Bombarded by statistics, assailed by advertisers and advocates of all persuasions, the average person needs mathematics to make sense of the world. This course aims to give students the tools needed to critically examine the quantitative issues of our times. Students will learn the basics of logical reasoning, the use of graphs and algebra to create quantitative models, and the role of statistics and probability in analyzing data. We will apply these ideas to assess the quantitative claims raised in contemporary case studies commonly discussed in the media.
3 hr./wk.
Bombarded by statistics, assailed by advertisers and advocates of all persuasions, the average person needs mathematics to make sense of the world. This course aims to give students the tools needed to critically examine the quantitative issues of our times. Students will learn the basics of logical reasoning, the use of graphs and algebra to create quantitative models, and the role of statistics and probability in analyzing data. We will apply these ideas to assess the quantitative claims raised in contemporary case studies commonly discussed in the media.
4 hr./wk.
Descriptive statistics and frequency histograms; measures of location and dispersion; elementary probability; permutations and combinations; multiplication rule and conditional probability; Bayes' Theorem; independent events; random variables, expected values; applications to binomial, hypergeometric, uniform and normal distributions; the Central Limit Theorem; testing statistical hypotheses; correlation; linear regression and least squares.
Placement by the Department.
4 hr./wk.
Investigation of the basis for elementary operations in concrete situations, diagrams, and symbolic representation. Understanding of, and problem-solving in, the following areas: numerical operations, ratios and percents, linear and exponential growth in situations, formulas, and graphs; rate of change; geometry of measurement; units, dimension, and scaling.
Placement by the Department.
4 hr./wk.
Investigation of the basis for elementary operations in concrete situations, diagrams, and symbolic representation. Understanding of, and problem-solving in, the following areas: numerical operations, ratios and percents, linear and exponential growth in situations, formulas, and graphs; rate of change; mensurational geometry; units, dimension, and scaling.
4 hr./wk.
Problem solving, sets, operations with sets, functions, numerical systems with different bases, topics in number theory, probability and geometry. Includes writing exercises and collaborative work. This course is for potential education majors only.
A grade of C or higher in MATH 18000 or placement by the department.
4 hr./wk.
Sets, operations with sets, relations, functions, construction of numerical systems, numerical systems with different bases, topics in number theory, geometry. Required for Early Childhood Education majors.
4
Introduction to functions, rational expressions and their applications, rational exponents, conic sections, Gaussian elimination and determinants, nonlinear systems of equations, introductions to trigonometric functions.
Placement at college entry or by subsequent examination.
4 hr./wk.
Intervals, inequalities, operations on functions, inverse functions, graphing polynomial functions, exponential and logarithmic functions, trigonometric functions and formulas.
A grade of C or higher in MATH 19000 or placement by the department.
4 hr./wk.
Limits, continuity, derivatives, differentiation and its applications, differentials, definite and indefinite integrals.
A grade of C or higher in MATH 19500 or placement by the Department. Credit will be given for only one of the following courses: MATH 20100 (part of sequence MATH 20100, MATH 21200, MATH 21300).
4 hr./wk.
Techniques Introduction to integration and areas; application to solids of revolution and work; definition of exponential and logarithmic functions; integration of trigonometric, exponential and logarithmic functions, analytical and numerical methods of integration, improper and infinite integrals, infinite sequences and series,polar coordinates; parametric equations, vectors and the geometry of space, functions of several variables and partial differentiation representation of curves.
A grade of C or higher in
MATH 20100 or placement by the Department. After completion of MATH 20900, only 3 credits will be given for MATH 20200. (Part of sequence
MATH 20100, MATH 20200, MATH 20300.)
4 hr./wk.
Used for transfer credit.
Limits, derivatives, rules of differentiation, differentials, graph sketching, maximum and minimum problems, related rates, exponential and logarithmic functions, differential equations, anti-derivatives, area, volume, applications to economics.
A grade of C or higher in MATH 19500 or placement by the Department. Credit will be given for only one of the following courses: MATH 20100 or MATH 20500. (Recommended for Architecture and Economics majors.)
4 hr./wk.
Introduction to differential equations including numerical methods; qualitative analysis of solutions; phase plane analysis for systems; biological applications; analysis of univariate and bivariate data; regression and correlation; random variables; the normal, Poisson and binomial distributions; statistical inference. A spreadsheet program such as Excel is used throughout the course.
A grade of C or higher in MATH 20500 or placement by the Department. (Part of sequence MATH 20500, MATH 20900 for Biology majors.)
4 hr./wk.
Techniques of integration, improper integrals, infinite sequences and series, parametric equations, vectors and the geometry of space, functions of several variables and partial differentiation.
A grade of C or higher in
MATH 20100, or placement by the Department. (part of consequence
MATH 20100, MATH 21200, MATH 21300.)
4 hr./wk.
Applications of partial differentiation, vector-valued functions, multiple integrals, vector fields, line integrals, and theorems of Green, Stokes, and Gauss.
A grade of C or higher in Math 21200 or placement by the Department. (Part of sequence MATH 20100,
MATH 21200, MATH 21300.)
4 hr./wk.
Approval of Department Honors Advisor required.
Credit flexible but usually 3 credits per term.
This course explores the logical and foundational structures of mathematics, with an emphasis on understanding and writing proofs. Topics include set theory, logic, mathematical induction, relations and orders, functions, Cantor's theory of countability, and development of the real number system.
A grade of C or higher in MATH 20300 or
MATH 21300 or placement by the Department.
3 hr./wk.
A program of independent study under the direction of a member of the Department with the approval of the Assistant Chair.
Credit may be from 1-4 credits, as determined before registration by the instructor with the approval of the Assistant Chair.
Independent Study. This course can be repeated at most 3 times for a maximum of 3 credits total.
1 hr./wk.
Independent Study. This course can be repeated at most 3 times for a maximum of 6 credits total.
2 hr./wk.
Independent Study. This course can be repeated at most 3 times for a maximum of 9 credits total.
3 hr./wk.
Independent Study. This course can be repeated at most 3 times for a maximum of 12 credits total.
4 hr./wk.
Topics in mathematics. This course can be repeated at most 3 times for a maximum of 9 credits total.
Credits
Credits and hours will be determined by the instructor and the department, with a maximum of 4 credits per course.
Departmental consent required.
Sequences, properties of continuous functions, derivatives and differentials, functions defined by series, integrability and integrals, convergence of function sequences.
Grade of C or higher in
MATH 30800 or placement by the Department.
4 hr./wk.
In this course, students will examine the topics in the high school curriculum through the lens of advanced college level mathematics courses (including Calculus, linear algebra, modern geometry, real analysis, abstract algebra and number theory). Connections between the mathematics taught in high school and college will be stressed, and students will also develop increased understanding of the connections between algebraic, geometric, and logical thinking. Students will be asked to interpret mathematical ideas in contexts and will be expected to communicate effectively about connections they see, representations they create and generalizations they make.
Calculus, Linear Algebra and at least one proof-intensive course such as Abstract Algebra, Number Theory, Logic or Real Analysis
3 hr./wk.
Sequences, continuity, compactness, completeness, differentiation and integration in Rn, implicit and inverse function theorems, line and surface integrals, theorems of Green, Gauss and Stokes.
4 hr./wk.
Solution of equations by iteration techniques; Lagrange and Newton interpolation, Neville's method, divided differences, cubic splines; numerical integration, Romberg integration; systems of linear equations and pivoting techniques; Runge-Kutta methods for initial value problems.
3 hr./wk.
Historical development of mathematical ideas and methods in geometry, theory of numbers, algebra, and analysis.
3 hr./wk.
Divisibility, primes, fundamental theorem of arithmetic, congruences, number theory from an algebraic viewpoint, quadratic reciprocity, number theoretic functions, diophantine equations.
A grade of C or higher in
MATH 30800 or placement by the Department.
3 hr./wk.
Vector spaces, basis and dimension, matrices, linear transformations, determinants, solution of systems of linear equations, eigenvalues, and eigenvectors.
MATH 21200, or MATH 20300, or departmental permission.
3 hr./wk.
Sets, mappings, rings, isomorphisms, integral domains, properties of integers, fields, rational numbers, complex numbers, polynomials, groups.
Grades of C or higher in
MATH 30800 and
MATH 34600 or placement by the Department. Partial credit may be given for
MATH 44900 after completion of
MATH 34700. Recommended for prospective teachers and others who want a basic course in abstract algebra.
Spring only
4 hr./wk.
Logical deficiencies in Euclidean geometry, Euclid's parallel postulate, introduction to non-Euclidean geometry, the logical consistency of the non-Euclidean geometries, Hilbert's Axioms.
A grade of C or higher in
MATH 30800 or placement by the Department.
Fall only
3 hr./wk.
The three problems of combinatorics (existence, counting, optimization), basic counting rules, graph theory, generating functions, principles of inclusion and exclusion, pigeonhole principle, selected additional topics.
A grade of C or higher in MATH 21200 or MATH 20300.
4 hr./wk.
Calculus, linear algebra, elements and applications of probability theory are examined through programming. Topics selected from symbolic and numerical problems in analysis; matrices, linear mappings, eigenvalues and applications; queueing theory; random numbers and simulations; graphics.
3 hr./wk.
Permutations and combinations, conditional probability, independent events, random variables, probability distributions and densities, expectation, moments, moment generating functions, functions of random variables, Central Limit Theorem, sampling, confidence intervals.
A grade of C or higher in MATH 20300 or
MATH 21300.
4 hr./wk.
The gamma, chi-square, T, F, and bivariate normal distributions; Central Limit Theorem; confidence intervals and tests of hypothesis; the Neymen-Pearson Theorem; likelihood ratio test; estimation; sufficiency, unbiasedness, completeness; the Rao-Blackwell Theorem; the Rao-Cramer inequality; the method of maximum likelihood; the chi-square test; introduction to the analysis of variance and regression.
A grade of C or higher in
MATH 37500 or placement by the Department.
Spring only
4 hr./wk.
Introduction to SPSS; Introduction to Matlab; modeling and construction of random variables; study of Z, chi-square, t, and F distributions; study of order statistics; determination of p-values; understanding of hypothesis testing and confidence intervals; organization of data; various descriptive statistics such as measures of variability and location; categorical variables; sampling distributions with SPSS; statistical inference, linear regression models; regression analysis; analysis of variance; the jackknife methodology of computer based estimation, discriminant analysis, factor analysis, cluster analysis.
3 hr./wk.
Definitions of options and exotic options on stocks, interests rates and indices; binomial trees; volatility and methods to estimate volatility; continuous models and Black-Scholes; hedging; bond models and interest rate options; spreadsheet methods and computational methods including difference methods and Monte Carlo simulations.
A grade of C or higher in MATH 20200 or
MATH 21200 or placement by the Department.
Fall only
3 hr./wk.
Review of discrete time models and binomial trees. Cox, Ross, Rubinstein approach to the Black-Scholes model; Black-Scholes equation and option pricing formulae; Brownian motion and stochastic differential equations; Ito's calculus and Ito's lemma; stopping times; the heat equation; option pricing and the heat equation; numerical solution of parabolic partial differential equations; interest rate models; simulation and financial models.
A grade of C or higher in
MATH 38100 or placement by the Department.
Spring only
3 hr./wk.
First order equations; higher order linear equations with constant coefficients, undetermined coefficients, variation of parameters, applications; Euler's equation, series solutions, special functions; linear systems; elementary partial differential equations and separation of variables; Fourier series.
A grade of C or higher in
MATH 21300 or Math 20300, or departmental permission.
3 hr./wk
Matrix theory, linear equations, Gauss elimination, determinants, eigenvalue problems and first order systems of ordinary differential equations, vector field theory, theorems of Green, Stokes, and Gauss.
A grade of C or higher in MATH 20300 or placement by the Department. (After completion of
MATH 34600 only 2 credits will be given for
MATH 39200.)
3 hr./wk.
Fourier series, the Fourier transform, discrete fourier analysis, wavelet analysis, multiresolution analysis, computer applications using Matlab.
A grade of C or higher in
MATH 39100 or placement by the Department.
4 hr./wk.
Algebra and geometry of complex numbers; elementary transcendental and algebraic functions and their conformal mappings; Cauchy-Riemann equations, contour integrals, Cauchy integral formula, analyticity and power series, the residue theorem and applications.
4 hr./wk.
Topics to be chosen from graduate mathematics and related fields. This course can be repeated at most 2 times for a maximum of 12 credits total.
Department consent.
4 hr./wk.
Cauchy-Riemann equations, conformal mapping, elementary, entire, meromorphic, multiple-valued functions, Cauchy integral theorems, series expansion.
A grade of C or higher in
MATH 32404 or placement by the Department.
4 hr./wk.
Lebesgue measure and integration on the real line, differentiation of real functions and the relation with integration, classical Lp spaces.
A grade of C or higher in
MATH 32300 or permission of the instructor.
4 hr./wk.
First order equations, shock waves; classification and canonical forms of higher order equations, characteristics, the Cauchy problem for the wave equation: Huygens' principle; the heat equation; Laplace's equation; the Dirichlet and Neuman problems; harmonic functions; eigenvalue expansions; Green's functions.
4 hr./wk.
Axioms of Zermelo-Fraenkel set theory; relations, functions, equivalences and orderings; cardinal numbers and cardinal arithmetic; well-ordered sets; ordinal numbers, transfinite induction and recursion; the Axiom of Choice and the Continuum Hypothesis.
A grade of C or higher in
MATH 32300 or permission of the instructor.
4 hr./wk.
The propositional calculus, the sentential calculus, normal forms, first order theories, consistency, categoricity, decidability, Godel's incompleteness theorem, the Loewenheim-Skolem theorem.
A grade of C or higher in
MATH 32300 or permission of the instructor.
4 hr./wk.
Dynamical systems in one and more dimensions, symbolic dynamics, chaos theory, hyperbolicity, stable manifolds, complex dynamics.
C or better om
MATH 32404 or permission of the instructor.
4 hr./wk.
Linear systems, matrix decompositions, inner product spaces, self-adjoint transformations, spectral theory, discrete Fourier Transforms.
C or better in
MATH 34600 or permission of the instructor.
4 hr./wk.
Fall only
4 hr./wk.
The theory of curves and surfaces in three-dimensional space: frames, fundamental forms, geodesics; curvature of surfaces; surface area; surfaces with boundary, the Gauss-Bonnet Theorem; introduction to Riemannian metrics.
4 hr./wk.
A course in general topology. Sets of points on the real line and in general abstract spaces, relations between sets of points and between a set and the space containing it, operations with sets, open sets, countability, compactness, connectedness, maps, continuity, metric spaces, general topological spaces.
A grade of C or higher in
MATH 32404 or placement by the Department.
4 hr./wk.
A first course in algebraic number theory which assumes some abstract algebra. Topics include: unique factorization in the integers and Euclidean domains, structure of the groups Z/mZ and their multiplicative units, quadratic residues and quadratic reciprocity, algebraic number fields, finite fields.
Grade of C or better in
MATH 34700 or departmental permission.
4 hr./wk.
Problems from industry, mathematical models, process of mathematical abstraction, problem-solving techniques, application of solutions.
3 hr./wk.
Permutations, combinations, generating functions and recurrence relations, inclusion and exclusion, applications to matching theory, linear and dynamic programming, Polya's theory of counting, introduction to graph theory and coloring theory.
4 hr./wk.
Special topics in probability such as stochastic processes, Markov chains.
4 hr./wk.
The multivariate normal distribution, multiple and partial correlation, regression and least squares, the analysis of variance.
Fall only
4 hr./wk.
Topics to be chosen from the areas of algebra, analysis, topology, geometry, and logic. This course can be repeated at most 3 times for a maximum of 12 credits total.
Departmental consent.
4 hr./wk.
Topics to be chosen from the areas of probability, statistics, game theory, combinatorial analysis, etc. This course can be repeated at most 2 times for a maximum of 12 credits total.
Departmental consent.
4 hr./wk.