420. PROBABILITY AND STATISTICS I  4 cr.  Prerequisite: MT 233. Combinatorial probability, discrete and continuous distributions, simulation of sampling distributions and the central limit theorem, introduction to data analysis, estimation and hypothesis testing; use of CAS and statistical software.

421. PROBABILITY AND STATISTICS II  3 cr.  Prerequisite: MT 420. Mathematical treatment of estimation and hypothesis testing, including one and two-factor analysis of variance, simple regression and correlation, and nonparametric analyses.

422. APPLIED STATISTICS  3 cr.  Prerequisites: MT 342, 420.  Categorical data analysis, multiple regression, analysis of variance of various designs, introduction to design of experiments.  Use of statistical software.

425. OPERATIONS RESEARCH  3 cr.  Prerequisite: MT 342.  Linear programming,  sensitivity analysis and duality, queuing theory, and topics from networks, decision making, game theory, Markov chains, dynamic programming, and simulation.

431. ADVANCED CALCULUS OF ONE VARIABLE  3 cr.  Prerequisites: MT 233, 341. Real-number system, limits, continuity, differentiability, Riemann integral, properties of continuous and differentiable functions, sequences and series of functions.

432. ADVANCED CALCULUS OF SEVERAL VARIABLES  3 cr.  Prerequisites: MT 233, 342.  Development of and motivation for vector‑valued functions, calculus of functions of several variables, implicit functions and Jacobians, multiple integrals, line integrals.

436. INTRODUCTION TO COMPLEX ANALYSIS  3 cr.  Prerequisite: MT 341 or 342 or permission of department chair. Complex number plane, analytic functions, integration of complex functions, sequences and series. Residue theorem, evaluation of real integrals.

438. ORDINARY LINEAR DIFFERENTIAL EQUATIONS  3 cr.  Prerequisites: MT 233, 342. Linear equations and systems, existence and uniqueness theorems, oscillation theory.  Autonomous equations and systems, their solutions and qualitative properties.

441. ABSTRACT ALGEBRA  3 cr.  Prerequisite: MT 341. Groups, rings, domains, fields, extension fields, introduction to Galois Theory.

442. LINEAR ALGEBRA  3 cr.  Prerequisite: MT 342. Vector spaces, linear transformations, characteristic values and applications.

450. EUCLIDEAN AND NON‑EUCLIDEAN GEOMETRY  3 cr.  Prerequisite: MT 341 or 342 or permission of department chair. Alternative ways of investigating the Euclidean plane, including transformational geometry; examination of the parallel postulate and how it can be changed to create new geometries; hyperbolic geometry.

452. ELEMENTARY TOPOLOGY  3 cr.  Prerequisite: MT 341. Topological spaces, homeomorphisms, connected spaces, compact spaces, regular and normal spaces, metric spaces.

456. FRACTAL GEOMETRY  3 cr.  Prerequisites: MT 233, 341. Topics from metric spaces, transformations, iterated function systems, dynamical systems, fractal dimension, Julia sets, and Mandelbrot sets.

468. THEORY OF NUMBERS  3 cr.  Prerequisite: MT 341. Divisibility theorems, number‑theoretic functions, primitive roots, quadratic congruences and reciprocity, partitions.