doron ZEILBERGER 1
• REFINED ASYMPTOTICS AND EXPLICIT RECURRENCES FOR THE NUMBERS OF YOUNG TABLEAUX IN THE (k, l) HOOK FOR k + l 5
• PROOF of CONWAY'S LOST COSMOLOGICAL THEOREM Shalosh B. Ekhad1 and Doron Zeilberger1
• Sharp Upper Bounds for the Orders of The Recurrences Outputted by the Zeilberger and q-Zeilberger Algorithms
• A Symbolic Computation Approach to a Problem Involving Multivariate Poisson Distributions
• The Joy of Brute Force: The Covariance of The number of Inversions and the Major Index
• FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Probability* Moa APAGODU and Doron ZEILBERGER
• Finite Versions of Szemer'edi's Theorem on Arithmetical Progressions Paul RAFF1 and Doron ZEILBERGER1
• HOW TO PROVE GEORGE ANDREWS' AND DAVE ROBBINS' q-TSPP CONJECTURE
• Proof of the Riemann Hypothesis, and some other Hitherto Undemonstrated Proposi* Shalosh B. Ekhad1
• NSF Proposal: AUTOMATING COMBINATORICS: Project Description AUTOMATING COMBINATORICS: PROJECT DESCRIPTION
• Review of Dave Bressoud's "Proofs and Confirmations" Doron ZEILBERGER 1
• Automatic CounTilings Doron ZEILBERGER1
• 5 n n 2 Proofs that k k+1 if k < n=2.
• In How Many Ways Can n (Straight) Men and n (Straight) Women Get Married, if Each Person Has Exactly k Spouses?
• You Don't Have To Be an Einstein to Figure Out that Sara Should (Asympt* *otically) Eat
• Bijections for an identity of Young Tableaux A. Regev and D. Zeilberger
• Patterns and Fractions Aaron Robertson
• A Sharp Upper Bound for the Order of The Recurrence Outputted by Zeilberger's A* *lgorithm 1
• THE COMPUTATIONAL CHALLENGE OF ENUMERATING HIGH-DIMENSIONAL ROOK WALKS
• Temple_University___________________Philadelphia,_Pennsylvania_19122-2595______* Department of Mathematics e-mail: zeilberg@math.temple.edu
• IS DREIDEL EXPECTED TO LAST O(NUT S2) SPINS? Doron ZEILBERGER 1
• A Eulogy for Jack Good Doron ZEILBERGER1
• PROJECT SUMMARY RIGOROUS EXPERIMENTAL COMBINATORICS
• The Quasi-Holonomic Ansatz and Restricted Lattice Walks Manuel KAUERS1 and Doron ZEILBERGER2
• Proof of a Conjecture of Amitai Regev About Hook Multi-Sets Doron ZEILBERGER1
• How Many Singles, Doubles, Triples, Etc., Should The Coupon Collector Expec* Doron ZEILBERGER 1
• DECONSTRUCTING the ZEILBERGER algorithm Doron ZEILBERGER 1
• ON A CONJECTURE OF R.J.SIMPSON ABOUT EXACT COVERING CONGRUENCES Doron ZEILBERGER
• 1. "Real" Analysis is a Degenerate Case of Discrete Analysis, Appeared in: "Ne* *w Progress in
• CURRICULUM VITAE OF DORON ZEILBERGER Last Update: Nov. 16, 2007
• THE UMBRAL TRANSFER-MATRIX METHOD. V. The Goulden-Jackson Cluster Method for Infinitely Many Mistakes
• On Vince Vatter's Brilliant Extension of Doron Zeilberger's Enumeration Schemes for Herb Wilf's Classes
• WZ THEORY, CHAPTER II Doron ZEILBERGER 1
• A HIGH-SCHOOL ALGEBRA1 , WALLET-SIZED PROOF, OF THE BIEBERBACH CONJECTURE [After L. Weinstein]
• The Automatic Central Limit Theorems Generator (and Much More!) Doron ZEILBERGER1
• THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL
• Book Review of "Mathematics by Experiments" by J. Borwein and D. Bailey and "Experimentation in Mathematics" by J. Borwein, D. Bailey and R. Girgensohn
• How Adam Marcus and Gabor Tardos Divided and Conquered the Stanley-Wilf Conjecture
• IDENTITIES IN SEARCH OF IDENTITY 1 Doron Zeilberger 2
• Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms and the
• Searching for Strange Hypergeometric Identities By Sheer Brute Force Moa APAGODU and Doron ZEILBERGER1
• Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms and the
• Another Proof that Euler Missed: Jonas Sj"ostrand's Amazingly Simple (and Lovel* *y!) Proof
• COMBINATORIAL PROOFS OF CAPELLI'S AND TURNBULL'S IDENTITIES FROM
• How Sister Celine Fasenmyer and Dick Duffin Shaped my Mathematical Personali* Doron ZEILBERGER1
• th The nn-2 Proof Of The Formula For The Number Of Labelled Trees
• The Gift Exchange Problem, Part II By Moa Apagodu, David Applegate, Neil Sloane, and Doron Zeilberger
• An Explicit Formula for the Number of Solutions of X2 = 0 in Triangular Matrice* *s Over a Finite Field
• A Proof of Morley's Theorem (From The (Devil's) Book) Shalosh B. Ekhad1
• THE UMBRAL TRANSFER-MATRIX METHOD. V. The Goulden-Jackson Cluster Method for Infinitely Many Mistakes
• I Am Sorry, Richard Ehrenborg and Margie Readdy, About Your Two Conjectures, But One is FAMOUS, While The Other Is FALSE
• MATH 151 (17-19), Dr. Z. , Answers for the Practice For Midterm II, These posted answers refer to the Nov. 20, 7:30pm version. If you have an earli*
• Aufgabe VII.47 of P'olya-Szeg"o Immediately Implies Dave Robbins's Multi-Integr* *al Evaluation
• Dr. Z's Math151 Handout #3.8 [Derivatives of Logarithmic Functions] By Doron Zeilberger
• Dr. Z's Math151 Handout #5.2 [The Definite Integral] By Doron Zeilberger
• Dr. Z's Math151 Handout #2.4 [Limits and Continuity] By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 6 Handout By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 15 Handout: The Heat Equation By Doron Zeilberger
• The Discrete Analog of the Malgrange-Ehrenpreis Theorem Doron ZEILBERGER1
• Dr. Z.'s Calc5 Lecture 16 Handout: The Wave Equation By Doron Zeilberger
• A New Algorithm for Proving Global Asymptotic Stability of Rational Difference Equations
• The Discrete Analog of the Malgrange-Ehrenpreis Theorem Doron ZEILBERGER1
• Dr. Z.'s Calc5 Lecture 20 Handout: Fourier Integrals By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 23 Handout: Numerical Solutions of Partial Differential Equations By Doron Zeilberger
• The Discrete Analog of the Malgrange-Ehrenpreis Theorem Doron ZEILBERGER1
• The C-FINITE ANSATZ Doron ZEILBERGER1
• The Expected Number of Blocks in an Ordered Set Partition of n objects is n=log* *(4) + O(1),
• P n Two Proofs that k=0(-1)kk!S(n, k) = (-1)n
• i _________________| * * _i_|
• Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf
• The Discrete Analog of the Malgrange-Ehrenpreis Theorem Doron ZEILBERGER1
• Dr. Z.'s Calc5 Cheatsheet [Note: This is the only sheet allowed in any of the quizzes and exams. No calculators of course!]
• Dr. Z.'s Calc5 Lecture 9 Handout: Fourier Cosine and Sine Series By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 21 Handout: Fourier Transform By Doron Zeilberger
• The C-FINITE ANSATZ Doron ZEILBERGER1
• Dr. Z.'s Calc5 Lecture 10 Handout: Complex Fourier Series By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 8 Handout: Fourier Series By Doron Zeilberger
• Two Proofs that k!S(n, k) = (-1)n
• Dr. Z.'s Calc5 Lecture 22 Handout: Numerical Solutions of Ordinary Differential Equations By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 12 Handout: Fourier-Legendre Series and Linear Recurrences By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 4 Handout By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 19 Handout: Applications of the Laplace Transfrom for solving Partial Differential Equations
• Dr. Z.'s Calc5 Lecture 17 Handout: Laplace's Equation By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 2 Handout By Doron Zeilberger
• FORMUL FOR THE NUMBER OF PARTITIONS OF n INTO AT MOST m PARTS
• Dr. Z.'s Calc5 Lecture 13 Handout By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 18 Handout: Laplace's Equation in Polar Coordinates By Doron Zeilberger
• Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf
• Dr. Z.'s Calc5 Lecture 3 Handout By Doron Zeilberger
• The CFINITE ANSATZ Doron ZEILBERGER 1
• The Discrete Analog of the MalgrangeEhrenpreis Theorem Doron ZEILBERGER 1
• The Discrete Analog of the MalgrangeEhrenpreis Theorem Doron ZEILBERGER 1
• The Expected Number of Blocks in an Ordered Set Partition of n objects is n/log(4) +O(1), its Variance is (n/log(4))(1/log(4) -1/2) +O(1),
• Two Proofs that (-1) k k!S(n, k) = (-1) n
• Balls in Boxes: Variations on a Theme of Warren Ewens and Herbert Wilf
• Page (PS/TeX): 1 / 1, COMPOSITE # ``pmn'' ---2011/9/1 ---15:20 ---page 1 ---#1
• Dr. Z.'s Calc5 Lecture 14 Handout By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 1 Handout By Doron Zeilberger
• Dr. Z.'s Calc5 Lecture 7 Handout: Orthogonal Functions By Doron Zeilberger
• Answers to Dr. Z.'s Math 421 (Calc5) Homework assignments (when applicable) Disclaimer: not responsible for any errors. The first finder of any error will get $1.
• The Expected Number of Blocks in an Ordered Set Partition of n objects is n/log(4) + O(1), its Variance is (n/log(4))(1/log(4) -1/2) + O(1),
• Dr. Z.'s Calc5 Lecture 11 Handout: Sturm-Liouville Problem By Doron Zeilberger
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• TOWARD A LANGUAGE THEORETIC PROOF OF THE FOUR COLOR THEOREM
• Solutions to Dr. Z.'s Math 421(1), Exam #1 (Oct. 6, 2011) 1. (15 points) Using the definition find the Laplace transform L{f(t)} (alias F(s)) of
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful The* that the number of n-permutations that contain the Pattern 321 Exactly Once E*
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful The* that the number of n-permutations that contain the Pattern 321 Exactly Once E*
• RADEMACHER'S INFINITE PARTIAL FRACTION CONJECTURE IS (almost certainly) FALSE
• Amanda Folsom and Ken Ono's Error Could Have (and Should Have!) been Discovered by Their Computers (in Less than Three Seconds!)
• RADEMACHER'S INFINITE PARTIAL FRACTION CONJECTURE IS FALSE ANDREW V. SILLS AND DORON ZEILBERGER
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• The Binomial Theorem for (N + n)r (where Nf(n)=f(n+1)) Moa APAGODU, Shalosh B. EKHAD, and Patrick GASKILL
• A Maple One-Liner that is a MUCH Better ANSWER than George Andrews' "Explicit" Formula for the Rademacher Coefficients
• On Rademacher's Infinite Partial Fraction Conjecture Andrew V. Sills and Doron Zeilberger
• A Tribute to Herb Wilf Doron ZEILBERGER1
• Frank Garvan's Counterexample to the Folsom-Ono Andrews SPT Parity Theorem Can Be Discovered in Less Than 17 seconds
• Solutions to Dr. Z.'s Math 421(2), Exam #1 (Oct. 6, 2011) 1. (15 points) Use any method to compute L{f(t)} if
• The Binomial Theorem for (N + n)r (where Nf(n)=f(n+1))
• Eigenvalues and Eigenvectors Edinah K. Gnang
• Dr. Z.'s Shortcut Methods for Solving Boundary Value Problems for PDEs By Doron Zeilberger
• Dr. Z.'s Calc5 Last Handout and SCC Problems : The Art of Checking Your Answer and Avoiding Nonsense By Doron Zeilberger
• Solutions to MATH 421 (1), Dr. Z.'s , Exam 2, Tue., Nov. 22, 2011, 10:20-11:40am, 1. (15 pts.) Solve (from scratch!) the boundary value problem
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful Theorem that the number of npermutations that contain the Pattern 321 Exactly Once Equals
• A Tribute to Herb Wilf Doron ZEILBERGER 1
• On Rademacher's Infinite Partial Fraction Conjecture Andrew V. Sills and Doron Zeilberger
• RADEMACHER'S INFINITE PARTIAL FRACTION CONJECTURE IS FALSE ANDREW V. SILLS AND DORON ZEILBERGER
• Frank Garvan's Counterexample to the FolsomOno Andrews SPT Parity Theorem Can Be Discovered in Less Than 17 seconds
• Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful Theorem that the number of npermutations that contain the Pattern 321 Exactly Once Equals
• RADEMACHER'S INFINITE PARTIAL FRACTION CONJECTURE IS (almost certainly) FALSE
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• The Binomial Theorem for (N + n) r (where Nf(n)=f(n+1)) Moa APAGODU, Shalosh B. EKHAD, and Patrick GASKILL
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• A Maple OneLiner that is a MUCH Better ANSWER than George Andrews' ``Explicit'' Formula for the Rademacher Coe#cients
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• RADEMACHER'S INFINITE PARTIAL FRACTION CONJECTURE IS (almost certainly) FALSE
• HOW TO GAMBLE IF YOU'RE IN A HURRY SHALOSH B. EKHAD, EVANGELOS GEORGIADIS, AND DORON ZEILBERGER
• Solutions to Dr. Z.'s MATH 421 (2) Exam 2, Tue., Nov. 22, 2011, 12:00noon-1:20pm, 1. (15 pts.) Find the general expression, in polar coordinates, for the steady-state temperature
• RADEMACHER'S INFINITE PARTIAL FRACTION CONJECTURE IS FALSE ANDREW V. SILLS AND DORON ZEILBERGER
• On Rademacher's Infinite Partial Fraction Conjecture Andrew V. Sills and Doron Zeilberger
• Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful Theorem that the number of n-permutations that contain the Pattern 321 Exactly Once Equals
• A Tribute to Herb Wilf Doron ZEILBERGER1
• Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful Theorem that the number of n-permutations that contain the Pattern 321 Exactly Once Equals
• Frank Garvan's Counterexample to the Folsom-Ono Andrews SPT Parity Theorem Can Be Discovered in Less Than 17 seconds
• Amanda Folsom and Ken Ono's Error Could Have (and Should Have!) been Discovered by Their Computers (in Less than Three Seconds!)
• A Maple One-Liner that is a MUCH Better ANSWER than George Andrews' "Explicit" Formula for the Rademacher Coefficients
• Using GENERATINGFUNCTIONOLOGY to Enumerate DistinctMultiplicity Partitions Doron ZEILBERGER 1
• A Maple OneLine Proof of George Andrews's Formula that Says that the Number of Triangles with Integer Sides Whose Perimeter is n Equals { n 2
• The Composition Enumeration Reciprocity Theorem: The Number of Compositions of n Into Parts k ( mod a) (k < a) Equals
• Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type
• A Maple OneLine Proof of George Andrews's Theorem that the Number of Triangles with Integer Sides Whose Perimeter is n Equals { n 2
• The Discrete Analog of the MalgrangeEhrenpreis Theorem Doron ZEILBERGER 1
• The Reciprocal of 1+ab+aabb+aaabbb+... for NONCOMMUTING a and b Vladimir RETAKH 1 and Doron ZEILBERGER 1
• The number of mDimensional Partitions of Eleven and Twelve Shalosh B. EKHAD 1
• Computational and Theoretical Challenges On Counting Solid Standard Young Tableaux Shalosh B. EKHAD and Doron ZEILBERGER 1
• The [NameRemoved] Determinant Identity is Purely Routine Doron ZEILBERGER 1
• The Jiang ZengM.IshikawaH.Tagawa qCatalan Hankel Determinant Identity is Purely Routine Doron ZEILBERGER 1
• Solutions to the Attendance Quiz for Oct. 31, 2011 1. A string of length 10 meters coincides with the interval [0, 10] on the x-axis. Set up the
• Solution to the Attendance Quiz for Nov. 10, 2011 uxx + uyy = 0 , 0 < x < , 0 < y < 1 ,
• Solutions to Dr. Z.'s MATH 421 (2) Exam 2, Tue., Nov. 22, 2011, 12:00noon-1:20pm, 1. (15 pts.) Find the general expression, in polar coordinates, for the steady-state temperature
• Solutions to the Attendance Quiz for Sept. 12, 2011 1. Find L-1
• Solutions to Dr. Z.'s Math 421(2), (Fall 2011, RU) REAL Quiz #8 (Nov. 17, 2011) 1. (5 points) Solve the boundary value pde problem
• Using GENERATINGFUNCTIONOLOGY to Enumerate Distinct-Multiplicity Partitions Doron ZEILBERGER1
• Solution to the Attendance Quiz for Oct. 24, 2011 1. Find the first three coefficients of the Fourier-Legendre expansion of
• Solutions to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #4 (Oct. 20, 2011) 1. Find the Fourier series of
• The Jiang Zeng-M.Ishikawa-H.Tagawa q-Catalan Hankel Determinant Identity is Purely Routine Doron ZEILBERGER1
• Solutions to the Attendance Quiz for Oct. 20, 2011 1. Find the eigenfunctions and eigenvalues for the following boundary value problem.
• Solutions to the Attendance Quiz for Oct. 17, 2011 1. (a) Find the complex Fourier series of f(x) = 4x on the interval -2 < x < 2.
• The number of m-Dimensional Partitions of Eleven and Twelve Shalosh B. EKHAD 1
• Computational and Theoretical Challenges On Counting Solid Standard Young Table* Shalosh B. EKHAD and Doron ZEILBERGER1
• The Jiang Zeng-M.Ishikawa-H.Tagawa q-Catalan Hankel Determinant Identity is Pur* *ely Routine
• Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type
• The Reciprocal of 1+ab+aabb+aaabbb+... for NON-COMMUTING a and b Vladimir RETAKH1 and Doron ZEILBERGER1
• A Maple One-Line Proof of George Andrews's Formula that Says that the Number 2 n *
• Using GENERATINGFUNCTIONOLOGY to Enumerate Distinct-Multiplicity Partitions Doron ZEILBERGER1
• The [NameRemoved] Determinant Identity is Purely Routine Doron ZEILBERGER1
• A Maple One-Line Proof of George Andrews's Theorem that the Number 2 n *
• Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci *
• The Composition Enumeration Reciprocity Theorem: The Number of Compositions of n Into Parts k ( mod a) (k < a) Equals
• The Discrete Analog of the Malgrange-Ehrenpreis Theorem Doron ZEILBERGER1
• Solutions to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #8 (Nov. 17, 2011) 1. (5 points) Solve the boundary value pde problem
• Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci Number!
• Solutions to the Attendance Quiz for Oct. 27, 2011 1. Find product solutions, if possible, to the partial differential equation
• Solutions to Dr. Z.'s Math 421(2), (Fall 2011, RU) REAL Quiz #5 (Oct. 27, 2011) 1. Find the eigenfunctions and eigenvalues for the following boundary value function.
• A Maple One-Line Proof of George Andrews's Theorem that the Number of Triangles with Integer Sides Whose Perimeter is n Equals {n2
• NAME: (print!) E-Mail address
• Attendance Quiz for Dec. 1, 2011 1. Find the cosine and sine integral representation of the function f(x) = e-2x
• Solutions to the Attendance Quiz for Sept. 26, 2011 x(0) = 0 , y(0) = 3 .
• Solutions to the Attendance Quiz for Nov. 7, 2011 Corrected version of Nov. 8, 2011, thanks to Joey Reichert (who won a dollar) (In the
• Solutions to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #3 (Oct. 13, 2011) 1. Show that the given functions are orthogonal on the given interval.
• A Maple One-Line Proof of George Andrews's Formula that Says that the Number of Triangles with Integer Sides Whose Perimeter is n Equals {n2
• The number of m-Dimensional Partitions of Eleven and Twelve Shalosh B. EKHAD 1
• 1 Introduction 9 1.1 History and Systems . . . . . . . . . . . . . . . . . . . . . . . . . 10
• Dr. Z.'s Math 421(2), (Fall 2011, RU) REAL Quiz #3 (Oct. 13, 2011) 1. Show that the given functions are orthogonal on the given interval.
• Solutions to the Attendance Quiz for Oct. 10, 2011 1 Find the Fourier series of f(x) = 2x on the interval (-2, 2).
• Solutions to Dr. Z.'s Math 421(2), (Fall 2011, RU) REAL Quiz #10 (Dec. 8, 2011) 1. (10 points) Find the Fourier integral representation of
• Solutions to Dr. Z.'s Math 421(1), Exam #1 (Oct. 6, 2011) 1. (15 points) Using the definition find the Laplace transform L{f(t)} (alias F(s)) of
• Solutions to Dr. Z.'s Math 421(2), Exam #1 (Oct. 6, 2011) Version of Dec. 21, 2011 (thanks to Laura Norkute)
• Solutions to the Attendance Quiz for Sept. 29, 2011 1. Find all the eigenvalues of the matrix
• Solutions to the Attendance Quiz for Sept. 8, 2011 1. Using the definition find the Laplace transform L{f(t)} (alias F(s)) of
• Solution to Dr. Z.'s Math 421(2), (Fall 2011, RU) REAL Quiz #2 (Sept. 22, 2011) 1. Use the Laplace Transform to solve the given initial-value problem.
• Solutions to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #5 (Oct. 27, 2011) 1. (a) (8 points) Find the complex Fourier series f(x) = x on the interval -< x < . (b) (2
• Solution to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #10 (Dec. 8, 2011) 1. (10 points) Find the Fourier integral representation of
• Solutions to the Attendance Quiz for Nov. 28, 2011 1. Solve the pde
• Simplified Solution to the Attendance Quiz for Nov. 10, 2011 uxx + uyy = 0 , 0 < x < , 0 < y < 1 ,
• Solution to the Attendance Quiz for Dec. 5, 2011 1. Solve the heat equation 4uxx = ut, -< x < , t > 0 subject to
• Computational and Theoretical Challenges On Counting Solid Standard Young Tableaux Shalosh B. EKHAD and Doron ZEILBERGER1
• The [NameRemoved] Determinant Identity is Purely Routine Doron ZEILBERGER1
• Solutions to Dr. Z.'s Math 421(2), (Fall 2011, RU) REAL Quiz #4 (Oct. 20, 2011) 1. Find the Fourier series of f(x) = 2x2
• The Reciprocal of 1+ab+aabb+aaabbb+... for NON-COMMUTING a and b Vladimir RETAKH1
• Solutions to Attendance Quiz for Sept. 1, 2011 1. Differentiate the following functions
• The Composition Enumeration Reciprocity Theorem: The Number of Compositions of n Into Parts k ( mod a) (k < a) Equals
• Solutions to the Attendance Quiz for Nov. 3, 2011 1. Using the ready-made formula (don't do it from scratch) solve the boundary value problem
• Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type
• Solution to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #2 (Sept. 22, 2011) Version of Sept. 24, 2011. Correcting a typo (thanks to Viraj Pandya)
• The Discrete Analog of the Malgrange-Ehrenpreis Theorem Doron ZEILBERGER1
• NAME: (print!) E-Mail address
• Solutions to Dr. Z.'s Math 421(1), (Fall 2011, RU) REAL Quiz #7 (Nov. 10, 2011) 1. Solve the boundary value problem
• Solutions to MATH 421 (1), Dr. Z.'s , Exam 2, Tue., Nov. 22, 2011, 10:20-11:40am, 1. (15 pts.) Solve (from scratch!) the boundary value problem
• Solutions to the Attendance Quiz for Dec. 8, 2011 1.: Use the improved Euler method to find an approximate value for y(3) if y(x) is the solution
• SIAM J. COMPUT. Vol. 6, No. 3, September 1977