# 3000 Level

**MTH 3300 - Foundations of Mathematics**

Prerequisite(s): A grade of C or above in MTH 1321.

Core concepts of advanced mathematics: proofs, induction, sets, functions, equivalence relations, divisibility, modular arithmetic, real numbers, sequences and limits.

**MTH 3312 - Foundations of Combinatorics and Algebra**

Prerequisite(s): A grade of C or above in MTH 3300.

Introduction to combinatorics and algebra. Topics include elementary counting principles, mathematical syntax, fundamentals of set operations, maps and relations, fundamental properties of the integers, the ring of integers modulo n and rings of polynomials, irreducible polynomials, the construction of finite fields, and combinatorial designs.

**MTH 3318 - Data and Chance**

Prerequisite(s): A grade of C or above in MTH 1316.

Designed for the prospective teacher seeking an EC-4 generalist or a 4-8 mathematics certification. Core ideas from probability and statistics, including collection of data, patterns in data, and inference from data, in an active, lab-like environment. Credit may not be received after completion of STA 2381 or STA 3381. Does not apply toward the mathematics major.

**MTH 3323 - Introduction to Analysis**

Prerequisite(s): A grade of C or above in MTH 2321 and 3300.

A rigorous treatment of the real number system, sequences of real numbers, limits, continuous functions, and elements of differentiation and integration.

**MTH 3324 - Numerical Methods** (Cross-listed with CSI 3324)

Prerequisite(s): CSI 1430 and MTH 1321.

Numerical differentiation and integration, linear systems of equations, numerical solutions of ordinary differential equations, curve fitting, and computational techniques.

**MTH 3325 - Ordinary Differential Equations**

Prerequisite(s): A grade of C or above in MTH 2321 or concurrent enrollment.

Differential equations of first order, linear equations of order two and higher, introduction to power series methods, elements of the Laplace Transform, some facts from linear algebra and systems of differential equations.

**MTH 3326 - Partial Differential Equations**

Prerequisite(s): A grade of C or above in MTH 2321 and 3325.

Partial differential equations of physics, the method of separation of variables, orthogonal sets of functions, Fourier Series, boundary value problems, Fourier integrals and applications.

**MTH 3327 - Partial Differential Equations for the Social Sciences**

Prerequisite(s): A grade of C or above in MTH 2321 and 3325.

Introduction of partial differential equations that model social behavior, from crowd dynamics to optimal control. Topics include linear and nonlinear transport equations, Hamilton-Jacobi equations, and diffusions, with some applications to game theory.

**MTH 3340 - Mathematics through Technology**

Prerequisite(s): Credit for twelve hours of mathematics courses, at least three hours of which are at the 2000 level or above. (This prerequisite cannot be satisfied using any hours transferred in under the generic titles MTH 1000 or MTH 2000.)

Designed for the prospective mathematics teacher seeking certification for grades 4-8 or 8-12. Use of technology to explore, communicate, and reinforce mathematical concepts and problem solving from several areas of mathematics. Attention given to graphing calculators, interactive geometry computer packages, computer-based algebra packages, and spreadsheets or statistical packages. Written and oral presentations. Does not apply toward the mathematics major.

**MTH 3350 - Structure of Modern Geometry**

Prerequisite(s): A grade of C or above in MTH 2311 or 2317.

A study of the foundations of Euclidean geometry by synthetic methods with a brief introduction to non-Euclidean geometry.

**MTH 3351 - Proof and Reasoning in Mathematics for Middle School Math Teachers**

Pre-requisite(s): A grade of C or better in both MTH 2317 and 3318, or concurrent enrollment

Concepts taken from probability and statistics, algebra and number concepts, and Euclidean and non-Euclidean geometry, with a focus on the role and history of proof and reasoning as the cornerstone in arriving at mathematical conclusions. Does not apply toward the mathematics major or as a secondary mathematics elective.

**MTH 3370 - Mathematical Methods of Operations Research**

Prerequisite(s): A grade of C or above in MTH 2311.

A survey of models and methods used in operations research. Topics include linear programming, dynamic programming, and game theory, with emphasis on the construction of mathematical models for problems arising in a variety of applied areas and an introduction to basic solution techniques.

**MTH 3374 - Introduction to Mathematical Modeling**

Prerequisite(s): A grade of C or above in MTH 1322 or in both MTH 2317 and 3318.

An introduction to the process of mathematical modeling, including problem identification, model construction, model selection, simulation, and model verification. Individual and team projects.

**MTH 3V90 - Advanced Undergraduate Research in Mathematics**

Prerequisite(s): Consent of Instructor.

Advanced independent study or research in topics not available in other courses. May be repeated for a maximum of 3 hours.