Barnard, Josh - Department of Mathematics and Statistics, University of South Alabama

• Calculus II Math 126-102
• Calculus III Mini-test 2 Solutions July 3, 2008 x dA, where D is the region in the xy-plane bounded by the curve y = x2
• Precalculus Algebra Math 112-103 Summer 2011
• Math 125-101 MF 9:1010:25, ILB 410
• Calculus III Test 3 Sample Problems 1. Express the area of the surface (u, v) = u cos v, u sin v, 2v , with domain 0 u 1,
• Linear Algebra I Math 237-101 Summer 2011
• The symmetric group: The symmetric group Sn is defined as the set of all permutations of the set n = {1, 2, 3, . . ., n}. Thinking of a permutation Sn as a one-to-one map : n n, we
• Linear Algebra I Test 1 Solutions September 24, 2004 If possible, find (a) BT
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• Linear Algebra I Worksheet 11 Solutions May 3, 2007 1. Compute eA
• Calculus III Test 2 Solutions July 2, 2010 1. Below is shown a contour diagram for a function f (x, y).
• Instructor: Prof. Josh Barnard Office: 817 Physical Sciences Center [PHSC]
• Linear Algebra I Test 1 Solutions February 15, 2007 1. (a) Show that the set of vectors of the form
• The aim of this short preliminary chapter is to introduce a few of the most com-mon geometric concepts and constructions in algebraic topology. The exposition is
• Linear Algebra I Test 2 Solutions March 15, 2007 1. Let L : P2 P2 be defined by L(at2
• Test 2 Solutions November 21, 2006 On all problems, "find the Taylor series" means either (i) find a
• Linear Algebra I Test 3 Solutions April 19, 2007 1. Prove the Pythagorean theorem: If u and v are orthogonal, then
• Linear Algebra I Worksheet 6 Solutions March 6, 2007 1. Consider the following bases for R2
• Solutions to practice problems for Linear Algebra Test III. 1. Suppose L: V W is a linear transformation, where the dimension of V is n and
• Calculus III Math 227-101 Summer 2010
• Linear Algebra I Worksheet 1 Solutions January 23, 2007 1. [6 pts] Use Gaussian elimination to solve the following linear system
• Coordinates, Transition Matrices, and Matrix Representations Notation: To simplify things, we'll assume V is 3dimensional and W is 2dimensional,
• Linear Algebra I Math 237-102 Spring 2011
• Foundations of Mathematics Test 3 Solutions November 22, 2010 1. Prove Bernoulli's Inequality: if x is any real number with x -1, then for all natural
• Information pertaining to Test I This test is all about multiple integrals. You should know how to do double (resp. triple)
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• Information pertaining to Test III This test covers chapter 17, and covers the following basic topics
• Linear Algebra I Test 1 Solutions June 17, 2010 1. Determine whether 2t2 -11t + 12 lies in the span of {t2 + 2t + 1, t2 -t + 3} (in F(R)).
• DISTORTION OF SURFACE GROUPS IN CAT(0) FREEBYCYCLIC GROUPS
• Linear Algebra I Worksheet 10 Due April 17, 2007 Name: OUID
• Calculus II Mini-Test 1 Solutions April 5, 2009 1. Use integration to compute the volume of the solid shown below.
• Calculus IV Test 3 Solutions November 17, 2005 1. I need to hang a curtain along the side of a stage, to separate the visible part of the stage from
• Practice problems for Linear Algebra Test I. b) Find AB c) Find 7A -2B
• Advanced Calculus I Test 1 Solutions October 7, 2009 1. [20 pts] Prove one of the following
• Week 7 worksheet solutions 1. Consider the vector space R2
• Review information for Calculus III Test I. The test will cover sections 12.112.10. Here is a list of useful problems to review in
• Geometric Group Theory Prof. Josh Barnard Math 490-101
• Calculus III Test 1 Solutions June 16, 2010 1. Let C denote the portion of the graph of y = x2 + x -2 with 0 x 1, and let
• A LOOP THEOREM/DEHN'S LEMMA FOR SOME ORBIFOLDS JOSH BARNARD
• April 6, 2011 Linear Algebra Test 2 Solutions 1. Suppose v1, v2, and v3 are vectors in a vector space V.
• Topology I Test 1 Solutions October 13, 2008 1. Do FIVE of the following
• Linear Algebra I Test 3 Solutions March 28, 2005 1. Use the Gram-Schmidt process on R3
• Test 1 Solutions October 5, 2006 1. Determine whether the series converges or diverges, being sure to justify your
• Solutions to Worksheet 1 1. Let V be the set of all 2 1 matrices
• Math 3333-004 Linear Algebra I
• Introduction to Spans The span of a set of vectors is the collection of all possible linear combinations
• Calculus II Test 2 Solutions July 17, 2009 1. Consider the parametrized curve c(t) = (t2
• Test 2 Solutions Advanced Calculus I November 7, 2007
• Test 2 Solutions Calculus I October 10, 2008 1. Use the definition of the derivative to find
• Test 2 Solutions Calculus II November 9, 2007
• April 27, 2011 Linear Algebra Test 3 Solutions 1. Suppose T is the basis T =
• Linear Algebra I Test 3 Solutions July 20, 2010 1. In a homework assignment, you found that the matrix representation for a certain
• Series Summary A power series centered at c is a series of the form
• History of Mathematics Review Sheet Show that if n is a multiple of five, then 2/n can be broken into the sum of two unit fractions,
• Linear Algebra I Test 1 Solutions June 15, 2007 1. (a) Suppose W is a subspace of R5
• Calculus II Math 126-101
• Line Integrals 1. Integrating a function along a curve
• Linear Algebra I Test 1 Solutions February 7, 2005 If possible, find (a) BT
• Linear Algebra I Worksheet 7 Solutions July 23, 2007 1. Compute eA
• Solutions to practice problems for Linear Algebra Test III. 1. Suppose L: V W is a linear transformation, where the dimension of V is n and
• Calculus III Test 2 July 18, 2008 ds, where C is given by r(t) = t, ln(sec t) for 0 t
• Line Integrals 1. Integrating a function along a curve
• Matrix Exponentials Suppose A is a square matrix. We then make the following definition
• GEOMETRICALLY INFINITE SURFACE ACTIONS ON CONTRACTIBLE #HYPERBOLIC 3--MANIFOLDS
• Linear Algebra I Worksheet 2 Solutions January 30, 2007 1. (1.3 #12) Consider the following matrices
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• Calculus I Test 2 Solutions October 25, 2004 1. Find the limit lim
• Linear Algebra I Worksheet 5 Solutions July 6, 2007 1. Suppose V is the set of all positive real numbers, and define operations and
• Test 2 Calculus II March 13, 2009 1. Find the Taylor series centered at zero for the indefinite integral
• Introduction to Linear Independence A collection of vectors S = {v1, . . . , vk} is linearly independent if there is no way
• History of Mathematics Math 410-102 Fall 2010
• Chapter 15 review answers True/False
• Desiderata and Suggestions: No. 2. The Theory of Groups: Graphical Representation Author(s): Professor Cayley
• A LOOP THEOREM/DEHN'S LEMMA FOR SOME ORBIFOLDS JOSH BARNARD
• Basic Definitions A series is an expression of the form
• MA 237-102 Linear Algebra I Test 3 Solutions 4/16/10 1. Consider the matrix A =
• Practice problems for Linear Algebra Test II. 1. (a) Find a basis S for R3
• Calculus I Test 3 Solutions December 3, 2004 1. Use a tangent line approximation to estimate the value of
• Conway's ZIP Proof George K. Francis Jeffrey R. Weeks
• Linear Algebra I Test 1 October 25, 2004 1. Use the Gram-Schmidt process on R3
• Week 2 worksheet (due Monday, June 19 at the beginning of class)
• Calculus I Test 1 Solutions September 24, 2004 1. Let f(x) be the function whose graph is on the board.
• Information pertaining to Test II Here is a list of problems in the Chapter 12 Review on pages 823824 that are worth
• Linear Algebra I Worksheet 4 Solutions June 27, 2007 1. Consider the following bases for R3
• Linear Algebra I Worksheet 2 Due January 30, 2007 Name: OUID
• Linear Algebra I Test 2 Solutions July 8, 2010 1. (i) Prove that if T :Rn Rm is an isomorphism, then n = m.
• Test 1 Solutions Calculus III June 20, 2008
• Linear Algebra I Math 237-102
• Practice problems for Linear Algebra Test II. 1. (a) Find a basis S = {v1, v2, v3} for R3
• 10/25/10 History of Mathematics Test Solutions Do six of the following problems, including at least one of the final three.
• Take-Home Test 1 Solutions Advanced Calculus II Due February 20, 2008
• [The following Smith's Prize Exam was taken by James Clerk Maxwell at Cambridge. Question 8 is Stokes' Theorem. (Stokes was a personal friend of Maxwell.) Maxwell
• Linear Algebra I Worksheet 5 Solutions February 27, 2007 1. [9 pts] You are given the following vector and two ordered bases for R3
• Foundations of Mathematics Test 2 Solutions November 1, 2010 1. Sketch the truth sets of the following statements.
• Rearranging the Alternating Harmonic Series Lawrence H. Riddle
• GEOMETRICALLY INFINITE SURFACE ACTIONS ON CONTRACTIBLE -HYPERBOLIC 3MANIFOLDS
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• SUPER-EXPONENTIAL DISTORTION OF SUBGROUPS OF CAT(-1) JOSH BARNARD, NOEL BRADY, AND PALLAVI DANI
• DISTORTION OF SURFACE GROUPS IN CAT(0) FREE-BY-CYCLIC GROUPS
• Feb 18, 2011 Linear Algebra Test 1 Solutions 1. Solve the following system of linear equations
• Applied Differential Equations I Math 238-101 Spring 2011
• Apr 11, 2011 Differential Equations Test 2 Solutions 1. Solve the initial value problem: y
• Elementary Geometry Math 321-501 Spring 2011
• Apr 6, 2011 Elementary Geometry Test 2 Name: Do five of the following eight problems. Please write neatly, show all your work, and
• Foundations of Mathematics Math 320-101 Fall 2010
• Foundations of Mathematics Test 1 Solutions September 20, 2010 1. Let F(x, t) mean "you can fool x at time t." Express the following statement using F
• Library Assignment #2: Periodical Literature Provide research summaries of ten papers on the history of mathematics (both words are crucial)
• Library Assignment #1: Your Mathematician Your Mathematician is
• Automathography Instructions Introduce your mathematical self to me. Tell me about the courses you have taken, what
• Calculus III Test 3 Sample Problem Answers/Solutions 1. Express the area of the surface (u, v) = u cos v, u sin v, 2v , with domain 0 u 1,
• Linear Algebra I Math 237-101
• MA 237-102 Linear Algebra I Test 3 --Take-Home Version Name: Due Wednesday, Apr 21, 1:25 pm.
• MA 237-102 Linear Algebra I Test 2 Solutions 3/12/10 1. Give explicit examples of 2 2 matrices as described
• MA 237-102 Linear Algebra I Test 1 Review 2/10/10 A subspace of a vector space V is a collection W of objects in V with the property
• Advanced Calculus II Math 335-501
• Calculus III Test 3 Solutions November 19, 2009 1. Use Green's theorem to compute
• Calculus III Test 3 Sample Problems 1. Express the area of the surface (u, v) = u cos v, u sin v, 2v , with domain 0 u 1,
• Calculus III Test 2 Solutions October 26, 2009 1. Let C be the curve r(t) = et sin(t)
• Calculus III Test 1 Solutions September 24, 2009 1. Compute the integral
• INTRODUCTION If C is a curve and f is a function defined at all points of C , then the integral of f over C
• Advanced Calculus I Prof. Josh Barnard Math 334-501
• Advanced Calculus I Test 2 Solutions November 9, 2009 1. [20 pts] Suppose f(x) = x2
• Test 1 Solutions Calculus II February 13, 2009 We use integration by parts, with u = x and dv = e-2x
• Topology II Math 543-101
• Math 125-109 MWF 10:15-11:05, ILB 360
• Test 1 Solutions Calculus I September 12, 2008 1. The graph of a function y = f(x) is shown below. Determine the following limits
• Contemporary Math/Stat Seminar Math/Stat 150-101
• Math 434/542-101 MW 3:00-4:15, ILB 360
• Calculus I Mini-test 2 Solutions July 3, 2008 1. Find the absolute maximum and minimum values of the function f(x) = (x2
• Test 1 Solutions Calculus I June 20, 2008
• Calculus III Math 227-101
• INTRODUCTION If S is a surface and f is a function defined at all points of S, then the integral of f over
• Calculus Mini-test 1 Solutions June 6, 2008 1. Find a parametrization of the line segment between the points (1, 3, 2) and (4, -1, 0).
• Calculus III Math 227-101
• INTEGRALS OVER SURFACES S An integral S
• INTRODUCTION If D is an object, and f is a function defined at all points of D, then the integral of f over D
• Test 3 Solutions Calculus III April 1, 2008
• Advanced Calculus II Math 335-501
• Mini-Test 2 Solutions Calculus II October 26, 2007
• Test 1 Solution Calculus II September 28, 2007
• Linear Algebra I Worksheet 6 Solutions July 12, 2007 1. Find the determinants of the following matrices
• Linear Algebra I Worksheet 5 Due July 6, 2007 Name: OUID
• Linear Algebra I Worksheet 2 Solutions June 13, 2007 1. (a) [3 pts] Show that the set of all vectors of the form
• Linear Algebra I Worksheet 1 Solutions June 8, 2007 1. [3 pts] Consider the following matrices
• Matrix Exponentials Suppose A is a square matrix. We then make the following definition
• Linear Algebra I Worksheet 9 Solutions April 10, 2007 1. [6 pts] Find the Fourier polynomial of degree 2 for sin2
• Linear Algebra I Worksheet 8 Solutions April 3, 2007 1. Let V be the vector space of continuous functions on [0, 1] and define an inner
• Linear Algebra I Worksheet 6 Due March 6, 2007 Name: OUID
• Linear Algebra I Worksheet 4 Solutions February 13, 2007 1. [3 pts] Do the following vectors span R4
• Week 6 worksheet solutions 1. Find the eigenvalues and corresponding eigenvectors for the matrix
• Week 5 worksheet solutions 1. Find the determinants of the following matrices (show your work)
• Test 1 Solutions July 5, 2006 1. Let L : P2 P2 be defined by L(at2
• Solutions to review problems for test one Chapter Three
• Week 3 worksheet solutions 1. Let L : P1 P2 be a linear transformation for which we know that
• Calculus IV Test 3 Solutions April 20, 2006 Name: 1. A wire in space traces out the curve described by r(t) = t2
• Calculus IV Test 2 Solutions March 9, 2006 1. Consider the following
• Calculus III Test 3 Solutions November 22, 2005 1. Sketch the traces of the surface described by the equation below. Each trace graph should have
• Information pertaining to Test III This test covers all of chapter 13, including the geometry and algebra of vectors; the dot product,
• Calculus III Test 2 Solutions October 25, 2005 1. (a) Use known series to find a Taylor series (centered at x = 0) for the following indefinite
• Calculus III Test 1 Solutions September 15, 2005 1. Sketch the curve traced out by the parameter in the following parametric equations
• Information pertaining to Test I The major topics to be covered on Test I are
• INTRODUCTION If D is an object, and f is a function defined at all points of D, then the integral of f over D
• Calculus IV Test 1 Solutions September 15, 2005 1. Suppose z = g(u, v, w), where u = u(x, y), v = v(x, y), and w = w(x, y). Draw a dependency
• Review information for Calculus III Test II. The test will cover sections 11.111.4 and 13.113.5. Here is a list of useful problems
• Calculus III Test 2 Solutions July 13, 2005 1. Consider the parametrized curve
• Review information for Calculus III Test III. The test will cover sections 13.613.7 and 14.114.4. Here is a list of useful problems
• Linear Algebra I Test 2 Solutions February 25, 2005 1. (a) Verify that the 2 1 matrices of the form
• Linear Algebra I Test 4 Review Coordinates
• Linear Algebra I Test 4 April 18, 2005 Suppose T = {t2
• Practice problems for Calculus I Test I. 1. Write the precise -definition of the following: lim
• Solutions to practice problems for Calculus I Test I. 1. Write the precise -definition of the following: lim
• Practice problems for Calculus I Test III. The test covers sections 3.9, 3.10, 4.1, 4.2, 4.3, 4.4, 4.5, 4.7.
• Linear Algebra I Instructor: Prof. Josh Barnard
• Practice problems for Linear Algebra Test I. b) Find AB c) Find 7A -2B
• Linear Algebra I Test 3 Solutions November 22, 2004 1. Suppose L: V W is a linear transformation, where the dimension of V is n and
• Name: Calculus II ID: April 17, 2009
• Test 3 Solutions Calculus I November 10, 2008 1. (a) Use Rolle's theorem to show that g(x) = x5
• Linear Algebra I Worksheet 7 Solutions March 13, 2007 1. [12 pts] Consider the subset S = {t2
• Calculus II Test 1 Solutions June 19, 2009 We let w = x2
• Calculus IV Test 2 Solutions October 13, 2005 1. Consider the following integral
• Notation: S = {v1, v2, v3} and S = {v1, v2, v3} bases for V ; T = {w1, w2} and T = {w1, w2} bases for W .
• Calculus II Math 126-104
• Information pertaining to Test I The major topics to be covered on Test I are
• MA 237-102 Linear Algebra I Test 1 Solutions 2/12/10 1. For the following matrix A, find a basis for the column space and for the nullspace
• SUPER-EXPONENTIAL 2-DIMENSIONAL DEHN FUNCTIONS JOSH BARNARD, NOEL BRADY, AND PALLAVI DANI
• Apr 29, 2011 Elementary Geometry Test 3 Solutions 0. Solve the equation y = ax+b
• Test 1 Solutions Advanced Calculus I September 26, 2007
• Math 2433-001 Calculus III
• Linear Algebra I Worksheet 8 Solutions Not Due 1. Consider the inner product space R2
• Calculus IV Test 1 Solutions February 14, 2006 1. Complete the definition: A function f(x, y) is continuous at (a, b) if
• SUPEREXPONENTIAL DISTORTION OF SUBGROUPS OF CAT(-1) JOSH BARNARD, NOEL BRADY, AND PALLAVI DANI
• Calculus III Test 1 Solutions June 23, 2005 1. Use known series to find Taylor series (centered at x = 0) for the following functions. Find at
• Linear Algebra I Worksheet 10 Solutions April 17, 2007 1. [3 pts] Suppose is an eigenvalue of the n n matrix A. Show that the set of
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• Calculus III Test 3 Solutions July 21, 2010 1. Use Stokes' theorem to compute
• Advanced Calculus II Test 2 Solutions 1. (a) Let be a continuous function on [a, b], and let be the function on
• Introduction to Bases A collection of vectors S = {v1, . . . , vn} is said to form a basis for a vector space
• Linear Algebra I Worksheet 3 Solutions February 6, 2007 1. [12 pts] Let L : R4
• Linear Algebra I Test 2 Solutions June 29, 2007 1. Suppose L : R3
• Abstract Algebra Math 413-501 Fall 2011
• Test 1 Review June 15, 2011 Definitions (be able to complete the definition)
• Finite Mathematics Math 110-104 Fall 2011
• Linear Algebra Test 3 Solutions July 14, 2011 1. Consider the matrix A =
• Linear Algebra Test 2 Solutions June 30, 2011 1. Verify the rank-nullity theorem for the following linear map by finding a basis for the
• 6/28/11 Precalculus Algebra Test 2 Solutions 1. Let f(x) = x -3 and g(x) =
• Test 3 Review Solutions July 12, 2011 1. Consider the linear map f : R3
• 6/13/11 Precalculus Algebra Test 1 Solutions 1. Consider the equation 6x -4y = -4. Is (2/3, 5/4) a solution? What about (1, 5/2)?
• Linear Algebra Test 1 Solutions June 17, 2011 1. Complete the definition: A function f :Rn
• 10/21/11 Finite Mathematics Test 2 Solutions 1. Each student at State University has a student I.D. number consisting of three digits 09
• 11/21/11 Finite Mathematics Test 3 Solutions 1. The following table shows the average monthly rainfall in Mobile in inches for the period
• Abstract Algebra Test 1 Solutions September 26, 2011 1. (i) State the Well-Ordering Principle and the Division Algorithm.
• Abstract Algebra Take-Home Test 3 Solutions 1. (i) Prove or disprove that Z Z is cyclic.
• Abstract Algebra Test 2 Solutions November 2, 2011 1. State and prove Lagrange's theorem; give full details. Use this result to prove that
• Presentation Instructions First choose a date during the semester to give your presentation by writing you name on the schedule in
• Abstract Algebra Take-Home Test 3 Solutions 1. (i) Prove or disprove that Z Z is cyclic.
• Test 1 Topics Natural Numbers: N = {1, 2, 3, . . .}
• BOUNDING SURFACE ACTIONS ON HYPERBOLIC SPACES JOSH BARNARD
• Abstract Algebra Math 413-501 Fall 2011
• Solutions to Test 2 Practice Questions 1. Show how to perform 74 -58 and 62 -35 using the equal additions method.
• Mathematics for Elementary Teachers I Math 201-501 Spring 2012
• Abstract Algebra Test 2 Solutions November 2, 2011 1. State and prove Lagrange's theorem; give full details. Use this result to prove that
• Abstract Algebra Test 1 Solutions September 26, 2011 1. (i) State the Well-Ordering Principle and the Division Algorithm.
• Test 2 Topics Mental Math: additive compensation, multiplicative compensation, equal additions
• Foundations of Mathematics Math 320-101 Spring 2012
• 2/16/2012 Foundations Test 1 Solutions 1. Suppose A and B are sets.
• 10/21/11 Finite Mathematics Test 2 Solutions 1. Each student at State University has a student I.D. number consisting of three digits 09
• Test 1 Practice Question Solutions 1. Consider the set A = -5,
• 11/21/11 Finite Mathematics Test 3 Solutions 1. The following table shows the average monthly rainfall in Mobile in inches for the period
• Finite Mathematics Math 110-104 Fall 2011
• 2/9/12 MA 201 Test 1 Solutions 1. Consider the inequality 2 < 5.