# Mathematics

**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 (41 hours):

Course |
Title |
Hours Required |

MATH 1513 | College Algebra | 3 |

MATH 1613 | Trigonometry | 3 |

MATH 1745 | Calculus & Analytic Geometry I | 5 |

MATH 2225 | Calculus & Analytic Geometry II | 5 |

MATH 3233 | Linear Algebra * | 3 |

MATH 3243 | Calculus III | 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 7-12. For a program checklist for teacher certification or information about the provisional teaching endorsement, students should consult the mathematics education advisor.

Required Professional Education Core (30 hours)

Required Math Core (48 hours):

Course |
Title |
Hours Required |

MATH 1513 | College Algebra | 3 |

MATH 1613 | Trigonometry | 3 |

MATH 1745 | Calculus & Analytic Geometry I | 5 |

MATH 2225 | Calculus & Analytic Geometry II | 5 |

MATH 3233 | Linear Algebra | 3 |

MATH 3243 | Calculus III | 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 |
||

PHYS 1301 | General Physics Laboratory I | 1 |

PHYS 2114 | General Physics I | 4 |

**Minor in Mathematics **

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

Course |
Title |
Hours Required |

MATH 1745 | Calculus & Analytic Geometry I | 5 |

MATH 2225 | Calculus & Analytic Geometry II | 5 |

MATH 3233 | Linear Algebra | 3 |

MATH 3243 | Calculus III | 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 & Statistics I | 3 |

MATH 4403 | Probability & 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, polynomicals, 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. 3 hours. Prerequisite: MATH 0123 *or* an ACT mathematics score of 19 or higher.

** 1613 TRIGONOMETRY**

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

** 1745 CALCULUS & ANALYTIC GEOMETRY I**

Differential and integral calculus of elementary functions, with associated analytic geometry. 5 hours. Prerequisites: MATH 1513 *and* MATH 1613 (*or* the equivalent of these).

**2113 NUMBER SYSTEMS AND PROBLEM SOLVING**

Materials and content of the mathematics commonly included or related to today's lower elementary school curriculum. Does not meet degree requirements for math majors. 3 hours. Prerequisites: IDS 1223 and MATH 0123 or an ACT mathematics score of 19 or higher.

** 2203 ELEMENTARY STATISTICS**

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

** 2213 FINITE MATH**

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

**2225 CALCULUS & ANALYTIC GEOMET RY II**

Theory and techniques of single variable calculus, including differentiable functions, limits and theory of curves. 5 hours. Prerequisite: MATH 1745.

**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**

Materials and content of the mathematics commonly included or related to today's curriculum in the intermediate grades. Does not meet degree requirements for math majors. 3 hours. Prerequisite: MATH 2113 *and* admission to Teacher Education.

**3233 LINEAR ALGEBRA**

Systems of linear equations, vector spaces, linear transformations and matrices, dot products and cross products, eigenvalues, and eigenvectors. 3 hours. Prerequisite: MATH 1745 *or* equivalent.

**3243 CALCULUS III**

Theory and techniques of single and multivariable calculus, partial differentiation, multiple integration, and linear differential equations. 3 hours. Prerequisites: MATH 2225.

**3253 FOUNDATIONS OF MATHEMATICS**

Study of logic structure in mathematics, mathematical language and proof, set theory, relations and functions, and number system. 3 hours. Prerequisite: MATH 2225.

**3313 ADVANCED EUCLIDEAN GEOMETRY**

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

**3323 MODERN ALGEBRA I**

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

**3333 MODERN ALGEBRA II**

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

**3353 DIFFERENTIAL EQUATIONS**

Study of some ordinary differential equations, their applications, and methods of obtaining solutions. 3 hours. Prerequisite: MATH 3243.

**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. 3 hours. Prerequisite: MATH 3243.

**3373 ADVANCED CALCULUS II**

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

**4303 PROBABILITY AND STATISTICS I**

Probability and statistical theory including such topics as conditional probability; distributions; moment generating functions; estimation and confidence intervals. 3 hours. Prerequisite: MATH 2225.

**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. 3 hours. Prerequisites: MATH 3243 *and* MATH 4303.

**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. 3 hours. Prerequisites: CSCI 2243 *and* MATH 3243.

**4423 COMPLEX VARIABLE THEORY**

Complex numbers, elementary functions and analytic functions, conformal mappings, complex integrals, power series, and integration by the method of residues. 3 hours. Prerequisite: MATH 3243.

**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. 3 hours. Prerequisite: admission to Teacher Education in mathematics. Education credit only.

**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).