The course begins a two-semester review of the arithmetic and algebra of the real numbers. Topics include problem solving, sets, arithmetic operations on integers, rational numbers, and real numbers, variable expressions, rectangular coordinate system and graphs, relations and functions, properties of functions, solution techniques and applications of first-degree equations, absolute value, linear functions, systems of linear equations, applications and solution methods for simultaneous linear equations.

This review course is available only for those students who have a need to review elementary algebra. It schedules extra help and instruction and progresses through the material in a paced manner. The course meets five days a week. **This course does not apply toward general education or graduation requirements**. (Fall, Spring)

Prerequisite: MATH 011 with a grade of a C– or higher.

A continuation of the review of algebra begun in MATH 011. Topics include rational expressions and rational equations, proportions, radical expressions and rational exponents, the pythagorean theorem, operations on radical expressions, radical functions, introduction to complex numbers, quadratic equations, solution methods for quadratic equations, and properties of quadratic functions.

This review course is available only for those students who have a need to prepare for a further mathematics course. It schedules extra help and instruction and progresses through the material in a paced manner. This course meets five days a week. **This course does not apply toward general education or graduation requirements.** (Fall, Spring)

Prerequisite: SAT mathematics score of at least 500 or an ACT mathematics score of at least 21, or MATH 011 with a grade of A– or higher, or MATH 012 with a grade of C– or higher.

A study of algebraic expressions, equations, inequalities, and functions. Includes function composition, inverse functions, and graphs of functions. Solutions of linear and quadratic functions are presented (including complex numbers) with extension to other polynomial functions. Topics also include properties and graphs of rational functions, exponential and logarithmic functions and applications, and systems of linear equations and their solutions including matrix methods and determinants. (Fall, Spring)

Prerequisite: SAT mathematics score of at least 500 or an ACT mathematics score of at least 21 and a high school Algebra II with a grade of at least a B, or MATH 110, with a grade of C– or higher, or permission of the department.

A review of basic properties of functions including their domain, range, graphs, and relationship to their inverse functions. An introduction to trigonometry including basic definitions of the trigonometric functions and their properties, identities, and specific trigonometric formulae such as addition and subtraction, double-angle, and half-angle. Applications to triangles are covered utilizing the laws of sines and cosines. Other topics such as polar coordinates and conic sections are presented. This course includes an introduction to sequences, series, limits, and aspects of calculus. (Fall, Spring)

Prerequisite: MATH 121 with a grade of C– or higher, or a high school precalculus course and permission of the instructor.

A study of algebraic and transcendental functions of one variable, limits, continuity, differentiation, integration, and applications of derivatives and integrals. (Spring)

Prerequisite: ENGL 121, MATH 181

An introduction to the library research skills used in mathematics. The use of primary and secondary sources will be discussed as well as publication styles. Students will be exposed to the mathematical software used in mathematics research, and will engage in activities to sharpen critical thinking. In this course, majors in mathematics begin the process of senior portfolio development. **This course fulfills the requirement for UNIV 201; Research in an Academic Discipline, as specified in Southwestern's Quality Enhancement Plan**. (Spring)

Prerequisite: SAT mathematics score of at least 500 or an ACT mathematics score of at least 21 and high school Algebra II with a grade of at least a B or MATH 012 with a grade of A– or higher, or MATH 110 with a grade of C– or higher, or permission of the department.

An introduction to the statistical processes of sampling, descriptive statistics, presentation of data, and inferential statistics. Included are elements of probability, discrete and continuous random variables, and the probability basis for hypothesis testing. Specific statistical techniques and concepts include use of the normal distribution, the t-distribution, Χ^{2} distribution, analysis of variance, correlation, and linear regression. (Fall, Spring)

Prerequisite: MATH 181 with a grade of C– or higher.

A study of the calculus of transcendental functions, introduction to differential equations, applications of integration, techniques of integration, and infinite series. (Fall)

Prerequisite: MATH 282 with a grade of C– or higher.

A study of vectors in two and three dimensions, motion in space, polar, cylindrical and spherical coordinate systems, functions of several variables, partial derivatives, multiple integrals, and differentiation and integration in scalar and vector fields. (Spring)

Prerequisite: Approval by the department chair.

Designed for the student who wishes to do independent study or research. Content and method of study must be arranged prior to registration. May be repeated for a total of 2 credits.

Prerequisite: MATH 283. This is a study of ordinary differential equations with emphasis on the analytic methods for solving them. (Fall, even years)

Prerequisite: MATH 282. This course is a study of Euclidean and non-Euclidean geometry. (Spring, even years)

Prerequisite or corequisite: MATH 283. An introduction to vector spaces and matrix theory over the field of real numbers. (Spring, odd years)

Prerequisite: MATH 283. This course is a study of analytic functions, power series, calculus of residues, and conformal mappings. (Spring, odd years)

Prerequisite: MATH 283 and knowledge of a computer programming language.

This is a course in numerical methods for solving mathematical problems. The writing of computer programs for solving problems is a part of the course. (Spring, even years)

Prerequisite: MATH 361. A study of the abstract systems: groups, rings, fields, and integral domains. (Fall, odd years)

Prerequisite: MATH 282.

A study of the basic ideas of probability theory, discrete and continuous random variables, and their distributions.** This course fulfills the requirement for an upper-division class with QEP components as specified in Southwestern's Quality Enhancement Plan.** (Fall, odd years)

Prerequisite: MATH 282.

A study of topics including Diophantine equations, congruences, prime numbers, and applications. Emphasis is placed on proving theorems. **This course fulfills the requirement for an upper-division course with components as specified in Southwestern's Quality Enhancement Plan.** (Fall, even years)

Prerequisite: MATH 283.

This is a study of functions of one real variable, and the conditions for differentiability and for integrability of these functions. Emphasis is placed on proving theorems. (Spring, odd years)

**This course fulfills the requirement for a capstone/portfolio completion course with components as specified in Southwestern's Quality Enhancement Plan. **(Spring)

Prerequisite: Approval by the department chair.

Designed for the student who wishes to do independent study or research as well as a mathematics lecture based course covering a topic not routinely offered. Content and method of study must be arranged prior to registration. May be repeated for a total of 3 credits.