# 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, 2 ^{k} and 3^{k} 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

I**ntroduction 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.

## 4330 Advanced Linear Algebra

**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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