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Undergraduate

MATH 0260
Intermediate Algebra
Review of the real number system; linear equations, and inequalities in one and two variables; functions; systems of linear equations; exponents, polynomials and polynomial functions; factoring; rational expressions and functions; roots, radicals and root functions; quadratic equations, inequalities and functions.
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MATH 1200
College Algebra
Brief review of algebraic essentials, graphs, functions and their graphs, linear and quadratic functions, polynomial and rational functions, exponential and logarithmic functions, systems of linear equations. Intended for students needing more preparation before taking MATH 1320 or MATH 1400.
Prerequisite(s): 2 years of high school algebra or a grade of C- or better in MATH 0250 or MATH 0260.
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MATH 1220
Finite Mathematics
Brief review of algebraic essentials, graphs, functions and their graphs, linear and quadratic functions, polynomial and rational functions, exponential and logarithmic functions, systems of linear equations. Intended for students needing more preparation before taking MATH 1320 or MATH 1400.
Prerequisite(s): 2 years of high school algebra or a grade of C- or better in MATH 0250 or MATH 0260.
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MATH 1240
Mathematics and the Art of M.C. Escher
An inquiry course open to all undergraduates. The art of M.C. Escher is used to explore topics in geometry such as symmetry, tessellations, wallpaper patterns, the geometry of the sphere and hyperbolic geometry. Taught in a computer classroom.
Prerequisite(s): 3.5 years of high school mathematics or a grade of C- or better in MATH 1200.
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MATH 1250
Math Thinking in Real World
An inquiry course open to all undergraduates. In this course, aimed at students in the humanities and social sciences, we study some of the greatest ideas of mathematics that are often hidden from view in lower division courses. Topics selected from number theory, the infinite, geometry, topology, chaos and fractals, and probability. Taught in a computer classroom.
Prerequisite(s): Three years of high school mathematics or a grade of C- or better in MATH 1200. (An understanding beyond MATH 0260 is needed.)
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MATH 1320
Survey of Calculus
Linear equations and graphs; functions and graphs; limits; the derivative; rules of differentiation; curve sketching and optimization; antiderivatives; the definite integral; multivariable calculus and partial derivatives.
Prerequisite(s): 3.5 years of high school mathematics or a grade of C- or better in MATH 1200.
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MATH 1400
Pre-Calculus
Functions, graphs and models; modeling with linear and quadratic functions; polynomial and rational functions; modeling with exponential and logarithmic functions; trigonometric functions; trigonometric identities and conditional equations; additional topics in trigonometry; additional topics in analytic geometry; parametric equations.
Prerequisite(s): 3.5 years of high school mathematics or a grade of C- or better in MATH 1200.
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MATH 1510
Calculus I
Functions; continuity; limits; the derivative; differentiation from graphical, numerical and analytical viewpoints; optimization and modeling; rates and related rates; the definite integral; antiderivatives from graphical, numerical and analytical viewpoints.
Prerequisite(s): 4 years of high school mathematics or a grade of C- or better in MATH 1400.
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MATH 1520
Calculus II
Symbolic and numerical techniques of integration, improper integrals, applications using the definite integral, sequences and series, power series, Taylor series, differential equations.
Prerequisite(s): A grade of C- or better in MATH 1510.
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MATH 1650
Cryptology
An inquiry course open to all undergraduates. Aimed at students who require a course at the level of calculus or higher and who are interested in the mathematical basis for cryptology systems. Topics include permutation based codes, block cipher schemes and public key encryption.
Prerequisite(s): 4 years of high school mathematics.
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MATH 1660
Discrete Mathematics
Concepts of discrete mathematics used in computer science; sets, sequences, strings, symbolic logic, proofs, mathematical induction, sums and products, number systems, algorithms, complexity, graph theory, finite state machines.
Prerequisite(s): A grade of 'C-' or better in MATH 1200 or equivalent.
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MATH 2530
Calculus III
Three-dimensional analytic geometry, vector-valued functions, partial differentiation, multiple integration, and line integrals. Fall and Spring semesters.
Prerequisite(s): A grade of 'C-' or better in MATH 1520.
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MATH 2660
Principles of Mathematics
Introduction to the basic techniques of writing proofs and to fundamental ideas used throughout mathematics. Topics covered include formal logic, proof by contradiction, set theory, mathematical induction and recursion, relations and congruence, functions.
Prerequisite(s): A grade of 'C-' or better in MATH 1510.
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MATH 2690
Mathematical Problem Solving
Intended primarily to train students for the William Lowell Putnam Mathematical Competition, this course covers a range of ingenious techniques for solving mathematics problems cutting across the entire undergraduate spectrum, including pre-calculus, calculus, combinatorics, probability, inequalities. Coverage tailored to students' interests. May be repeated for credit.
Prerequisite(s): None
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MATH 3110
Linear Algebra for Engineers
Systems of linear equations, matrices, linear programming, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, linear transformations, and numerical methods. Credit not given for both MATH 3110 and MATH 3120. Does not satisfy any requirements for the mathematics major.
Prerequisite(s): A grade of 'C-' or better in MATH 1520 and a knowledge of vectors.
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MATH 3120
Introduction to Linear Algebra
Matrices, row operations with matrices, determinants, systems of linear equations, vector spaces, linear transformations, inner products, eigenvalues and eigenvectors. Credit not given for both MATH 3110 and MATH 3120.
Prerequisite(s): MATH 2530 and MATH 2660
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MATH 3240
Numerical Analysis
Review of calculus; root finding, nonlinear systems, interpolation and approximation; numerical differentiation and integration.
Prerequisite(s): MATH 1520
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MATH 3270
Advanced Mathematics for Engineers
Vector algebra; matrix algebra; systems of linear equations; eigenvalues and eigenvectors; systems of differential equations; vector differential calculus; divergence, gradient and curl; vector integral calculus; integral theorems; Fourier series with applications to partial differential equations.
Prerequisite(s): MATH 3550
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MATH 3550
Differential Equations
Solution of ordinary differential equations, higher order linear equations, constant coefficient equations, systems of first order equations, linear systems, equilibrium of nonlinear systems, Laplace transformations.
Prerequisite(s): MATH 2530
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MATH 3600
Combinatorics
Advanced counting methods: permutations and combinations, generalized permutations and combinations, recurrence relations, generating functions; algorithms: graphs and digraphs, graph algorithms: minimum-cost spanning trees, shortest path, network flows; depth first and breadth-first searches; combinational algorithms: resource scheduling, bin-packing: algorithmic analysis and NP completeness.
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MATH 3760
Financial Mathematics
This course covers the theory of interest material for the Financial Mathematics exam of the Society of Actuaries. Time permitting, supplemental material covering financial derivatives will be discussed.
Prerequisite(s): MATH 1520
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MATH 3800
Elementary Theory of Probability
Counting theory; axiomatic probability, random variables, expectation, limit theorems. Applications of the theory of probability to a variety of practical problems. Credit not given toward the math major or minors for both MATH 3800 and either MATH 3810 or MATH 4800.
Prerequisite(s): MATH 2530
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MATH 3910
Internship
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MATH 4050
History of Mathematics
The development of several important branches of mathematics, including numeration and computation, algebra, non-Euclidean geometry, and calculus.
Prerequisite(s): MATH 1520
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MATH 4110
Introduction to Abstract Algebra
Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields.
Prerequisite(s): MATH 3120
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MATH 4120
Linear Algebra
Advanced linear algebra, including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators and spectral theory.
Prerequisite(s): MATH 4110
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MATH 4150
Number Theory
Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year.
Prerequisite(s): MATH 4110
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MATH 4210
Introduction to Analysis
Real number system, functions, sequences, limits, continuity, differentiation, integration and series.
Prerequisite(s): MATH 2530
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MATH 4220
Metric Spaces
Set theory, metric spaces, completeness, compactness, connected sets, category.
Prerequisite(s): MATH 4210
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MATH 4230
Multivariable Analysis
Introduction to analysis in multidimensional Euclidean space. Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multivariable Calculus (Green's Theorem, Stokes' Theorem, Divergence Theorem).
Prerequisite(s): MATH 4210
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MATH 4310
Introduction to Complex Variables
Complex number system and its operations, limits and sequences, continuous functions and their properties, derivatives, conformal representation, curvilinear and complex integration, Cauchy integral theorems, power series and singularities.
Prerequisite(s): MATH 2530
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MATH 4320
Complex Variables II
This course is a continuation of MATH 4310. Topics covered include series, residues and poles, conformal mapping, integral formulas, analytic continuation, and Riemann surfaces.
Prerequisite(s): MATH 4310
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MATH 4360
Geometric Topology
An introduction to the geometry and topology of surfaces and three dimensional spaces. Topics covered Include Euclidean, spherical and hyperbolic geometry, topology of surfaces, knot theory, and the fundamental group.
Prerequisite(s): MATH 4310
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MATH 4410
Foundations of Geometry
Historical background of the study of Euclidean geometry; development of two-dimensional Euclidean geometry from a selected set of postulates.
Prerequisite(s): MATH 1510
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MATH 4430
Non-Euclidean Geometry
The rise and development of the non-Euclidean geometries with intensive study of plane hyperbolic geometry.
Prerequisite(s): MATH 1510
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MATH 4480
Differential Geometry
Classical theory of smooth curves and surfaces in 3-space. Curvature and torsion of space curves, Gaussian curvature of surfaces, the Theorem Egregium of Gauss.
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MATH 4550
Nonlinear Dynamics and Chaos
Bifurcation in one-dimensional flows. Two-dimensional flows, fixed points and linearization, conservative systems, index theory, limit cycles. Poincare-Bendixson theory, bifurcations. Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors.
Prerequisite(s): MATH 3550
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MATH 4570
Partial Differential Equations
Fourier series, Fourier Integrals, the heat equation, Sturm-Liouville problems, the wave equation, the potential equation, problems in several dimensions, Laplace transforms numerical methods.
Prerequisite(s): MATH 3550
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MATH 4630
Graph Theory
Basic definitions and concepts, undirected graphs (trees and graphs with cycles), directed graphs, and operation on graphs, Euler's formula, and surfaces.
Prerequisite(s): MATH 2530
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MATH 4650
Cryptography
Classical cryptographic systems, public key cryptography, symmetric block ciphers, implementation issues. Related and supporting mathematical concepts and structures.
Prerequisite(s): MATH 1520
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Graduate

MATH 5011
Introduction to Abstract Algebra
Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields.
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MATH 5012
Linear Algebra
Advanced linear algebra including linear transformations and duality, elementary canonical forms, rational and Jordan forms, inner product spaces, unitary operators, normal operators, and spectral theory.
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MATH 5015
Number Theory
Introduction to algebraic number theory. Topics will include primes, Chinese remainder theorem, Diophantine equations, algebraic numbers and quadratic residues. Additional topics will vary from year to year.
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MATH 5021
Introduction to Analysis
Real number system, functions, sequences, limits, continuity, differentiation, integration and series.
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MATH 5022
Metric Spaces
Set theory, real line, separation properties, compactness, metric spaces, metrization.
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MATH 5023
Multivariable Analysis
Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multi-variable Calculus (Green's Theorem, Stokes Theorem, Divergence Theorem).
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MATH 5080
Probability Theory
Axioms of probability, conditional probability. Discrete and continuous random variables, expectation, jointly defined random variables. Transformations of random variables and limit theorems. Theory and applications, taught using statistical software.
Prerequisite(s): STAT 3850, (MATH 2660 or MATH 1660), and MATH 2530
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MATH 5110
Algebra I
Simple properties of groups, groups of transformations, subgroups, homomorphisms and isomorphisms, theorems of Schreier and Jordan-Hölder, mappings into a group, rings, integral domains, fields, polynomials, direct sums and modules.
Prerequisite(s): MATH 4120, MATH 4150, MATH 5102 or MATH 5105.
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MATH 5120
Algebra II
Rings, fields, bases and degrees of extension fields, transcendental elements, normal fields and their structures. Galois theory, finite fields; solutions of equations by radicals, general equations of degree n.
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MATH 5210
Real Analysis
The topology of the reals, Lebesgue and Borel measurable functions, properties of the Lebesgue integral, differential of the integral.
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MATH 5220
Complex Analysis
Holomorphic and Harmonic functions and power series expansions. Complex integration. Cauchy's theorem and applications. Laurent series, singularities, Runge's theorem, and the calculus of residues. Additional topics may include Analytic continuation, Riemann surfaces, and conformal mapping.
Prerequisite(s): MATH 5210 and MATH 5310. Recommended: MATH 4310.
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MATH 5230
Functional Analysis
Banach and Hilbert spaces. Linear functions and linear operators. Dual spaces, weak and weak topologies. Hahn-Banach, Closed Graph and Open Mapping Theorems. Topological Vector spaces.
Prerequisite(s): MATH 5210 and MATH 5310
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MATH 5240
Harmonic Analysis
Fourier Series on the circle, Convergence of Fourier series, Conjugate and maximal functions, Interpolation of Linear Operators, Lacunary Sequences, Fourier Transform on the line, Fourier transform on locally compact Abelian groups.
Prerequisite(s): MATH-5210. Recommended: MATH-5310.
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MATH 5310
General Topology I
Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces.
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MATH 5320
General Topology II
Compact surfaces, fundamental groups, force groups and free products, Seifert-van Kampen theorem, covering spaces.
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MATH 5930
Special Topics in Mathematics
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MATH 6310
Algebraic Topology
Homotopy theory, homology theory, exact sequences, Mayer-Vietoris sequences, degrees of maps, cohomology, Künneth formula, cup and cap products, applications to manifolds including Poincare-Lefshetz duality.
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MATH 6410
Differential Geometry I
The theory of differentiable manifolds, topological manifolds, differential calculus of several variables, smooth manifolds and submanifolds, vector fields and ordinary differential equations, tensor fields, integration and De Rham cohomology.
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MATH 6420
Differential Geometry II
Continuation of MATH 6410.
Prerequisite(s): MATH 6410
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Statistics

STAT 1100
Introduction to Statistics
Basic descriptive and inferential statistics. Emphasis on becoming a smart consumer of statistics . Will include the study of examples of statistics in the medical news. Credit not given for MATH 1300 or MATH 1260 or DSCI 2070 and STAT 1100.
Prerequisite(s): Two years of High School math or grade of C- or better in MATH 0260: Intermediate Algebra.
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STAT 1260 / MATH 1260
Statistics Including Sports and Politics
An inquiry course open to all undergraduates. Producing data through the use of samples and experiments; organizing data through graphs and numbers that describe the distribution of the data of one variable or the relationship between two variables; probability; statistical inference including confidence intervals and tests of significance.
Prerequisite(s): 3.5 years of high school mathematics or a grade of C- or better in MATH 1200.
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STAT 1300 / MATH 1300
Elementary Statistics with Computers
Data production and analysis; probability basics, distributions; sampling, estimation with confidence intervals, hypothesis testing, t-test; correlation and regression; crosstabulations and chi-square. Students learn to use a statistical package such as SPSS. Credit not given for MATH 1300 and any of the following: STAT 1300 or OPM 2070.
Prerequisite(s): MATH 1200 or equivalent.
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STAT 3850 / MATH 3850
Foundation of Statistics
Descriptive statistics, probability distributions, random variables, expectation, independence, hypothesis testing, confidence intervals, regression and ANOVA. Applications and theory. Taught using statistical software.
Prerequisite(s): MATH 1520.
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STAT 3910
Internship
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STAT 4800 / MATH 4800
Probability Theory
Axioms of probability, conditional probability. Discrete and continuous random variables, expectation, jointly defined random variables. Transformations of random variables and limit theorems. Theory and applications, taught using statistical software. Credit not given toward the math major or minors for both MATH 3800 and MATH 4800.
Prerequisite(s): STAT 3850, MATH 2530 and MATH 1660 or MATH 2660.
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STAT 4840 / MATH 4840
Time Series
Applied time series. Topics include exploratory data analysis, regression, ARIMA. Spectral analysis, statespace models. Theory and applications, taught using statistical software.
Prerequisite(s): STAT 3850
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STAT 4850 / MATH 4850
Mathematical Statistics
Theory of estimators, sampling distributions, hypothesis testing, confidence intervals, regression, bootstrapping, and resampling. Theory and applications, taught using statistical software.
Prerequisite(s): STAT 4800
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STAT 4860 / MATH 4860
Statistical Models
Poisson processes, Markov chains, hidden Markov models, continuous time Markov chains, queuing theory. Theory and applications, taught with statistical software.
Prerequisite(s): STAT 4800
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STAT 4870 / MATH 4870
Applied Regression
Linear regression, model selection, nonparametric regression, classification and graphical models. Theory and applications using statistical software.
Prerequisite(s): STAT 3850 and MATH 3110 or MATH 3120
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STAT 4880 / MATH 4880
Bayesian Statistics and Statistical Computing
This course introduces Bayesian statistical methods and statistical computing techniques using statistical computing software. Topics include Bayesian models, Markov chain Monte Carlo, hierarchical modeling, model comparison and regression models.
Prerequisite(s): STAT 3850
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