Richman, Fred - Department of Mathematical Sciences, Florida Atlantic University

• Transient limits Fred Richman and Katarzyna Winkowska-Nowak
• A CONSTRUCTIVE PROOF OF GLEASON'S THEOREM Fred Richman
• Answers to Homework 7 February 2008
• Answers to Homework 14 February 2008
• Equivalence of syllogisms Fred Richman
• 1. De...ne what it means for a sequence to be monotone. Give an example of a sequence that is monotone. Give an example of a sequence that is not
• Modern Analysis, Test 14, April 21, 2010 1 Consider Dirichlet's function
• Sets, complements and boundaries Douglas Bridges, Fred Richman, and Wang Yuchuan
• 1. List all the size-three multisets whose elements are selected from the set fa; b; cg. Then give the stars-and-bars representation for each of the mul-
• Confessions of a formalist, Platonist intuitionist
• Confessions of a formalist, Platonist intuitionist
• What should you know how to do for the ...nal examination? 1. Division algorithm. You should be able to state and execute the
• Treatise on the Arithmetical Triangle Blaise Pascal
• Section 8.2 1. Clearly 1 = 12
• Growing forests in abelian p-groups Fred Richman
• Section 2.2 1. What is N (a) for a in Z.
• Section 2.3 1. Show that the Gaussian number (3=5) + (4=5) i has norm 1. (3=5)2
• 1 Limited principle of omniscience (LPO) LPO says that for each binary sequence a1; a2; a3; : : : either
• An introduction to constructive algebra Spring 2008
• The regular element property Fred Richman
• Linear Algebra, Test 2 19 September 2008
• SIMPLY PRESENTED TAG MODULES Fred Richman
• The height that Kaplansky describes is called the p-height if we are dealing with groups that are not primary.
• Linear Algebra, Test 5 31 October 2008
• Interview with a constructive mathematician Fred Richman
• 1 Notes on Theorem 2 To quote Kaplansky,
• Subrings of zero-dimensional rings Jim Brewer1
• TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• FILTERED MODULES OVER DISCRETE VALUATION DOMAINS Fred Richman
• Near convexity, metric convexity, and Fred Richman
• 1. Let A be a subset of the real numbers. De...ne what an open cover for A De...nition 3.3.6: An open cover for A is a collection of open sets whose
• 1. How many ways can you arrange the seven characters a, b, c, d, 1, 2, 3 in a row so that
• A CONSTRUCTIVE PROOF OF GLEASON'S THEOREM Fred Richman
• Intuitionistic notions of boundedness in N Fred Richman
• Adjoints, absolute values and polar decompositions Douglas Bridges, Fred Richman, Peter Schuster
• Constructive mathematics without choice Fred Richman
• FILTERED MODULES OVER DISCRETE VALUATION DOMAINS Fred Richman
• Algebraic functions, calculus style Fred Richman
• Modern Analysis, Final Exam, May 5, 2010 1 Let an be a sequence of real numbers. Which of the following must be true?
• Flat dimension, constructivity, and the Hilbert syzygy theorem Fred Richman
• 1 A little cardinal arithmetic If there is a one-to-one map from A to B we write jAj jBj and say that the
• 1 The group B A long time ago we showed the group B to an algebraist who knew nothing
• 1 Lemmas 1,2,3 and Theorem 5 First a quick proof of the converse of Lemma 1
• 1 Kulikov's criterion First a word about the notion of an !-...ltered vector space. This is a vector
• 1 Simply presented p-groups By a tree (more properly, a forest), I mean a set T with equipped with a
• The central mysteries of analysis are The real numbers
• A constructive theory of minimal zero-dimensional extensions
• Van der Waerden's construction of a splitting Fred Richman
• INTUITIONISM AS GENERALIZATION Fred Richman
• 1. In the Gaussian integers, Z [i], Is 14 a multiple of 1 + i?
• 1. The ring Z[ 2] is a subset of the real numbers.
• Section 6.1 1. Two ips and a rotation, 4, unless it's a square.
• 1. How many four letter words (including nonsensical words) are there that do not have two consecutive letters the same? How many are there that
• 5. Show that Fn > 1:6n once n is big enough.
• 1. Let the sequence a0; a1; a2; : : : be de...ned by a0 = 0 and an = an 1 + n for n > 0. Show that an = n (n + 1) =2 for all positive integers n.
• 1. For the pairs of integer a, b given below, ...nd the integers q and r such that a = qb + r and 0 r < b
• 1. Working in Z10 (a) 3 + 3 = 6
• 1. We noticed that a graph with more than two vertices of odd degree cannot have an Eulerian trial, but connected graphs with zero or two
• Solutions to sample Test 4 1. The curvature of the curve (7 cos t; 7 sin t; 6t) at the point where t = 1
• Solutions to sample Test 5 1. Suppose z = f (x; y), x = g (t), and y = h (t). If g (3) = 3, g0
• Solutions to sample Test 7 1. The maximum value of the function xy subject to the constraint x2
• 1. Let G be a group. De...ne what an inner automorphism of G is. Show that the inner automorphisms of G form a group isomorphic to G=Z (G).
• 1. Let R = Z 19 : a; b 2 Z . Let N a + b
• Introduction to abstract algebra 2. Final examination. 1. Prove or give a counterexample
• NEW NUMBERS 1 1. NEW NUMBERS
• Modern Algebra, Quiz 7 27 February 2009
• Section 6.3 1. Compute (12345) (12345)
• Modern Algebra, Quiz 9 20 March 2009
• Section 6.4 1. Find a cyclic subgroup of S3 and determine all of its generators.
• Modern Algebra, Quiz 10 27 March 2009
• Basic notions 1. For any X is a set, a permutation of X is a one-to-one function
• Linear Algebra, Test 1 5 September 2008
• Linear Algebra, Test 3 3 October 2008
• Linear Algebra, Test 4 17 October 2008
• Computational discrete mathematics with Fred Richman
• 1. De...ne what it means for a subset of R to be open. Give an example of a subset that is open. Give an example of a subset that is not open.
• Section 1.3 1. Find seven units in Z
• Numerical methods with JavaScript Fred Richman
• A division algorithm Fred Richman
• 1. What does it mean to say that two sets A and B have the same cardinality? What does it mean to say that a set S is countable?
• Enabling conditions for interpolated rings Fred Richman
• 1. What Gaussian integers are multiples of i? They all are. Each Gaussian integer can be written as a + bi where a and b are integers. But
• Growing forests in abelian pgroups Fred Richman
• 1. What is a rational number? Abbott says, "A rational number is any number that can be expressed in
• The textbook opens with Theorem 1.1.1 There is no rational number whose square is 2.
• Answers to Homework 21 February 2008
• 1. De...ne what it means for a subset of R to be perfect. De...nition 3.4.1. A subset of R is perfect if it is closed and contains no
• Here is an expansion of the proof of Lemma 4 Lemma 4. Let G be a group such that pr
• Section 3.2 2. If d = gcd (a; b), then a=d and b=d are relatively prime.
• INTUITIONISM AS GENERALIZATION Fred Richman
• Solutions to sample Test 6 1. The maximum rate of change of y2
• The regular element property Fred Richman
• Sample answers to Test 3 ; 2; t 1i dt, then the sum of the components of u is
• 1 Vector spaces, span, linear independence We want to consider vector spaces over an arbitrary ...eld. In most applica-
• 1. What does it mean for a sequence to be bounded? Give an example of a sequence which is bounded. Give an example of a sequence which is not
• Qualifying Examination in Algebra 30 August 2001
• 1. Let G be the graph in the ...gure. (a) How many dierent paths are there from a to b?
• Exercises 8.1 1. By de...nition, the inverse of a 1
• 46 Systems of linear equations and their solution. b. This method is only a little more complicated for a more exotic figure.
• Real numbers and other completions Fred Richman
• A division algorithm Fred Richman
• Trace-class operators Fred Richman Douglas Bridges
• Enabling conditions for interpolated rings Fred Richman
• FILTERED MODULES OVER DISCRETE VALUATION DOMAINS Fred Richman Elbert A. Walker
• Sets, complements and boundaries Douglas Bridges, Fred Richman, and Wang Yuchuan
• Omniscience principles and functions of bounded variation
• A MEASURE OF CONSANGUINITY Fred Richman
• Weakly integrally closed domains: minimum polynomials of matrices
• Adjoints and the image of the ball Fred Richman
• Spreads and choice in constructive mathematics
• GLEASON'S THEOREM HAS A CONSTRUCTIVE PROOF Fred Richman
• Adjoints, absolute values and polar decompositions Douglas Bridges, Fred Richman, Peter Schuster
• SIMPLY PRESENTED TAG MODULES Fred Richman
• A WEAK COUNTABLE CHOICE PRINCIPLE Douglas Bridges
• Section 3.0 1. Find gcd (7; 35).
• Section 30. 1. Prove that, if T is an orthogonal transformation on R2
• A MEASURE OF CONSANGUINITY Fred Richman
• 1. Let Kn be the complete graph on n vertices (each two vertices are adja-cent), and Km;n the complete bipartite graph: V = X[Y where X\Y = ;,
• Flat dimension, constructivity, and the Hilbert syzygy theorem Fred Richman
• Solutions to sample Test 8 dx dy after reversing the order of integration.
• Weak Markov's principle, strong extensionality, and countable choice
• 5 Subgroups of p -bounded groups
• The ascending tree condition Fred Richman
• Constructive Mathematics Without Countable Choice
• The regular element property Fred Richman
• Confessions of a formalist, Platonist intuitionist
• SIMPLY PRESENTED TAG MODULES Fred Richman
• GENERALIZED REAL NUMBERS IN CONSTRUCTIVE MATHEMATICS
• Nontransitivity of locatedness for subspaces of a Banach space
• Pointwise dioeerentiability Fred Richman
• INTUITIONISM AS GENERALIZATION Fred Richman
• Sets, complements and boundaries Douglas Bridges, Fred Richman, and Wang Yuchuan
• Modern Algebra, Quiz 12 10 April 2009
• Annotated answers to the January 22 assignment 1. (Page 57)
• A MEASURE OF CONSANGUINITY Fred Richman
• 1 Universal summands are injective This is a generalization of Exercise 6 which says that if a group is a summand
• Linear Algebra, Test 6 14 November 2008
• 2. Show that 1 + 2 + 3 + + n =
• Interview with a constructive mathematician Fred Richman
• 1. Let p and q be distinct prime numbers. Determine the number of abelian groups of order p3
• 1. Write the graphs whose pictures appear in the text as pairs of sets (a) (f1; 2; 3; 4; 5; 6g; ff1; 2g; f1; 4g; f2; 3g; f2; 5g; f3; 6g; f4; 5g; f5; 6gg)
• SuperHare: an algorithm for proportional representations
• Pre-abelian clan categories Fred Richman
• Growing forests in abelian p-groups Fred Richman
• Computable Calculus, Oliver Aberth, Academic Press 2001, ISBN 0-12-041752-9, 192+xiv, with compact disk 0-12-141753-7
• Constructive mathematics without choice Fred Richman
• The fundamental theorem of algebra: a constructive development without choice
• Interview with a constructive mathematician Fred Richman
• Equivalence of syllogisms Fred Richman
• Is 0.999 . . .= 1? Fred Richman
• A CONSTRUCTIVE PROOF OF GLEASON'S THEOREM Fred Richman Douglas Bridges
• A WEAK COUNTABLE CHOICE PRINCIPLE Douglas Bridges Fred Richman
• Flat dimension, constructivity, and the Hilbert syzygy theorem Fred Richman
• LINEAR INDEPENDENCE WITHOUT CHOICE
• COMPUTING LIMITING STATIONARY DISTRIBUTIONS OF SMALL NOISY
• Van der Waerden's construction of a splitting oeld
• A WEAK COUNTABLE CHOICE PRINCIPLE Douglas Bridges
• 1 The product rule Suppose u and v are functions, and u0
• Calculus I, Test 2 2 September 2011
• Notes on Calculus 1 "Mathematics is common sense."Errett Bishop, 1970
• Calculus I, Test 4 16 September 2011
• Calculus I, Test 12 14 November 2011
• Calculus I, Test 6 30 September 2011
• Exercises for November 30 Find a function f satisfying the given conditions.
• Calculus I, Test 14 30 November 2011
• Calculus I, Test 11 4 November 2011
• Calculus I, Test 7 7 October 2011
• Calculus I, Test 8 15 October 2011
• Calculus I, Test 10 28 October 2011
• Calculus I, Test 9 21 October 2012
• Minimal zero-dimensional extensions Fred Richman
• Calculus I, Test 13 21 November 2011
• Algebraic functions, calculus style Fred Richman
• Florida Atlantic University Mathematics Competition
• CZF and Second Order Arithmetic Robert S. Lubarsky #
• On the Constructive Dedekind Reals Robert S. Lubarsky
• SignedBit Representations of Real Numbers Robert S. Lubarsky
• FAU/Stuyvesant Alumni Mathematics Competition (1) There are two isosceles triangles. One has with top angle
• Principles Weaker than BDN Robert S. Lubarsky and Hannes Diener
• Florida Atlantic University Mathematics Competition
• On the Cauchy Completeness of the Constructive Cauchy Reals
• Independence Results around Constructive ZF Robert S. Lubarsky
• IKP and Friends Robert S. Lubarsky #
• ITTMs with Feedback Robert S. Lubarsky
• Topological Forcing Semantics with Settling Robert S. Lubarsky
• GEOMETRIC SPACES WITH NO POINTS ROBERT S. LUBARSKY
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• Syllabus Fall 2011 Calculus with Analytic Geometry 1 (MAC 2311) 4 credits
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• 1 Antiderivative of cosecant The following functions are equal when sin x 6= 0. Their derivative is csc x.
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• Principles Weaker than BD-N Robert S. Lubarsky and Hannes Diener
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• Campaign ad war not for faint of heart -or wallet By CHARLES ELMORE
• Topological Forcing Semantics with Settling Robert S. Lubarsky
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• Expert: This GOP primary 'like ultimate fighting'; Will it leave general election wounds?
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• Logic (PHI 2102) 3 credits Instructor: Lab Section Leader
• The Kripke Schema in Metric Topology Robert Lubarsky, Fred Richman, and Peter Schuster
• Dierential Equations, Test 4 3 February 2012
• FAU Study Finds Babies Learn To Speak By Watching Mouths
• Syllabus Fall 2011 Calculus for Engineers 2 (MAC 2282) 4 credits
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• 2010/2011 ANNUAL REPORT Division of Student Affairs
• Posted on Sun, Dec. 04, 2011 As Miami's Omni area prospers, need for
• CZF and Second Order Arithmetic Robert S. Lubarsky
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• Point-Counterpoint: The political views of Martin Luther King
• (Story continues on next page) Dr. O'Corry-Crowe with Guillemot chicks
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• Independence Results around Constructive ZF Robert S. Lubarsky
• Topological Forcing Semantics with Settling Robert S. Lubarsky
• TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
• Principles Weaker than BD-N Robert S. Lubarsky and Hannes Diener
• CCA 2006 On the Cauchy Completeness of the
• On the Constructive Dedekind Reals Robert S. Lubarsky
• ITTMs with Feedback Robert S. Lubarsky
• IKP and Friends Robert S. Lubarsky*
• CZF and Second Order Arithmetic Robert S. Lubarsky*
• Signed-Bit Representations of Real Numbers Robert S. Lubarsky
• GEOMETRIC SPACES WITH NO POINTS ROBERT S. LUBARSKY
• MATH DAY 2011 at FAU Competition AIndividual
• Some derivative formulas restriction
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• ISM 4324 Computer Forensics Class Schedule: Wednesday 4:00PM-6:50PM, FL411 (Fleming Hall), Boca Raton Campus
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• GEOMETRIC SPACES WITH NO POINTS ROBERT S. LUBARSKY
• COT 4930/5930 Security for infrastructure systems Critical infrastructure are the systems that support our everyday life and the Dept. of
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• Computational discrete mathematics with Fred Richman
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