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# Mathematics Courses

## 1314 College Algebra

Linear and quadratic equations and inequalities, determinants, matrices, systems of equations, binomial theorem, exponential and logarithmic functions , theory of equations.
Prerequisites: 270 Math THEA or C or better in DMTH 0372.
If THEA exempt: 500 MATH SAT or 19 Math ACT.
Prepares for : MATH 1325, 1342, 1350, 3312.

## 1316 Trigonometry

Study of trigonometric functions, graphs, identities, inverse trigonometric functions, trigonometric equations, and applications of trigonometry. Recommended for students who have not had high school trigonometry.
Prerequisites: 270 Math THEA or C or better in DMTH 0372.
If THEA exempt: 500 MATH SAT or 19 Math ACT.
Prepares for: MATH 2310, 2413, 3313.

## 1320 Geometric Structures

Development of a mathematical way of thinking through a coherent first-hand experience. Emphasis on the student’s deductive powers and ability to use language precisely and efficiently. Study of Euclidean geometry; Hilbert’s axioms, neutral geometry, hyperbolic geometry; the axiomatic method; and an introduction to consistency, independence, and completeness of axiom systems.
Prerequisites: 270 Math THEA or C or better in DMTH 0372.
If THEA exempt: 500 MATH SAT or 19 Math ACT.

## 1325 Calculus for Business Applications

An introduction to calculus. The derivative, applications of the derivative, techniques of differentiation, exponential and natural logarithmic functions, an introduction to integral calculus.
Prerequisites: Grade of C or better in MATH 1314, or its equivalent .
Prepares for: MATH 2305, 2413.

## 1342 Elementary Statistics

Non-calculus based introduction to statistics, statistical measures of data, statistical description of data, elementary probability, random variables , binomial and normal distributions, estimation, testing hypotheses.
Prerequisites: Grade of C or better in MATH 1314 or its equivalent.
Prepares for: MATH 3370.

## 1350 Fundamentals of Math I

Concepts of sets, functions, numeration systems, number theory and properties of the natural numbers, integers, rational, and real number systems, with an emphasis on problem solving and critical thinking. This course is designed for students seeking EC-4 or 4-8 teacher certification.
Prerequisites: Grade of C or better in MATH 1314 or its equivalent.
Prepares for: MATH 3313.

## 1360 Honors College Algebra

Generally covers same topics as MATH 1314.
Prerequisites: 270 Math THEA or C or better in DMTH 0372.
If THEA exempt: 500 MATH SAT or 19 Math ACT.
Prepares for: MATH 2312.

## 2305 Discrete Mathematics

An introduction to combinatorial mathematics and finite mathematics required in the study of computer science. Topics include elementary set theory, relations and function, combinatorics, and introduction to graph theory with special emphasis on trees and search algorithms, an introduction to recurrence relations and generating functions, and finite state machines.
Prerequisites: Students should be currently enrolled in or have received a grade of C or better in MATH 1325, 2376, 2413, 2460, or 3316.
Prepares for: MATH 3321.

## 2310 Mathematical Modeling I

This course is specifically designed for students who will become teachers in grades 4-8. Students will examine characteristics of situations to select or create math models in algebra, geometry, and trigonometry using real world situations.
Prerequisites: Grade of C or better in MATH 1314 or its equivalent.

## 2312 Precalculus Mathematics

Intensive review of algebra, trigonometry and analytic geometry.
Prerequisites: 270 Math THEA or C or better in DMTH 0372.
If THEA exempt: 500 MATH SAT or 19 Math ACT.
Prepares for: MATH 2376, 2413, 2460.

## 2318 Linear Algebra

A first course in linear algebra, including vector and matrix arithmetic, solutions of linear systems and the Eigenvalue-Eigenvector problem, elementary vector spaces, and linear transformation theory.
Prerequisites: Mathematics majors should be currently enrolled in or have received a grade of C or better in MATH 2413 or its equivalent; 4-8 teacher certification students should be currently enrolled in or have received a grade of C or better in MATH 3316 or its equivalent.
Prepares for: MATH 3321, 4315, 4330.

## 2376 Calculus for the Social and Life Sciences

Sets, functions, limits, derivatives and applications, introduction to integral calculus. Designed for students majoring in social and life sciences and students seeking 4-8 math teacher certification.
Prerequisites: Grade of C or better in MATH 1314 or its equivalent.
Prepares for: MATH 2305, 2413.

## 2413 Calculus and Analytical Geometry I

Functions, limits, derivatives of algebraic, trigonometric, exponential and logarithmic functions, curve sketching , related rates, maximum and minimum problems, definite and indefinite integrals with applications.
Prerequisites: Grade of C or better in MATH 2312 or its equivalent.
Prepares for: MATH 2305, 2318, 2414.

## 2414 Calculus and Analytical Geometry II

Methods of integration, polar co-ordinates, parametric equations, sequences and series, and vectors.
Prerequisites: Grade of C or better in MATH 2413 or its equivalent.
Prepares for: MATH 2415, 3301, 3321, 3322, 3370.

## 2415 Calculus and Analytical Geometry III

Functions of several variables, partial derivatives, vector analysis, and multiple integrals.
Prerequisites: Grade of C or better in MATH 2414 or its equivalent.
Prepares for: MATH 4302, 4310.

## 2460 Honors Calculus and Analytic Geometry I

Generally covers same topics as MATH 2413.
Prerequisites: Grade of C or better in MATH 2312 or its equivalent.
Prepares for: MATH 2414.

## 3225 Statistical Analysis with SPSS or MINITAB

Introduction to data analysis with SPSS, correlation, regression, prediction, choice of appropriate statistics, presentation of data.
Prerequisites: Grade of C or better in Math 1342 or consent of Instructor.

## 3300 History of Mathematics

Historical origin and development of mathematical concepts through the sixteenth century. Topics include Egyptian and Babylonian mathematics, Greek mathematics, and early European mathematics.
Prerequisites: Junior standing and grade of C or better in six hours of mathematics.

## 3301 Ordinary Differential Equations

First order equations : modeling and population dynamics, stability, existence and uniqueness theorem for nonlinear equations, Euler’s method. Second order equations: nonlinear equations via reductions methods, variation of parameters, forced mechanical vibrations, resonance and beat. Laplace Transform: general forcing functions, the convolution integral. Systems of ODEs: eigenvalues and phase plane analysis.
Prerequisites: Grade of C or better in MATH 2414 or its equivalent.
Prepares for: MATH 4302, 4315.

## 3311 Foundations of Mathematics I

Introduction to mathematical logic and the language and nature of proofs. Applications to sets, mathematical induction, relations, and functions.
Prerequisites: Grade of C or better in nine semester hours of mathematics.
Prepares for: MATH 3314, 3315.

## 3312 Probability, Statistics, and Statistical Modeling

This course is specifically designed for students who will become teachers in Grades EC-4 and 4-8. It includes principles and applications of probability and statistics with an emphasis on using real-world data collected, organized, and analyzed by the students.
Prerequisites: Grade of C or better in MATH 1314 or its equivalent.

## 3313 Elementary Geometry

The development of Euclidean geometry, introduction to proofs, concepts of measurement and co-ordinate geometry.
Prerequisites: Grade of C or better in MATH 1350 or MATH 1316 or its equivalent.
Prepares for: MATH 3316.

## 3314 Foundations of Mathematics II

This course is specifically designed for students who will become teachers in grades 4-8. It includes principles and applications of axioms, theorems, and proofs for the natural numbers, integers, and real numbers.
Prerequisites: Grade of C or better in MATH 3311 or its equivalent.

## 3315 Elementary Number Theory

A development of the elementary theory of numbers, Diophantine equations, congruences, Fibonacci numbers, and magic squares .
Prerequisites: Grade of C or better in MATH 3311 or its equivalent.

## 3316 Calculus Concepts – Mathematical Modeling II

This course is specifically designed for students who will become teachers in grades 4-8. It includes principles and conceptual foundations of calculus and applications to middle school mathematics.
Prerequisites: Grade of C or better in MATH 3313 or its equivalent.
Prepares for: MATH 2318.

## 3317 Problem Solving

Study of heuristics and strategies used in solving problems , with extensive practice in solving word problems involving skills in arithmetic, algebra, geometry, and logic.
Prerequisites: Grade of C or better in nine semester hours of mathematics.

## 3321 Discrete Structures

Combinatorics, graphs, Boolean algebra, algebraic structures, coding theory, finite state machines, machine design, and computability.
Prerequisites: Grade of C or better in MATH 2318 and 2414, and satisfactory completion of COSC Requirement.

## 3322 Introduction to Advanced Mathematics

An introduction to logic and methods of proof with applications to basic set operations , relations, functions, cardinality, and the real number system.
Prerequisites: Grade of C or better in MATH 2414 or its equivalent.
Prepares for: MATH 3330, 3350, 3380, 4330.

## 3330 Higher Geometry

Axiomatic and set-theoretic treatment of geometry, analysis of the metric and synthetic approaches to Euclidean geometry, introduction to non-Euclidean geometries.
Prerequisites: Grade of C or better in MATH 3322 or consent of the instructor.

## 3350 Abstract Algebra I

An introduction to abstract algebraic structures concentrating mainly in group theory . Topics in group theory include cyclic groups, normal subgroups, quotient groups, homomorphisms,  isomorphisms, permutation groups, the Sylow theorems, and the structure theorem for finite abelian groups.
Prerequisites: Grade of C or better in MATH 3322 or its equivalent.
Prepares for: MATH 3351.

## 3351 Abstract Algebra II

Continuation of MATH 3350. The abstract algebraic structures studied here include rings, fields, and modules. MATH 3351 is strongly recommended for undergraduates contemplating graduate study in mathematics.
Prerequisites: Grade of C or better in MATH 3350 or its equivalent.

## 3370 Introduction to the Theory of Statistical Inference

A calculus-based introduction to statistics, probability, special probability distributions , nature of statistical methods, sampling theory, estimation, testing hypotheses.
Prerequisites: Grade of C or better in MATH 2414 or its equivalent.
Prepares for: MATH 4380.

## 3380 Analysis I

The real number system, Completeness Axiom, metric spaces, sequences, compactness, continuity, differentiation, Intermediate Value Theorem, Extreme Value Theorem, the Riemann integral, Fundamental Theorem of Calculus.
Prerequisites: Grade of C or better in MATH 3322 or its equivalent.
Prepares for: MATH 3381, 4340.

## 3381 Analysis II

Stieltjes integral, convergence, uniform convergence, sequences and series of functions, bounded variation, the Implicit Function Theorem.
Prerequisites: Grade of C or better in MATH 3380 or its equivalent

## 4131 Special Problems

Special advanced problems in mathematics to suit the needs of individual students.
Prerequisites: Consent of Instructor.

## 4231 Special Problems

Special advanced problems in mathematics to suit the needs of individual students.
Prerequisites: Consent of Instructor.

## 4302 Partial Differential Equations

Boundary value problems with simple geometries in 1, 2, or 3 space dimensions for the heat equation, wave equation, and potential (Laplace) equation, separation of variables, Fourier Series, Sturm-Liouville eigenvalue problems and Helmholts equation, Rayleigh Quotient, introduction to finite difference methods.
Prerequisites: Grade of C or better in MATH 2415, 3301 or their equivalents.

## 4310 Complex Variables

Complex numbers, analytic functions, complex line integrals, Cauchy integral formula , and applications.
Prerequisites: Grade of C or better in MATH 2415 or its equivalent

## 4313 Introduction to Regression Analysis

Simple linear regression, theory of least squares, multivariate analysis, theory of the general linear model, application to real life data, modeling, and interpretation of computer-generated graphical and numerical results in regression analysis.
Prerequisites: Grade of C or better in MATH 3370 or its equivalent.

## 4315 Numerical Analysis

Algorithms for solving linear and non-linear equations and systems thereof, interpolating polynomials, finite difference approximations of derivatives, techniques of numerical integration, one- step and multi -step methods for solving ordinary differential equations and systems thereof.
Prerequisites: MATH 2318, 3301, and satisfactory completion of COSC Requirement.
Prepares for: MATH 4316.

## 4316 Topics in Applied Numerical Methods

Topics chosen from linear programming, optimization, numerical simulation, or other fields of interest to students and instructor.
Prerequisites: Grade of C or better in MATH 4315 or its equivalent.

## 4317 Introduction to Probability Theory and Stochastic Processes

Probability, well-known distributions, conditional probability, Bayes’ formula, Markov chain, counting process, Poisson process, Chapman-Kolmogorov equations, gambler’s ruin, branching process.
Prerequisites: Grade of C or better in MATH 3370 or its equivalent

## 4319 Introduction to Design of Experiments

Basic statistical concepts, analysis of variance, randomized blocks, Latin-squares, general factorial designs , 2k and 3k designs, modeling and analysis using MINITAB or SPSS.
Prerequisites: Grade of C or better in MATH 3370 or its equivalent

## 4321 Topics in Secondary Mathematics Education

Introduction to essential topics for pre-service 8-12 mathematics educators. Topics include quantitative reasoning, algebraic thinking, geometry, spatial reasoning, measurement, precalculus, mathematics models, and AP Calculus and Statistics.
Prerequisites: Completion of all other mathematics content courses.

Vector spaces, linear transformations, matrices, determinants, Eigenvalues, Eigenvectors, canonical forms, bi-linear mappings and quadratic forms.
Prerequisites: Grade of C or better in MATH 2318, 3322 or their equivalents.

## 4331 Special Problems

Special advanced problems in mathematics to suit the needs of individual students.
Prerequisites: Consent of Instructor

## 4340 Topology

An introduction to point set topology, including metrizability, compactness, embeddings, Urysohn’s lemma, and homotopy.
Prerequisites: Grade of C or better in MATH 3380 or its equivalent.

## 4380 Theory of Statistical Inference

A formal introduction to statistical inference, sampling theory, general principles of statistical inference, goodness of fit tests, regression and correlation, and analysis of variance.
Prerequisites: Grade of C or better in MATH 3370 or its equivalent.

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