MTH 103. Intermediate Algebra. 3 credits. FA, SP, SU

Topics from second-year algebra to form an introduction to college algebra.

MTH 105. Math for Elementary Teachers. 4 credits.

Typical elementary school topics will be reviewed and extended to related topics of exponential notation, significant figures, measures of change, economic principles and the normal distribution. In so doing, all applicable NCTM Standards will be covered.

MTH 125. Practical Math. 3 credits.

To present common situations requiring quantitative analysis or calculations, to prepare the student to think logically through these situations, to model them mathematically, and to reach an accurate conclusion. Two years of high school algebra is expected. This course is repeatable up to nine credit hours.

MTH 131. Earth Algebra. 3 credits. FA, OD

College Algebra material; environmental issues; functions; atmospheric carbon dioxide concentration; composite functions and inverses; global temperature and ocean level; quadratic functions; systems of linear equations and matrices; carbon dioxide emission. P: Four semesters of high school algebra.

MTH 139. Precalculus. 3 credits. FA, SP

This course will cover the basic concepts that are required for further study of mathematics including a course in calculus. The course topics include solving linear, quadratic, exponential and logarithmic equations; linear and quadratic inequalities; properties and graphs of polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions; angles; right triangles; trigonometric identities and equations.

MTH 141. Applied Calculus. 3 credits. FA, SP, SU

Main topic is differential and integral calculus and applications. Includes sections on partial derivatives. CR: Heider College of Business students only.

MTH 161. Business Statistics. 3 credits.

An introduction to descriptive and inferential statistics for business. Topics include measures of central tendency and dispersion, sampling and estimation, confidence intervals, regression and correlation, and relevant examples from business, finance and economics. CR: Heider College of Business students and Economics majors and minors in CCAS only.

MTH 205. Mathematics for the Modern World. 2 credits.

Foundations course in mathematics for those not needing calculus. Topics include basic number theory, graphs, estimation, data analysis and curve fitting, probability and analysis of risk, and fairness in voting systems.

MTH 206. Mathematical Reasoning and Statistics. 3 credits.

This is a 3-credit online course for students not needing calculus. We will be considering basic number theory, graphs, estimation, data analysis, probability, statistics, and analysis of risk. You will become familiar with these topics and demonstrate mastery via weekly homework, discussion posts, and quizzes, two written projects, and one cumulative exam.

MTH 231. Calculus for the Biological Sciences. 3 credits.

Differential and integral calculus and a brief introduction to differential equations, with applications to the biological sciences. NOTE: Not intended for CHM, MTH and PHY majors.

MTH 245. Calculus I. 4 credits. FA, SP, SU

Differential and integral calculus of algebraic and transcendental functions.

MTH 246. Calculus II. 4 credits. FA, SP, SU (Same as MTH 249)

Techniques of integration, infinite series, and other topics. Satisfies Magis Core: Mathematical Reasoning. P: MTH 245.

MTH 249. Modeling the Physical World I. 3 credits. (Same as MTH 246)

First semester in the sequence on mathematical modeling using calculus. Course is taught jointly with PHY 221. Topics include elementary differential equations, techniques of integration, sequences and series, vector analysis, and applications. Satisfies Magis Core: Mathematical Reasoning. This course is equivalent to MTH 246. P: MTH 245 or IC. CO: PHY 221.

MTH 260. Introduction to Statistics. 3 credits.

In this course students will learn to use basic statistical concepts, including hypothesis testing. Students will be expected to accurately analysis statistical information in both written and oral form and will be expected to apply the ideas in this course to their specific field of study.

MTH 310. Introduction to Abstract Mathematics. 3 credits. FA, SP

A systematic study of the basic concepts in mathematics, including set theory; logic; proof techniques, basic properties of integers; relations; functions; congruences; introduction to groups; sequences and series, and basic properties of a topological space. P: MTH 246 or MTH 249.

MTH 321. Euclidean and Non-Euclidean Geometry. 3 credits.

Basic geometric concepts and applications. P: MTH 246 or MTH 249.

MTH 323. Mathematical and Computational Neuroscience. 3 credits.

Selected topics in mathematical and computational methods in neuroscience. Model of neurons and neural networks; neural network architecture; and theories of neural coding. Overview of foundational and current research in the subject. P: CSC 222 or MTH 246 or PSY 437 or PSY 441, or IC.

MTH 347. Calculus III. 3 credits. FA, SP

This course covers vector algebra and calculus in two- and three-dimensional space. P: MTH 246 or MTH 249.

MTH 349. Modeling the Physical World II. 3 credits.

Second semester in the sequence on mathematical modeling using calculus. Course is taught jointly with PHY 222. Topics include multivariable functions and calculus, series integration (Green's, Stokes', and Divergence theorems) and applications. P: MTH 249 and PHY 221. CO: PHY 222.

MTH 350. Applied Linear Algebra and Differential Equations. 3 credits.

This course is a survey of the techniques to solve elementary differential equation and linear algebra problems. Topics include solving linear systems, eigenvalues, eigenvectors, exact equations, integrating factors, and constant coefficient systems of ODE. The class is computational in nature and is suitable for students in the applied sciences. P: MTH 246 or MTH 249.

MTH 360. Elementary Probability and Statistics. 3 credits.

Non-calculus approach with emphasis on measures of central tendency and variability, distributions and testing of hypothesis. Designed for students in natural and social sciences, or business. Satisfies Magis Core: Designated Statistical Reasoning and Designated Technology. P: Mathematical Reasoning course.

MTH 361. Probability and Statistics in the Health Sciences. 3 credits.

This course covers topics in probability and statistics considered useful to those students planning on a career in the health sciences. The topics covered include probability principles and distributions in health sciences, types of epidemiologic study designs, estimation of medical parameters in defined patient populations, test of hypothesis, measures and analysis of treatment of the sick, analysis of variance, methods of medical outcome prediction, and prospective, retrospective and cross-sectional studies of disease occurrence. Satisfies Magis Core: Designated Statistical Reasoning and Designated Technology. P: Mathematical Reasoning course.

MTH 362. Statistical Modeling. 3 credits.

Inferential statistical methods, ANOVA, design and analysis of experiments, regression and nonparametric methods. P: MTH 360 or MTH 361 or IC.

MTH 400. Current Issues in Mathematics. 1 credit.

MTH 400 is a capstone course where students make oral presentations of current mathematics topics. Students will be guided through picking a topic, finding materials, writing up a presentation, and making a presentation. The students will offer constructive criticism of each other's presentations. P: Ethics course, Oral Communication course, MTH 310, and one of the following: MTH 347, MTH 349 or MTH 350; CR: Jr. or Sr. stdg.

MTH 411. Combinatorics. 3 credits.

Basic counting methods, generating functions, spanning trees, recurrence relations, network algorithms and the inclusion-exclusion formula, applications to information processing and retrieval. P: MTH 310 or IC.

MTH 429. Advanced Linear Algebra. 3 credits.

Vector spaces and subspaces; linear transformations; matrices, eigenvalues and eigenvectors. P: MTH 350.

MTH 443. Numerical Analysis. 3 credits.

Numerical differentiation and integration; solutions of equations and systems of equations; polynomial approximation; error analysis and eigenvectors; applications to digital computers. P: MTH 246 or MTH 249.

MTH 445. Advanced Differential Equations. 3 credits.

Systems of differential equations, qualitative, theory, Laplace and Fourier transforms, partial differential equations, series solutions, Fourier series. P: MTH 350.

MTH 446. Partial Differential Equations. 3 credits.

Integral curves and surfaces of vector fields; the Cauchy-Kovalevsky theorem; general linear PDEs, their characteristics and classification; solutions to, and applications of, linear and quasi-linear first order and second order PDEs; Laplace's equation, the heat equation and the wave equation. P: MTH 445.

MTH 447. Mathematics in Medicine and the Life Sciences I. 3 credits.

This course is intended to be an overview of a variety of mathematical topics considered useful to those students intending to pursue a career in medicine or the life sciences. The topics covered include mathematics of populations, infectious diseases, and excitable cells. P: MTH 246 or MTH 249 CO: MTH 350.

MTH 448. Mathematics in Medicine and Life Sciences II. 3 credits.

This course continues the investigation of math modeling in biomedical sciences. Biological topics include excitable cells, the cardiovascular system, tumors, and the immune system, metabolic systems, and chemotaxis; mathematical techniques include ordinary, stochastic, and partial differential equations. P: MTH 350, MTH 447 or IC.

MTH 451. Differential Geometry. 3 credits.

Calculus of curves, surfaces and manifolds; topics will include hyperbolic geometry, vectors and tensors, fundamental forms, curvature, covariant derivatives, with applications to special and general relativity. P: MTH 347 or MTH 349.

MTH 455. Chaotic Dynamical Systems. 3 credits.

This course will study discrete dynamical systems. Topics covered will include one-dimensional and higher-dimensional dynamical systems, fixed points, stability theory, linearization, phase spaces, bifurcation theory, index theory, limit cycles and periodicity, chaos, and attractors. Applications to Biology, Physics, Chemistry, and other areas will be studied. P: MTH 350; MTH 347 or MTH 349.

MTH 457. Graph Theory. 3 credits.

Basic properties of graphs, subgraphs, simple graphs, walks, paths, circuits, cycles, connectivity, Eulerian and Hamiltonian graphs, adjacency and incidence matrices, trees, spanning trees, planar graphs, graph coloring, networks. P: MTH 310.

MTH 459. Topology. 3 credits.

Set theory; metric space; topological spaces; connectedness; compactness; selected related topics. P: MTH 246 or MTH 249.

MTH 467. Operations Research. 3 credits.

Introductory course in operations research. Linear models and solutions using the simplex method, duality theory and sensitivity analysis. P: MTH 350.

MTH 471. Mathematical Analysis. 3 credits.

Properties of Euclidean spaces and their applications to functions. P: MTH 310 and Contemporary Composition course.

MTH 472. Mathematical Analysis II. 3 credits.

Continuation of MTH 471; functions in metric space. P: MTH 471.

MTH 473. Complex Analysis. 3 credits.

Complex arithmetic, polar representations, functions of a complex variable, analyticity and the Cauchy-Riemann equations, complex integration, Cauchy Integral Formula, series, poles and residues, applications to real integration, conformal mappings. P: MTH 347 or MTH 349.

MTH 481. Modern Algebra I. 3 credits.

Groups, rings; fields; applications to coding theory. P: MTH 310.

MTH 482. Modern Algebra II. 3 credits.

Rings; ideals; field extensions; Galois theory; applications to coding theory. P: MTH 481.

MTH 492. Internship in Mathematics. 3 credits.

Internship in Mathematics.

MTH 493. Directed Independent Readings. 1-3 credits. FA, SP

May be repeated up to six credit hours. CR: DC.

MTH 495. Directed Independent Study. 1-3 credits. FA, SP

May be repeated up to six credit hours. CR: DC.

MTH 497. Directed Independent Research. 1-3 credits. FA, SP

May be repeated up to six credits hours. CR: DC.

MTH 509. Discrete Structures. 3 credits.

Logic; Boolean algebra; switching circuits; graphs; groups; semi-groups; finite state machines; coding theory; grammars; algorithms. P: CSC 221; 6 credit hours of college MTH.

MTH 525. Automata, Computability, and Formal Languages. 3 credits. OD

Finite state concepts; acceptors; formal grammars; computability; Turing machines. P: MTH 246 or MTH 249.

MTH 541. Mathematics for Data Scientists. 3 credits.

Matrix algebra, vector spaces, bases, linear transformations, linear operators and their properties, introduction to the fundamental principles of mathematical models, especially those useful in data science. P: MTH 246 with a grade of B or better.

MTH 561. Mathematical Statistics I. 3 credits. FA, SU

Introduction to probability and probability distributions including techniques for finding expected values and variance of discrete and continuous variables. These distributions and their properties are examined to establish their application to applied statistical methods. P: MTH 246 or MTH 249.

MTH 562. Mathematical Statistics II. 3 credits. SP

Using probability distributions as a foundation and random sampling, methods for estimating distribution parameters are developed with applications to hypothesis testing. The course also includes an introduction to linear models, regression analysis, analysis of variance and design of experiments. P: MTH 561.

MTH 563. Mathematical Statistics III. 3 credits. OD

Optimal decision procedures, further normal distribution theory, noncentral chi-square and F distributions, introduction to the theoretical basis for analysis of variance, nonparametric methods. P: MTH 562.

MTH 573. Probabilistic Models. 3 credits. OD

Queuing theory, inventory theory, Markov processes, simulation and nonlinear programming. P: MTH 561.

MTH 575. Introductory Stochastic Processes. 3 credits. OD

Random walk, normal processes and covariance stationary processes, counting processes and Poisson processes, renewal counting processes, discrete and continuous parameter Markov chains. P: MTH 561.

MTH 599. Seminar. 1-3 credits. OD

Topics in advanced mathematics selected by the instructor. This course is repeatable up to 15 credit hours. CR: IC.