MATH 201. Multivariable Calculus.

Sample Syllabus Satisfies Pathways MQR Requirement

4 hr.; 4 cr. Prereq.: MATH 143 or 152.

A continuation of the work of MATH 143 or 152. The topics include polar coordinates, vectors, solid analytic geometry, vector valued functions, double and triple integrals, functions of several variables, partial derivatives. Wherever possible, applications are made to problems of geometry and physics. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

MATH 202. Advanced Calculus.

Sample Syllabus Satisfies Pathways MQR Requirement

4 hr.; 4 cr. Prereq.: MATH 201 and either MATH 231 or 237, or permission of the chair.

Vector-valued functions, higher-order derivatives, maxima and minima of functions of several variables, integrals over paths and surfaces, vector analysis.

MATH 205. Mathematical Problem Solving.

⚠ This course does not count toward a pure, applied, or DSS math major.

3 hr.; 3 cr. Prereq. or coreq.: one year of college mathematics.

This course presents techniques and develops skills for analyzing and solving problems mathematically and for proving mathematical theorems. Students will learn to organize, extend, and apply the mathematics they know and, as necessary, will be exposed to new ideas in areas such as geometry, number theory, algebra, combinatorics, and graph theory. Not open to students who are taking or who have received credit for MATH 505.

MATH 209. Elementary Set Theory.

3 hr.; 3 cr. Prereq.: MATH 122 or the equivalent.

Basic axioms of set theory, algebra of sets, relations and functions, orders, countable and uncountable sets, and additional topics at the discretion of the instructor. The course will introduce some basic proof techniques, with no background in proof-writing assumed. Not open to students who are taking or have received credit for MATH 509 or 609.

MATH 218. Mathematical Problem Solving.

⚠ This course does not count toward a pure, applied, or DSS math major.

3 hr.; 3 cr. Prereq.: one course in linear algebra.

A course in advanced Euclidean geometry for current and prospective mathematics teachers that will provide mathematical background for teaching geometry in secondary schools. The course will focus on definitions, theorems, existence proofs, and constructions. Not open to students who are taking or who have received credit for MATH 518.

MATH 220. Discrete Mathematics.

3 hr.; 3 cr. Prereq.: One semester of calculus.

Discrete structures including sets, relations, and functions. Enumeration. Propositional and predicate logic. Proof techniques. Graphs, trees, and networks. Not open to students who are taking or have received credit for MATH 120.

MATH 223. Differential Equations with Numerical Methods I.

3 hr.; 3 cr. Prereq.: MATH 201 and 231.

First order linear, separable, and exact equations; second order linear equations; series solutions; existence and uniqueness theorem; numerical solutions; applications.

MATH 224. Differential Equations with Numerical Methods II.

3 hr.; 3 cr. Prereq.: MATH 223, and either MATH 231 or 237.

Linear systems of equations; stability of linear systems, orbits, phase portraits, periodic solutions, stability; boundary value problems; applications.

MATH 231. Linear Algebra I.

Satisfies Pathways MQR Requirement

4 hr.; 4 cr. Prereq.: Math 141 or 151.

An introduction to linear algebra with emphasis on techniques and applications. Topics to be covered include solutions of systems of linear equations, vector spaces, bases and dimension, linear transformations, matrix algebra, determinants, eigenvalues, and inner products. Not open to students who are enrolled in or who have completed MATH 237. Students who fail or withdraw from this course multiple times may be prohibited from majoring in the sciences or mathematics; see the bulletin language for your major.

MATH 232. Linear Algebra II.

3 hr.; 3 cr. Prereq.: MATH 231.

A second course in linear algebra. Topics include a continuation of matrices and linear transformations, canonical forms, invariants, equivalence relations, similarity of matrices, eigenvalues and eigenvectors, orthogonal transformations and rigid motions, quadratic forms, bilinear maps, symmetric matrices, reduction of a real quadratic form and applications to conic sections and quadric surfaces. Not open except by permission of the chair to students who are enrolled in or who have completed MATH 237.

MATH 241. Introduction to Probability and Mathematical Statistics.

Satisfies Pathways MQR Requirement

3 hr.; 3 cr. Prereq.or coreq.: MATH 143 or 152.

An introduction to the basic concepts and techniques of probability and statistics with an emphasis on applications. Topics to be covered include the axioms of probability, combinatorial methods, conditional probability, discrete and continuous random variables and distributions, expectations, confidence interval estimations, and tests of hypotheses using the normal, t- and chi-square distributions. Students taking this course may not subsequently receive credit for MATH 114, except by permission of the chair. Not open to students who are taking or have received credit for MATH 611.

MATH 242. Methods of Mathematical Statistics.

Sample Syllabus

3 hr.; 3 cr. Prereq.: MATH 241.

A study of those methods of mathematical statistics that are most frequently used in the natural and social sciences, as well as actuarial science. Topics include estimation testing of statistical hypotheses, nonparametric tests, analysis of variance, correlation and regression analysis, and other methods of statistical analysis.

MATH 245. Mathematical Models.

3 hr.; 3 cr. Prereq.: MATH 132 or 142 or 152, and permission of the instructor.

Construction, analysis, and assessment of mathematical models as they arise in the physical, biological, and social sciences. Specific topics to be announced in advance. May be repeated for credit with permission of the chair.

MATH 247. Linear Programming and Game Theory.

Sample Syllabus

3 hr.; 3 cr. Prereq.: MATH 231 or 237.

Methods for handling optimization problems that arise in management, engineering, physical sciences, and social sciences. Topics include convex geometry, the simplex algorithm, duality theory, and the Von Neumann minimax theorem of game theory.

MATH 248. Nonlinear Programming.

3 hr.; 3 cr. Prereq.: MATH 201 and either MATH 231 or 237.

Iterative methods for solving nonlinear optimization problems; techniques for handling problems with and without constraints; termination criteria and convergence analysis.

MATH 250. Mathematical Computing.

3 hr.; 3 cr. Prereq.: MATH 201 or MATH 231.

Introduction to a mathematical programming language such as Mathematica, Maple, MATLAB, or Sage. Students will learn algorithmic thinking and apply these ideas to explore problems arising in various areas of mathematics. No prior experience in programming is necessary.

MATH 255. Introduction to Game Theory.

⚠ This course does not count toward a pure or DSS math major.

3 hr.; 3 cr. Prereq.: One of the following: MATH 120, 142, 152, 209, 220, or 509.

Elements of mathematics of game theory. Foundational material, combinatorial games, zero and non-zero sum games. Two-player matrix games, pure and mixed strategies, pay-offs, equilibrium pairs. This is a proof-based course with an emphasis on examples and applications, especially in economics. Not open to students who are taking or who have received credit for MATH 555.

MATH 271. Actuarial Mathematics I: Preparation for Exam P, the Actuarial Society examination on Probability

⚠ This course does not count toward a pure, applied, or DSS math major.

[First of two courses]. 1 hr.; 1 cr. Prereq.: MATH 241 (or MATH 611). Coreq.: MATH 201.

This course covers probability and probability-based actuarial mathematics required for the Exam P examination of the Society of Actuaries.

MATH 272. Actuarial Mathematics II: Preparation for Exam P, the Actuarial Society examination on Probability

⚠ This course does not count toward a pure, applied, or DSS math major.

[Second of two courses]. 1 hr.; 1 cr. Prereq.: MATH 241 (or MATH 611), and MATH 201.
Coreq.: At least one of MATH 242, 621, and 633, where MATH 633 is probably the most efficient.

This course covers probability and probability-based actuarial mathematics required for the Exam P examination of the Society of Actuaries. MATH 272 focuses on problems similar to those covered in MATH 271, but with an increased emphasis on MATH 201 topics, such as double integrals and functions of two or more variables.

MATH 290. Studies in Mathematics.

Prereq.: Permission of the chair.

Topic announced in advance. May be repeated for credit if topic is different.

MATH 301. Abstract Algebra I.  (Previously MATH 333)

4 hr.; 4 cr. Prereq.: MATH 231 or the equivalent.

Theory of groups, including cyclic and permutation groups, homomorphisms, normal subgroups and quotient groups. Theory of rings, including integral domains and polynomial rings. Additional topics may be discussed. Not open to students who are taking or who have received credit for MATH 601 or 702.

MATH 302. Abstract Algebra II.

3 hr.; 3 cr. Prereq.: MATH 301 (or 601) or the equivalent.

This is a continuation of Math 301. Advanced topics in group and ring theory. Fields and field extensions. Not open to students who are taking or who have received credit for MATH 602 or 702.

MATH 305. Number Theory.

3 hr.; 3 cr. Prereq.: MATH 231 or MATH 237.

Prime numbers, the unique factorization property of integers, linear and non-linear Diophantine equations, congruences, modular arithmetic, quadratic reciprocity, contemporary applications in computing and cryptography. Not open to students who are taking or have received credit for MATH 605.

MATH 310. Elementary Real Analysis.

Sample Syllabus

3 hr.; 3 cr. Prereq.: MATH 201.

Rigorous introduction to functions of a real variable. Topics include real numbers and the completeness property; limits of sequences; elementary topological concepts; continuity and uniform continuity; sequences and series of functions, derivatives; Taylor’s theorem; the Riemann integral.

MATH 316. Complex Analysis.

3 hr.; 3 cr. Prereq.: MATH 202.

Topics covered include analytic functions, Cauchy?s Integral Theorem, Taylor’s theorem and Laurent series, the calculus of residues, singularities, meromorphic functions. Not open to students who are taking or have received credit for MATH 616.

MATH 317. Foundations of Analysis.

Sample Syllabus

3 hr.; 3 cr. Prereq.: MATH 201.

Language of logic and set theory; relations and functions; Peano systems; iterative processes; the natural numbers; integers and integral domains; rational numbers and fields; completeness and the real numbers; alternative characterizations of the real numbers; Archimedean order. Undergraduate students may elect MATH 617 in place of MATH 317. Students may not take both courses.

MATH 318. Foundations of Geometry.

3 hr.; 3 cr. Prereq.: MATH 201 and two proof-based courses in mathematics such as MATH 209, 220, 301, 302, 310, or 320.

The course is an exploration of Euclid’s fifth postulate, often referred to as the parallel postulate. Development of the basics of Euclidean geometry with a focus on understanding the role of the fifth postulate. Development and exploration of hyperbolic geometry, a non-Euclidean geometry. Not open to students who are taking or have received credit for MATH 618.

MATH 320. Point-Set Topology.

Sample Syllabus

3 hr.; 3 cr. coreq.: MATH 201.

The basic concepts and fundamental results of point-set topology. The course includes a review of sets and functions, as well as the study of topological spaces including metric spaces, continuous functions, connectedness, compactness, and elementary constructions of topological spaces. Not open to students who are taking or who have received credit for MATH 620.

MATH 328. Introduction to Partial Differential Equations.

3 hr.; 3 cr. Prereq.: MATH 223.

Topics covered include partial differential equations, Fourier series, and boundary value problems.

MATH 334. Graph Theory.

3 hr.; 3 cr. Prereq.: MATH 231.

Families of graphs, graph statistics, graph isomorphism, coloring, cycles, connectivity, planarity, graph algorithms. Not open to students who are taking or have received credit for MATH 634.

MATH 336. Combinatorics.

3 hr.; 3 cr. Prereq.: Linear Algebra.

Techniques in enumeration. Permutations, combinations, distributions, equivalence classes, principle of inclusion/exclusion, bijective proof, combinatorial proof, generating functions, partitions, Catalan numbers. Not open to students who are taking or have received credit for MATH 636.

MATH 340. Probability Theory for Data Science.

4 hr.; 4 cr. Prereq.: MATH 241. Coreq: Math 201 and Math 231.

Topics include introducing common random variable models, the central limit theorem, law of large numbers, random variable convergence. Topics may also include order statistics, probability inequalities, Slutsky’s Theorem, Markov chains and stochastic gradient descent. Probability computation using modern software. Not open to students who are taking or who have received credit for MATH 640.

MATH 341. Statistical Theory for Data Science.

4 hr.; 4 cr. Coreq.: MATH 340.

Point estimation, confidence sets and hypothesis testing from both the Frequentist
and Bayesian perspectives. Topics may also include power calculations, multiple
comparisons, model selection and randomized experimentation. Not open to students who are taking or who have received credit for MATH 641

MATH 342W. Data Science via Machine Learning.

6 hr.; 4 cr. Prereq.: ENGL 110, MATH 231, MATH 241, CSCI 111 (or equivalent)

Philosophy of modeling with data. Prediction via linear models and machine learning including support vector machines and random forests. Probability estimation and asymmetric costs. Underfitting vs. overfitting and model validation. Formal instruction of data manipulation, visualization and statistical computing in a modern language. Not open to students who are taking or who have received credit for MATH 642. Writing Intensive (W). Recommended corequisites include ECON 382, 387, MATH 341, MATH 343 or their equivalents.

MATH 343. Computation Stats for Data Science.

3 hr.; 3 cr. Prereq.: MATH 341. Coreq.: MATH 342W.

Topics may include the Score and generalized likelihood ratio tests, chi-squared tests, Kolmogorov-Smirnov test, basic linear model theory, ridge and lasso, Metropolis-within-Gibbs sampling, permutation tests, the bootstrap and survival modeling. Special topics. Not open to students who are taking or who have received credit for MATH 643.

MATH 385W. Mathematical Foundations of the Secondary School Curriculum.

Sample Syllabus ⚠ This course does not count toward a pure, applied, or DSS math major.

6 hr.; 4 cr. Prereq.: MATH 201, 231, 241, SEYS 201, 221, and minimum 2.67 mathematics GPA, and permission of the instructor.

Designed to give prospective secondary school mathematics teachers an understanding of the mathematics they will be teaching as well as the history of mathematics. An examination will be made of the thought underlying the secondary curriculum, from a consideration of the nature of mathematics and mathematical thought to the construction of simple mathematical models drawn from secondary school topics. Students will work in small groups to create and implement lessons.

MATH 390. Studies in Mathematics.

Prereq.: Permission of the chair.

Topics announced in advance. May be repeated for credit if topic is different.

MATH 391, 392. Special Problems.

Prereq.: Junior or senior standing and permission of the chair.

Each student works on a minor research problem under the supervision of a member of the department. Only students of exceptional mathematical ability and promise are admitted to the course.

MATH 395. Honors Seminar I.

Prereq.: Permission of the instructor.

A specific area of current research interest will be studied. As the specific material covered may vary from year to year, this course may be taken for credit more than once if the subject matter changes.

MATH 396. Honors Seminar II.

Prereq.: MATH 395.

Continuation of MATH 395.