# Mathematics Courses

**NOTE:** Not more than 10 semester hours of credit may be earned from the following courses: MTH 101, 105, 109, 110, and 111. Credit will not be given for MTH 101, 105, or 109 to students with credit for MTH 112 or 115. Credit will not be given for MTH 101, 105, 109, 110, 112, or 115 to students with credit for MTH 119 or MTH 121. Credit will not be given for both MTH 116 and MTH 122. Students majoring in departments in the Foster College of Business and the Caterpillar College of Engineering and Technology are advised to check college requirements for additional restrictions and limitations.

**MTH 101 - The Art of Mathematical Thinking**
*(3 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Great ideas in mathematics, problem solving, contemporary applications.

**MTH 105 - Finite Mathematics**
*(3 hours)*

Topics from finite mathematics: sets, matrices, systems of linear equations, linear programming, elementary probability, multistage processes, and Markov chains.

**MTH 109 - College Algebra**
*(3 hours)*

For students who need to strengthen their algebra skills: factoring polynomials; solving quadratic and other equations; exponents, logarithms, and graphing. Prerequisite: The sum of the mathematics placement exam score and the mathematics ACT score (or a converted mathematics SAT score) is at least 35.

**MTH 111 - Elementary Statistics**
*(3 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Probability, descriptive statistics, statistical models, correlation and regression, testing hypotheses, confidence limits, and selected applications.

**MTH 112 - Precalculus**
*(4 hours)*

For students needing further background in mathematics before enrolling in calculus (especially MTH 121). Thorough study of algebraic, transcendental, and trigonometric functions; emphasis on graphing and use of algebra. Prerequisite: Grade of C or better in MTH 109; or the sum of the mathematics placement exam score and the mathematics ACT score (or a converted mathematics SAT score) is at least 45.

**MTH 114 - Applied Finite Mathematics**
*(3 hours)*
**Core Curr. QR**

A survey of the most common mathematical techniques used in business. Topics include: linear functions, non-linear functions (polynomials, exponentials, logarithms), systems of linear equations, linear programming, sets and probability, introduction to basic statistics. Prerequisite: Grade of C or better in MTH 109 or 112; or the sum of the mathematics placement exam score and the mathematics ACT score (or a converted mathematics SAT score) is at least 45.

**MTH 115 - Brief Calculus With Applications I**
*(4 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Differential and integral calculus with emphasis on understanding through graphs. Topics in analytic geometry, limits, derivatives, antiderivatives, definite integrals, exponential and logarithmic functions, and partial derivatives. Prerequisite: Grade of C or better in MTH 109 or 112; or the sum of the mathematics placement exam score and the mathematics ACT score (or a converted mathematics SAT score) is at least 45.

**MTH 116 - Brief Calculus With Applications II**
*(3 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Continuation of MTH 115. Includes trig functions, integration techniques, series, differential equations, and multivariable calculus. Prerequisite: C or better in MTH 115.

**MTH 118 - Calculus With Review A**
*(4 hours)*

Topics in analytic geometry, limits, continuity, derivative, and pertinent algebra review. Prerequisite: The sum of the mathematics ACT score and the mathematics placement exam score is at least 45

**MTH 119 - Calculus With Review B**
*(4 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Continuation of MTH 118. Topics in analytic geometry, definite integral, Fundamental Theorem of Calculus, and pertinent algebra review. Prerequisite: grade of C or better in MTH 118.

**MTH 120 - Discrete Mathematics**
*(3 hours)*

Introduction to graph theory, Boolean algebra, mathematical induction, and elementary combinatorics. Prerequisite: Grade of C or better in MTH 112; or the sum of the mathematics placement exam score and the mathematics ACT score (or a converted mathematics SAT score) is at least 50.

**MTH 121 - Calculus I**
*(4 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Topics in analytic geometry; limits; continuity; differentiation; introduction to integration; applications. Prerequisite: Grade of C or better in MTH 112; or the sum of the mathematics placement exam score and the mathematics ACT score (or a converted mathematics SAT score) is at least 56.

**MTH 122 - Calculus II**
*(4 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Topics in calculus of logarithmic, exponential, and trigonometric functions; techniques of integration; analytic geometry; indeterminate forms; improper integrals; infinite series. Prerequisite: Grade of C or better in MTH 119 or MTH 121 or its equivalent.

**MTH 190 - Topics in Mathematics for Middle School Teachers**
*(3 hours)*

Topics for middle school math teachers which may vary each time course is offered, rotating among: analytic geometry, problem solving,linear programming. May be repeated under different topics for a maximum of 6 hours credit. Prerequisite: C or better in MTH111 and C or better in one of MTH115, 119, or 121 and permission of the Chair.

**MTH 207 - Elementary Linear Algebra With Applications**
*(3 hours)*

Matrix algebra, determinants, theory of simultaneous equations, vector spaces, bases, Gram-Schmidt orthogonalization, eigenvalues, eigenvectors, transformations, and applications. Prerequisite: MTH 122, or consent of instructor.

**MTH 223 - Calculus III**
*(4 hours)*
**Gen. Ed. MA**
**Core Curr. QR**

Topics in vectors; calculus of functions of several variables; multiple integrals; vector calculus. Prerequisite: grade of C or better in MTH 122.

**MTH 224 - Elementary Differential Equations**
*(3 hours)*

Solution of second order equations with constant coefficients; Laplace transforms; power series methods; numerical methods; modeling; applications. Prerequisite: MTH 223

**MTH 300 - Topics for Middle School Math Teachers**
*(3 hours)*

Topics of special interest which may vary each time course is offered, rotating among geometry, algebra/number theory, and problem-solving. Historical motivations will be provided within each topic. For middle school teacher certification; does not count toward a math major or math minor. May be repeated under different topics for a maximum of 9 hours credit. Prerequisite: C or better in MTH 111 and C or better in one of MTH 115, 119, or 121 and permission of the Chair.

**MTH 301 - Combinatorics**
*(3 hours)*

Combinatorial analysis, recurrence relations, generating functions, and finite-state machines. Prerequisite: MTH 120, 122; or MTH 223.

**MTH 302 - Introduction to Graph Theory**
*(3 hours)*

Theory and applications of graphs, including historical motivations. Fundamental properties of graphs, circuits, cycles, trees, and graph algorithms; planarity and coloring. Prerequisite: MTH 120, 122; or MTH 223.

**MTH 305 - Modern Geometry**
*(3 hours)*

Introduction to properties of formal axiom systems. Study of Euclidean and non-Euclidean geometries, including historical motivations. Topics will be explored using appropriate dynamic software. Prerequisite: MTH 223.

**MTH 307 - Linear Algebra**
*(3 hours)*

Vector spaces, linear transformations, inner product spaces, Jordan canonical forms, spectral theorems, and selected topics. Prerequisite: MTH 207.

**MTH 310 - Introduction to Number Theory**
*(3 hours)*

Historical development of number theory; primes and their distribution; divisibility; unique factorization of integers; congruences; Diophantine equations; number theoretic functions. Prerequisite: MTH 223.

**MTH 325 - Probability and Statistics I**
*(3 hours)*

Probability and statistical concepts, theory, and applications: random variables, sampling, central limit theorem, theories of estimation and the testing of hypotheses, linear models, and nonparametric methods. Prerequisite: MTH 223

**MTH 326 - Probability and Statistics II**
*(3 hours)*

Probability and statistical concepts, theory, and applications: random variables, sampling, central limit theorem, theories of estimation and the testing of hypotheses, linear models, and nonparametric methods. Prerequisite: MTH 325

**MTH 335 - Topics in Actuarial Science**
*(3 hours)*

Topics may vary each time course is offered, rotating among compound interest, mathematics of life contingencies, and actuarial mathematics. Some topics will coincide with those on actuarial exams. May be repeated under different topics for a maximum of 9 hours credit. Prerequisite: MTH 207, MTH 223; or consent of instructor.

**MTH 345 - Differential Equations**
*(3 hours)*

Existence and uniqueness theorems; solution methods for initial and boundary value problems; linear and nonlinear systems; stability theory; difference equations. Prerequisite: MTH 207, 223; or consent of instructor.

**MTH 371 - History of Mathematics**
*(3 hours)*

A survey of the historical development of mathematics from antiquity to the twentieth century. Emphasis will be on the interrelations between the various areas of mathematics as well as the mathematical content itself. Prerequisite: MTH 207 and 3 semester hours from courses numbered MTH 301 or above; or consent of instructor.

**MTH 390 - Mathematical Modeling**
*(3 hours)*

Introduction to constructing and evaluating mathematical models for describing and analyzing real world phenomena. Continuous and/or discrete models. Prerequisite: MTH 223; consent of instructor.

**MTH 403 - Complex Variables I**
*(3 hours)*

Introduction to complex calculus: elementary functions, integration, Cauchy's formula, residue theory, and applications. Prerequisite: MTH 207, 223; or MTH 224.

**MTH 404 - Modern Algebra I**
*(3 hours)*

Basic theory of sets, integers, and mappings; elementary properties of groups, rings, and fields. Prerequisite: MTH 207, 223.

**MTH 405 - Modern Algebra II**
*(3 hours)*

Topics selected from theory of rings, field theory, and applications. Prerequisite: MTH 404.

**MTH 406 - Elementary Topology**
*(3 hours)*

Introduction to rudiments of point set topology. Concepts of compactness, connectedness, and continuity, in context of general topological spaces and metric spaces. Prerequisite: MTH 207, 223; or consent of instructor

**MTH 414 - Partial Differential Equations**
*(3 hours)*

Fourier series and applications to solutions of partial differential equations. Separation of variables, eigenfunction expansions, Bessel functions, Green's functions, Fourier and Laplace transforms. Credit will be given for only one of MTH 414, MTH 514. Prerequisite: MTH 224 or MTH 345

**MTH 420 - Introduction to Analysis**
*(3 hours)*

Real number system and functions of real variables: sequences, limits, continuity, differentiation, series, uniform convergence, and the Riemann-Stieltjes integral. Prerequisite: MTH 207, 223.

**MTH 421 - Advanced Calculus**
*(3 hours)*

Functions of several variables. Calculus of transformations, implicit and inverse function theorems, line and surface integrals, Fourier analysis, fixed point theorems, and applications. Prerequisite: MTH 420 or consent of instructor.

**MTH 427 - Applied Statistical Methods**
*(3 hours)*

Regression analysis, time series analysis, and forecasting Prerequisite: MTH325; MTH326 or consent of instructor.

**MTH 428 - Topics in Applied Statistics**
*(3 hours)*

A continuation of Math 427 to include further studies in statistics such as Bayesian statistics, statistical computing, or multivariate methods. May be repeated under different topics for a maximum of 6 hours credit. Prerequisite: Math 325; Math 326 or consent of instructor.

**MTH 435 - Stochastic Processes**
*(3 hours)*

Conditional probability and expectation, probability models, Markov chains, Poisson process, renewal theory, Brownian motion processes. Prerequisite: MTH 325 and MTH 207

**MTH 490 - Topics in Mathematics**
*(3 hours)*

Topics of special interest which may vary each time course is offered. Topic stated in current Schedule of Classes. Prerequisite: consent of instructor.

**MTH 491 - Directed Individual Studies in Mathematics**
*(1-16 hours)*

Individual work in special areas of mathematics for advanced, qualified undergraduate students. May register for more than 6 hrs. credit only if enrolled in an approved special off campus program. Prerequisite: consent of Department Chair.

**MTH 494 - Senior Project in Mathematics I**
*(0 hours)*

Topics in mathematics selected, studied, and discussed by students under faculty guidance. Each student explores an area of mathematics and selects a topic in which he or she has a particular interest. Prerequisite: Senior standing (junior standing with consent of instructor).

**MTH 495 - Senior Project in Mathematics II**
*(3 hours)*

A selected topic in mathematics is studied by a student under faculty guidance. Each student writes a paper and gives a presentation on his or her topic. Prerequisite: MTH 494; senior standing.

**MTH 501 - Topics in Applied Mathematics I**
*(3 hours)*

Theory, applications, and algorithms for basic problems of modern applied mathematics. Symmetric linear systems, minimum principles, equilibrium equations, calculus of variations, orthogonal expansions, and complex variables. Prerequisite: MTH 224 or 345.

**MTH 502 - Topics in Applied Mathematics II**
*(3 hours)*

Continuation of MTH 501. Selected numerical algorithms: Fast Fourier transform, initial value problems, stability, z-transforms, and linear programming. Prerequisite: MTH 501 or consent of instructor.

**MTH 510 - Numerical Methods I**
*(3 hours)*

Introduction to numerical and computational aspects of various mathematical topics: finite precision, solutions of non-linear equations, interpolation, approximation, linear systems of equations, and integration. Cross listed as CS 510. Prerequisite: CS 101; MTH 207 and 223.

**MTH 511 - Numerical Methods II**
*(3 hours)*

Continuation of CS/MTH 510: further techniques of integration, ordinary differential equations, numerical linear algebra, nonlinear systems of equations, boundary value problems, and optimization. Cross listed as CS 511. Prerequisite: MTH 224 or 345; CS/MTH 510.

**MTH 514 - Partial Differential Equations**
*(3 hours)*

Fourier series and applications to solutions of partial differential equations. Separation of variables, eigenfunction expansions, Bessel functions, Green's functions, Fourier and Laplace transforms. Prerequisite: MTH 224 or 345.