- Due Friday, November 19, 2010. 1. (5 pt) Show that any finite commutative ring with no nonzero zero divisors is a
- EXTRA CREDIT PROBLEMS 1. In class we noticed that if f(x) is either (always) increasing or (always) decreasing,
- SUMMER 2007 First a word about the homework problems in general. You will find that some of them are worth 3 points
- 1. (30 pt) Evaluate the following limits. b4x4 + 4x -b
- COURSE SYLLABUS Welcome to Math 265, my name is Jim Coykendall, and I will be your instructor for this course. My office is
- SPRING 2011 1. (40 pt) Evaluate the following integrals if they exist
- THE HALF-FACTORIAL PROPERTY IN INTEGRAL EXTENSIONS Jim Coykendall
- COURSE SYLLABUS RING EXTENSIONS
- Due Wednesday September 3, 2003. 1. (5 pt) Let Z denote the integers and let m, n Z both be nonzero. A greatest
- Due Friday, October 29, 2010. This assignment will be devoted to showing that the only nonabelian simple group
- SPRING 2010 1. (50 pt) Evaluate the following integrals
- AN EMBEDDING THEOREM JIM COYKENDALL AND BRENDA JOHNSON MAMMENGA
- Due Friday, December 12, 2003. 1. (5 pt) Let d be a square free integer. We define a quadratic ring of integers to be
- ALGEBRA PRELIMINARY EXAMINATION JANUARY 2004
- 1. (40 pt) Evaluate the following derivatives: a) f(x) = sin(ex
- ALGEBRA PRELIMINARY EXAMINATION AUGUST 2004
- ALGEBRA PRELIMINARY EXAMINATION JANUARY 2005
- ELASTICITY PROPERTIES PRESERVED IN THE NORMSET Jim Coykendall
- STRONG CONVERGENCE PROPERTIES OF SFT RINGS John T. Condo
- Due Friday September 17, 2004. 1. Let V be an inner product space over R. Suppose that {ei}iI is an orthonormal
- ON INTEGRAL DOMAINS WITH NO ATOMS Jim Coykendall, Department of Mathematics, North Dakota State
- SPRING 2011 Due Monday February 28, 2011. As is usual on exams, I am the only biological
- SPRING 2003 First a word about the homework problems in general. You will find that some of them are worth 3 points
- 1. Consider the ellipse x2 a) (5 pts) Set up a double integral to find the area enclosed by this ellipse.
- INTEGRAL DOMAINS HAVING NONZERO ELEMENTS WITH INFINITELY MANY PRIME DIVISORS
- 1. (42 pt) For the following functions, find the derivative. a) f(x) = sin(etan(x)
- SPRING 2003 1. (18 pt) Determine if the following sequences converge or diverge.
- SUMMER 2004 TAKE HOME PORTION
- ALGEBRA PRELIMINARY EXAMINATION SUMMER 1997
- ALGEBRA PRELIMINARY EXAMINATION SPRING 2002
- ALGEBRA PRELIMINARY EXAMINATION SPRING 2002
- ALGEBRA PRELIMINARY EXAMINATION SPRING 2002
- ALGEBRA PRELIMINARY EXAMINATION AUGUST 2003
- ALGEBRA PRELIMINARY EXAMINATION Notes. Z and Q are the integers and the rational numbers respectively. All
- THE PICARD GROUP OF A POLYNOMIAL RING JIM COYKENDALL Department of Mathematics, Cornell University, Ithaca,
- PROPERTIES OF THE NORMSET RELATING TO THE CLASS GROUP Jim Coykendall
- DIVISOR PROPERTIES INHERITED BY NORMSETS OF RINGS OF INTEGERS
- ON ZERO-DIMENSIONALITY AND FRAGMENTED RINGS Jim Coykendall
- AP-DOMAINS AND UNIQUE FACTORIZATION JIM COYKENDALL AND MUHAMMAD ZAFRULLAH
- ZERO-DIVISOR GRAPHS OF POLYNOMIALS AND POWER SERIES OVER COMMUTATIVE RINGS
- Irreducible Divisor Graphs Jim Coykendall
- A GENERALIZATION OF INTEGRALITY JIM COYKENDALL AND TRIDIB DUTTA
- HALF-FACTORIAL DOMAINS, Scott T. Chapman
- Extensions of Half-Factorial Domains: JIM COYKENDALL, North Dakota State University, Department of
- Mini-Conference on Factorization Problems
- THE ADVENTURE BEGINS This problem is based on a question fielded by Professor Davis Cope in our math department.
- SPRING 2004 1. (48 pt) Evaluate the following integrals
- SPRING 2005 1. (40 pt) Evaluate the following integrals
- SPRING 2006 1. (40 pt) Evaluate the following integrals
- SPRING 2007 1. (40 pt) Evaluate the following integrals
- SPRING 2003 1. (32 pt) Evaluate the following integrals
- SPRING 2005 1. (32 pt) Evaluate the following integrals if they exist
- SPRING 2006 1. (32 pt) Evaluate the following integrals if they exist
- SPRING 2010 1. (40 pt) Evaluate the following integrals
- SPRING 2008 1. (42 pt) Determine if the following series converge of diverge.
- SPRING 2009 1. (24 pt) Determine if the following sequences converge or diverge.
- SPRING 2010 1. (48 pt) Determine if the following series converge of diverge.
- SPRING 2004 Due Wednesday February 11, 2004.
- COURSE SYLLABUS Welcome to Math 165, my name is Jim Coykendall, and I will be your instructor for this course. My office is
- 1. (30 pt) Evaluate the following limits if they exist. x3 + x -10
- 1. (36 pt) Evaluate the following limits. t2 -5t + 6
- 1. (36 pt) Evaluate the following limits. a2x2 + bx -(ax + c)), a > 0
- 1. (36 pt) Evaluate the following limits. f(x) sin(x)
- 1. (40 pt) Evaluate the following derivatives: a) f(x) = sin(esin(x2)
- 1. (40 pt) The following define functions of y = f(x) explicitly or implicitly. In all cases, find y . a) f(x) = (x sin(x))tan(x)
- 1. (40 pt) The following define functions of y = f(x) explicitly or implicitly. In all cases, find y . a) f(x) = g(h(x)sin(x)
- 1. (24 pt) Evaluate the following limits. cos(t) -4t
- 1. (32 pt) Evaluate the following limits: , b = 0. b) lim
- 1. (32 pt) Evaluate the following limits: x + sin(3x)
- 1. (32 pt) Evaluate the following limits: , where f(0) = 0 and f (x) is continuous at 0.
- 1. (32 pt) Evaluate the following limits: x + sin(2x)
- 1. (5 pt) Find all critical numbers and classify local extrema for the function f(x, y) = x3 -y2 + xy. 2. (5 pt) Find the maximum and minimum values of the function g(x, y) = x4 -2x2y2 + y3 on the triangle
- COURSE SYLLABUS SUMMER 2007
- SUMMER 2007 Due Monday July 9, 2007.
- SUMMER 2007 HOMEWORK 13
- SUMMER 2004 1. (10 pt) Prove that for all n N
- SUMMER 2004 HOMEWORK 11
- SPRING 2003 Due Friday February 21, 2003.
- SPRING 2003 TAKE HOME PORTION
- SPRING 2003 Due Friday April 11, 2003.
- SPRING 2003 Due Wednesday April 23, 2003.
- SPRING 2003 HOMEWORK 11
- COURSE SYLLABUS Welcome to Math 720, my name is Jim Coykendall, and I will be your instructor for this course. My office is 301D
- Due Monday, November 17, 2003. 1. Let R be commutative with identity and I R an ideal. We define the radical of
- Arithmetic Rings and Integrality Jim Coykendall
- Due Wednesday October 19, 2005. 1. (5 pt) Show that R is a PID if and only if R is a UFD of dimension no more than
- Theory of Factorization Jim Coykendall
- Due Friday, February 19, 2010. 1. Let R be an integral domain. A nonzero nonunit element z R is said to be a
- Due Monday, March 8, 2010 1. Let d < 0 be a squarefree integer and R the ring of integers of the field Q(
- Due Monday, April 23, 2010 1. (5 pt) We have (or will have) shown that if R[x] is an HFD, then R must be
- Due Friday, September 8, 2006. 1. Let R be a domain, and a, b R. We define the greatest common divisor of a and b
- Due Friday, September 23, 2006. 1. Suppose that R is a UFD.
- COURSE SYLLABUS Welcome to Math 728, my name is Jim Coykendall, and I will be your instructor for this course. My office is
- ON UNIQUE FACTORIZATION DOMAINS JIM COYKENDALL AND WILLIAM W. SMITH
- You are responsible for only problems 1-4 if you turn this in by Wednesday, November 26, 2003. If you elect to wait to turn this in Monday, December 1, 2003
- 1. Consider the cone z2 and the plane z -my = 2 where m is a constant.
- SPRING 2004 1. (32 pt) Evaluate the following integrals if they exist
- The SFT property does not imply finite dimension for power series rings.
- SPRING 2006 1. (36 pt) Determine if the following series converge or diverge.
- Due Friday, December 10, 2010. 1. Let d be a square free integer. We define a quadratic ring of integers to be
- Jim Coykendall March 2, 2011
- SUMMER 2004 Due Wednesday July 7, 2004.
- SPRING 2005 1. (42 pt) Determine if the following series converge or diverge.
- SPRING 2011 Due Friday February 4, 2011.
- ALGEBRA PRELIMINARY EXAMINATION AUGUST 2006
- Monoid Domain Constructions of Antimatter Domains D. D. Anderson, J. Coykendall, L. Hill, and M. Zafrullah
- FACTORIZATION IN ANTIMATTER RINGS JIM COYKENDALL
- SUMMER 2004 Due Friday July 16, 2004.
- NORMSETS AND DETERMINATION OF UNIQUE FACTORIZATION IN RINGS OF ALGEBRAIC INTEGERS
- 1. Consider the function f(x, y) = x4 a) (5 pts) Find all critical points of f(x, y).
- SUMMER 2006 Due Monday July 3, 2006.
- SPRING 2004 Due Monday February 2, 2004.
- 1. (40 pt) Evaluate the following limits: You may assume that this limit exists.
- SPRING 2011 1. (48 pt) Determine if the following series converge of diverge.
- SPRING 2009 1. (40 pt) Evaluate the following integrals if they exist
- Due Monday November 29, 2010. 1. Let S be a subset of a commutative ring with identity, R. We say that S is
- Linear Algebra Jim Coykendall
- SUMMER 2004 First a word about the homework problems in general. You will find that some of them are worth 3 points
- Due Monday September 15, 2003. 1. Let H and K be subgroups of G.
- Due Monday, November 10, 2003. 1. Let R be a ring. We say that R is of characteristic n if there is a positive integer
- Sets with few intersection numbers from Singer subgroup orbits
- A REMARK ON ARITHMETIC EQUIVALENCE AND THE NORMSET Jim Coykendall
- COURSE SYLLABUS Welcome to Math 724, my name is Jim Coykendall, and I will be your instructor for this course. My office is
- 1. (36 pt) Evaluate the following limits. x2 + 5 + x -5
- Due Wednesday October 6, 2004. A category, C, is a collection of objects together with the following.
- COURSE SYLLABUS SUMMER 2011
- FRAGMENTED DOMAINS HAVE INFINITE KRULL DIMENSION Jim Coykendall
- SPRING 2007 1. (30 pt) Evaluate the following integrals if they exist.
- ALGEBRA PRELIMINARY EXAMINATION JANUARY 2006
- SUMMER 2004 Due Wednesday June 23, 2004.
- FINITELY GENERATED-FRAGMENTED DOMAINS JIM COYKENDALL AND TIBERIU DUMITRESCU
- Due Monday September 5, 2005. 1. Let R be a commutative ring with identity and N R the set of nilpotent elements
- SUMMER 2007 Due Friday July 20, 2007.
- 1. (36 pt) Evaluate the following derivatives: a) f(x) = sin(
- 1. (36 pt) Evaluate the following limits if they exist. x3 + x2 -2
- SPRING 2008 1. (50 pt) Evaluate the following integrals
- GD(1) and GD(2) are not preserved in integral Jim Coykendall
- SPRING 2003 1. (48 pt) Evaluate the following integrals
- SPRING 2004 Due Monday April 5, 2004. As is usual on exams, I am the only biological resource
- SUMMER 2006 Due Monday June 26, 2006.
- SUMMER 2007 Due Friday June 29, 2007.
- SUMMER 2003 Due Monday July 14, 2003.
- FORMAL POWER SERIES RINGS OVER ZERO-DIMENSIONAL SFT-RINGS John T. Condo
- On the integral closure of a half-factorial domain Jim Coykendall
- SPRING 2011 1. (50 pt) Evaluate the following integrals
- HALF-FACTORIAL DOMAINS IN QUADRATIC FIELDS Jim Coykendall
- SPRING 2003 TAKE HOME PORTION
- COURSE SYLLABUS SPRING 2011
- SPRING 2007 1. (36 pt) Determine if the following series converge or diverge.
- ALGEBRA PRELIMINARY EXAMINATION Notes. Z, Q, R, and C are the integers, the rational numbers, the real num-
- SPRING 2004 Due Monday February 23, 2004. As is usual on exams, I am the only biological
- SUMMER 2004 Due Friday July 2, 2004.
- SPRING 2003 HOMEWORK 10
- 1. (32 pt) Evaluate the following limits: (1 + tx)csc(sx)
- SPRING 2009 1. (50 pt) Evaluate the following integrals
- SUMMER 2004 HOMEWORK 10
- SPRING 2004 1. (42 pt) Determine if the following series converge or diverge.
- SPRING 2011 Due Monday April 18, 2011. As is usual on exams, I am the only biological resource
- SUMMER 2006 Due Friday, Bastille Day, 2006.
- ALGEBRA PRELIMINARY EXAMINATION SUMMER 2001
- SURVIVAL-PAIRS OF COMMUTATIVE RINGS HAVE THE
- Due Friday, January 29, 2010. 1. Let R be a domain, and a, b R. We define the greatest common divisor of a and b
- ALGEBRA PRELIMINARY EXAMINATION Abstract. In this examination all fields are commutative. All rings contain 1
- Due Wednesday, October 29, 2003. 1. (5 pt) Let p and q be distinct positive primes. Show that any group of order pq
- ANALYSIS EXAM August 2004 1. a) Give the definition of a complete metric space.
- SPRING 2008 1. (32 pt) Evaluate the following integrals if they exist
- COURSE SYLLABUS Welcome to Math 724, my name is Jim Coykendall, and I will be your instructor for this course. My office is
- Atomicity in Certain Pullbacks Jason G. Boynton
- A CHARACTERIZATION OF POLYNOMIAL RINGS WITH THE HALF-FACTORIAL PROPERTY
- THE HALF-FACTORIAL PROPERTY AND DOMAINS OF THE FORM A+XB[X]
- 1. (40 pt) Evaluate the following derivatives: a) f(x) = sin3
- EXAMINATION January 2003
- SUMMER 2007 Due Friday July 13, 2007.
- SUMMER 2004 Due Friday June 22, 2007.
- Some remarks on infinite products JIM COYKENDALL, North Dakota State University, Department of
- 1. (40 pt) For the following functions of x (defined explicitly or implicitly), find y . If implicitly defined, you need not solve for y .
- 1. (36 pt) Evaluate the following limits. x3 -x2 -4
- SUMMER 2011 1. (60 pt) Evaluate the following integrals.
- SUMMER 2011 1. (5 pt) Evaluate
- SUMMER 2011 1. Evaluate the following integrals.
- SUMMER 2011 1. Suppose that we want to estimate
- SUMMER 2011 1. (15 pt) Determine if the following series converge.
- SUMMER 2011 1. (15 pt) Determine if the following series converge or diverge.
- SUMMER 2011 1. Determine if the following series converge. If the series converges, find its sum.
- SUMMER 2011 1. (48 pt) Consider the parametric equations x = t4 -8t2 and y = t3 -12t.
- SUMMER 2011 1. Consider the power series
- COURSE SYLLABUS Welcome to Math 772 (Algebraic Number Theory), my name is Jim Coykendall, and I will be your instruc-
- SUMMER 2011 1. (5 pt) Suppose f(x) is a differentiable function and |f (x)| m for all a x b. Show that the
- SUMMER 2011 1. Evaluate the following integrals.
- SUMMER 2011 1. Consider the parametric equations x = t4
- SUMMER 2011 1. (30 pt) Find the center, radius and interval of convergence of the following power series.
- SUMMER 2011 1. (48 pt) Determine if the following series converge or diverge.
- SUMMER 2011 1. (5 pt) Sketch the graph of the following parametric curves (and indicate the direction as t
- SUMMER 2011 1. (5 pt) Find the surface area generated when the function f(x) = sin(x), 0 x is revolved
- SUMMER 2011 1. (5 pt) Show by induction that
- SUMMER 2011 a) (5 pt) Find f (x).
- COHEN-KAPLANSKY DOMAINS AND THE GOLDBACH JIM COYKENDALL AND CHRIS SPICER
- COURSE SYLLABUS Welcome to Math 165, my name is Jim Coykendall, and I will be your instructor for this course. My office is 412K
- SPRING 2011 Due Wednesday September 14, 2011.
- SUMMER 2011 1. Determine if the following sequences converge.
- SUMMER 2011 1. (15 pt) Let f(x) =
- SUMMER 2011 1. (15 pt) Determine if the following series converge.
- SUMMER 2011 1. (5 pt) Let f(x) = ln(| sec(x)|). Find the arclength of this function 0 x
- 1. (40 pt) Evaluate the following limits: f(x) = 0 and f (x) is continuous and nonzero at a.
- SUMMER 2011 1. Evaluate the following integrals.
- Number Theory Jim Coykendall
- SUMMER 2011 1. Evaluate the following integrals.
- SUMMER 2011 1. Consider the polar equation r = 1 + sin(1
- SUMMER 2011 1. Consider the region bounded by the curve f(x) = sin(x), 0 x and the x-axis.
- SUMMER 2011 1. For this problem, we will consider the differential equation
- 1. (30 pt) Evaluate the following limits (for part c) you may assume that the limit exists and is ; f, g are nonnegative and differentiable with f(a) = g(a) = 0, f (x) = (g(x))2
- 1. (30 pt) Evaluate the following limits: x3 -2x2 -9
- Due Monday, October 24, 2011. 1. Consider the rings of integers Z[
- 1. (32 pt) For the following functions of x (defined explicitly or implicitly), find y . If implicitly defined, you need not solve for y .
- SPRING 2011 Due Monday October 2, 2011.
- SPRING 2012 1. (50 pt) Evaluate the following integrals
- COURSE SYLLABUS SPRING 2012
- SPRING 2012 1. (60 pt) Evaluate the following integrals if they exist
- COURSE SYLLABUS SPRING 2012