# Mathematics

The USAO mathematics program is designed to meet the needs and interests of the general student, provide the mathematics background required by students in the physical and behavioral sciences, and develop the maturity and competence required by the student preparing for a teaching and/or research career in mathematics.

**Bachelor of Science in Mathematics**

Required Math Core (40 hours):

MATH 1513 College Algebra (3)

MATH 1613 Trigonometry (3)

MATH 1743 Calculus & Analytic Geometry I (3)

MATH 2223 Calculus & Analytic Geometry II (3)

MATH 2243 Calculus & Analytic Geometry III (3)

MATH 3233 Linear Algebra * (3)

MATH 3263 Calculus & Analytic Geometry IV (3)

MATH 3253 Foundations of Mathematics (3)

MATH 3313 Advanced Euclidean Geometry * (3)

MATH 3323 Modern Algebra I (3)

MATH 3333 Modern Algebra II * (3)

MATH 3353 Differential Equations * (3)

MATH 3363 Advanced Calculus I * (3)

MATH 3373 Advanced Calculus II * (3)

MATH 4303 Probability & Statistics I * (3)

MATH 4403 Probability & Statistics II * (3)

MATH 4413 Numerical Analysis * (3)

MATH 4423 Complex Variable Theory * (3)

*and*

PHYS 2114 General Physics I (4)

** Choose 4 of these courses for a total of 12 hours*

**Bachelor of Science in Mathematics/Teacher Certification**

This program qualifies individuals to obtain an Oklahoma teaching certificate and teach mathematics in grades 5-12. For a program checklist for teacher certification, students should consult the mathematics education advisor.

Required Professional Education Core (34 hours)

Required Math Core (44 hours):

MATH 1513 College Algebra (3)

MATH 1613 Trigonometry (3)

MATH 1743 Calculus & Analytic Geometry I (3)

MATH 2223 Calculus & Analytic Geometry II (3)

MATH 2243 Calculus & Analytic Geometry III (3)

MATH 3233 Linear Algebra (3)

MATH 3263 Calculus & Analytic Geometry IV (3)

MATH 3253 Foundations of Mathematics (3)

MATH 3313 Advanced Euclidean Geometry (3)

MATH 3323 Modern Algebra I (3)

MATH 4303 Probability & Statistics I (3)

MATH 4403 Probability & Statistics II (3)

MATH 4463 Teaching Mathematics in Secondary School (3)

*and*

IDS 2011 Foundations of Science Lab (1)

PHYS 2114 General Physics I (4)

**Minor in Mathematics**

18 hours in mathematics from the following *(with approval of math advisor)*:

MATH 1743 Calculus & Analytic Geometry I (3)

MATH 2223 Calculus & Analytic Geometry II (3)

MATH 2243 Calculus & Analytic Geometry III (3)

MATH 3233 Linear Algebra (3)

MATH 3263 Calculus & Analytic Geometry IV (3)

MATH 3253 Foundations of Mathematics (3)

MATH 3313 Advanced Euclidean Geometry (3)

MATH 3323 Modern Algebra I (3)

MATH 3353 Differential Equations (3)

MATH 4303 Probability and Statistics I (3)

MATH 4403 Probability and Statistics II (3)

**COURSE LISTINGS in MATHEMATICS**

0103 BASIC MATH SKILLS

Whole number, integer, and real number operations, fractions, decimals, ratio and proportion, percents. Tuition fee for a 3-hour course; no credit.

0123 BASIC ALGEBRA SKILLS

The real numbers, absolute value, polynomials, factoring, rational expressions, rational exponents, radicals, complex numbers, linear equations and applications, quadratic equations and applications, inequalities. Tuition fee for a 3-hour course; no credit. Prerequisite MATH 0103 or equivalent.

1513 COLLEGE ALGEBRA

Functions and graphs, quadratic equations including systems of quadratic equations; binomial theorem; progressions; logarithms; and exponential functions; determinants; inequalities. Prerequisite: MATH 0123 *or* an ACT mathematics score of 19 or higher. 3 hours

1613 TRIGONOMETRY

Study of trigonometric functions; identities; equations; and applications. Prerequisite or co-requisite: MATH 1513. 3 hours

1743 CALCULUS & ANALYTIC GEOMETRY I

Topics covered include equations of straight lines: conic sections; functions and their graphs; rates of change; limits and continuity of elementary functions; derivatives; applications of derivatives including extreme value problems and curve sketching. Prerequisites: MATH 1513 *and* MATH 1613 *or* the equivalent. 3 hours

2113 NUMBER SYSTEMS AND PROBLEM SOLVING

Inductive and deductive reasoning, relations and functions, number theory, the systems of whole numbers, integers, rational numbers and real numbers, mental math & estimation, proportional reasoning and percents. Prerequisites IDS 1223 or equivalent *and* MATH 0123 *or* an ACT mathematics score of 19 or higher. 3 hours

2203 ELEMENTARY STATISTICS

An introduction to statistical principles and probability, with applications in business, social and behavioral sciences. Prerequisite: MATH 0123 *or* an ACT mathematics score of 19 or higher. 3 hours

2213 FINITE MATH

Elements of set theory. Matrix and determinant, linear programming, decision theory, finance math, and probability theory. Prerequisite: MATH 0123 *or* an ACT mathematics score of 19 or higher. 3 hours

2223 CALCULUS & ANALYTIC GEOMETRY II

Topics covered include antiderivatives; definite integrals, indefinite integrals; applications of integrals; differential and integral calculus of transcendental functions. Prerequisite: MATH 1743. 3 hours

2243 CALCULUS & ANALYTIC GEOMETRY III

Topics covered include integration techniques; improper integral; sequences, infinite series, power series, calculus of polar curves, vector analysis. Prerequisite: MATH 2223. 3 hours

2880 SPECIAL TOPICS

Special topics in mathematics. 1-4 hours (may be repeated for total of 6 hours).

2900 WORKSHOP

Guided study in mathematics under faculty supervision; various topics and methods of instruction. 1-4 hours (may be repeated for total of 6 hours with change in title and topic).

2990 TUTORIAL

Independent study in mathematics under faculty supervision. 1-4 hours (may be repeated for total of 9 hours with change in title and content).

3113 FOUNDATIONS OF GEOMETRY AND MEASUREMENT

Spatial reasoning, constructions, congruence and similarity, concepts of measurement, motion geometry and tessellations, and graphical representations of data. Prerequisite: MATH 2113 *and* admission to Teacher Education. 3 hours

3233 LINEAR ALGEBRA

Systems of linear equations, vector spaces, linear transformations and matrices, dot products and cross products, eigenvalues, and eigenvectors. Prerequisite: MATH 1743 *or* equivalent. 3 hours

3253 FOUNDATIONS OF MATHEMATICS

Study of logic structure in mathematics, mathematical language and proof, set theory, relations and functions, and number system. Prerequisite: MATH 2223. 3hours

3263 CALCULUS & ANALYTIC GEOMETRY IV

Topics covered include vector calculus, multivariable functions and their derivatives; extreme values; Lagrange multipliers; multiple integrals; integration in vector fields. Prerequisite: MATH 2243. 3 hours

3313 ADVANCED EUCLIDEAN GEOMETRY

Logical structure and proofs in several geometries including affine, Euclidean and some finite geometries. Prerequisite *or* co-requisite: MATH 3253. 3 hours

3323 MODERN ALGEBRA I

Introduction to algebraic properties of groups, rings, fields and other abstract algebras. Prerequisite: MATH 3253. 3 hours

3333 MODERN ALGEBRA II

Continuation of MATH 3323. Prerequisite: MATH 3323. 3 hours

3353 DIFFERENTIAL EQUATIONS

Study of some ordinary differential equations, their applications, and methods of obtaining solutions. Prerequisite: MATH 3263. 3 hours

3363 ADVANCED CALCULUS I

Rigorous treatment of topics, including advanced topics in calculus of one variable, calculus of several variables, sequences and series, vector calculus, line and surface integrals. Green’s and Stoke’s theorems. Prerequisite: MATH 3263. 3 hours

3373 ADVANCED CALCULUS II

Continuation of MATH 3363. Prerequisite: MATH 3363. 3 hours

4303 PROBABILITY AND STATISTICS I

Probability and statistical theory including such topics as conditional probability; distributions; moment generating functions; estimation and confidence intervals. Prerequisite: MATH 2223. 3 hours

4403 PROBABILITY AND STATISTICS II

Continuation of MATH 4303. Study includes such topics as curve fitting; testing hypotheses; decision making; estimation; small sample distributions; nonparametric methods; regression; correlation and analysis of variance. Prerequisites: MATH 3263 *and* MATH 4303. 3 hours

4413 NUMERICAL ANALYSIS

Selected topics in this field including approximation theory; iterative methods for solving equations; interpolation; numerical differentiation and integration; and difference equations. Emphasis on methods of high speed computing. Prerequisites: CSCI 2243 *and* MATH 3263. 3 hours

4423 COMPLEX VARIABLE THEORY

Complex numbers, elementary functions and analytic functions, conformal mappings, complex integrals, power series, and integration by the method of residues. Prerequisite: MATH 3263. 3 hours

4450 SEMINAR

Selected topics in mathematics. Topic of study will vary; seminar may be repeated for additional credit with each change in content to total of 6 hours. 1-3 hours.

4463 TEACHING MATHEMATICS IN THE SECONDARY SCHOOL

Survey of methods and materials used in teaching mathematics in secondary school. Prerequisite: admission to Teacher Education in mathematics. Education credit only. 3 hours

4880 SPECIAL TOPICS

Special topics in mathematics. 1-4 hours (may be repeated for total of 6 hours).

4900 WORKSHOP

Related topics and problems in mathematics. 1-6 hours (may be repeated for total of 9 hours with change in title and content).

4990 TUTORIAL

Independent study in mathematics under faculty supervision. 1-4 hours (may be repeated for total of 9 hours with change in title and content).