# Mathematics

## Aims of the Program

First, we aim to give each student an understanding of basic mathematics and its application to solving problems expressible by algebraic equations and inequalities. Second, we aim to train students to understand the fundamental concepts of mathematics so that they can teach the subject on the elementary or secondary level. Third, we aim to give a solid foundation in the area of mathematics which will prepare students to pursue further studies in mathematics, the physical sciences, economics, and the engineering sciences.

### MATH 013 : Algebra

This course provides the student with a basic understanding of addition, subtraction, multiplication, and division of fractions and rational expressions in addition to an understanding of quadratic equations, inequalities, and graphing.

This course does not apply toward general education or graduation requirements.

3

### MATH 110 : College Algebra

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, and systems of linear equations and their solutions including matrix methods and determinants.

3

#### Prerequisites

ALEKS Placement Test Score of 46-60 or an SAT mathematics score of at least 530 or an ACT mathematics score of at least 21 or MATH 013 with a grade of C- or higher or permission of the department.

### MATH 115 : Mathematics in Society

A quantitative reasoning course designed to develop math literacy by considering common occurrences of mathematics topics encountered through living in today’s world. Topics include logical reasoning with sets, interpretation of data, using functional models in real-world applications such as growth and personal finance, basics of probability and statistics with an emphasis on interpreting results, and the design of voting systems by apportionment.

3

#### Prerequisites

SAT mathematics score of at least 530 or an ACT mathematics score of at least 21 or MATH 013 with a grade of C- or higher or permission of the department.

### MATH 116 : Mathematics and Humanity

A survey of general mathematical content with a focus on the human experience of engaging in mathematical thought. The course is taught with a focus on a few select topics which may change from year to year. Topics may include truth and certainty, games and puzzles, the infinite, patterns, art, sculpture, music, and dance.

3

#### Prerequisites

SAT mathematics score of at least 530 or an ACT mathematics score of at least 21 or MATH 013 with a grade of C- or higher or permission of the department.

### MATH 131 : Applied Mathematics

This course covers topics from number concepts and operations, patterns and algebra, geometry and measurement, and probability and statistics with an emphasis on problem solving in the real world. The course covers fundamental aspects of mathematics as required by the Texas Department of Education.

3

#### Prerequisites

ALEKS Placement Test Score of 46-60 or an SAT mathematics score of at least 530 or an ACT mathematics score of at least 21 or MATH 013 with a grade of C- or higher or permission of the department.

### MATH 141 : Introduction to Probability and Statistics

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, X2 distribution, analysis of variance, correlation, and linear regression.

3

#### Prerequisites

ALEKS Placement Test Score of 46-60 or an SAT mathematics score of at least 530 or an ACT mathematics score of at least 21 or MATH 013 with a grade of C- or higher or permission of the department.

### MATH 180 : Precalculus

A review of basic properties of functions including their domain, range, graphs, and relationship to their inverse functions with an emphasis on exponential and logarithmic functions and their applications. 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.

4

#### Prerequisites

ALEKS Placement Test Score of 61-75,  or a high school Algebra II course with a grade of at least a B along with an SAT mathematics score of at least 530 or an ACT mathematics score of at least 21, or MATH 110 with a grade of C- or higher, or permission of the department.

### MATH 181 : Calculus I

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

4

#### Prerequisites

ALEKS Placement Test Score of 76-100 or MATH 180 with a grade of C- or higher or a high school precalculus with a grade of at least a B and permission of the instructor.

### MATH 182 : Calculus II

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

4

#### Prerequisites

with a grade of C- or higher

### MATH 211 : Logic and Set Theory

An introduction to mathematical proofs, elementary logic, sets, equivalence relations, and functions. The emphasis is on understanding and writing of proofs.

3

#### Prerequisites

with a grade of C- or higher

### MATH 283 : Calculus III

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.

4

#### Prerequisites

with a grade of C- or higher

### MATH 298 : Individual Study Topics

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.

1 - 2

#### Prerequisites

Approval by the department chair

### MATH 299 : Directed Group Study Topics

Provides academic departments an opportunity to offer courses in specialized or experimental areas, either lower or upper division, not listed in the undergraduate Bulletin. May be repeated for a total of 3 credits.

1 - 3

#### Prerequisites

Approval by department chair

### MATH 321 : Differential Equations

This is a study of ordinary differential equations with emphasis on the analytic methods for solving them. This course covers first-order differential equations, higher-order differential equations, modeling with differential equations, system of linear differential equations, series solutions, and Laplace transforms.

3

### MATH 322 : Partial Differential Equations

Partial differential equations, Fourier series, boundary value problems, Bessel functions, Legendre polynomials. Offered via Southwestern's virtual classroom from Southern Adventist University.

3

### MATH 341 : Geometry

This course is a study of Euclidean and non-Euclidean geometry. The course is taught within a historical context with a chronological introduction to the history of geometry. The mathematics from ancient times to calculus, together with selected topics from the history of modern mathematics. Offered via Southwestern's virtual classroom from Southern Adventist University.

3

### MATH 361 : Introduction to Linear Algebra

An introduction to vector spaces and matrix theory over the field of real numbers.

3

#### Prerequisites

also recommended.

### MATH 371 : History of Mathematics

A survey of the development of classical mathematics from ancient times to calculus, together with selected topics from the history of modern mathematics. Offered Fall even years via Southwestern's virtual classroom from Southern Adventist University, and Spring even years via Southwestern's virtual classroom from Union College, NE.

3

### MATH 381 : Complex Variables

This course is a study of analytic functions, power series, calculus of residues, and conformal mappings. Offered via Southwestern's virtual classroom from Southern Adventist University.

3

### MATH 411 : Numerical Analysis with Application

This is a course in numerical methods for solving mathematical problems. It covers solution of linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, solution of ordinary differential equations, and error analysis. The writing of computer programs for solving problems is a part of the course. Offered via Southwestern's virtual classroom from Southern Adventist University.

3

#### Prerequisites

and knowledge of a computer programming language (CSIS 110 is recommended).

### MATH 431 : Abstract Algebra

A study of the abstract systems: groups, rings, fields, and integral domains. Offered fall even years via Southwestern's virtual classroom from Southern Adventist University.

3

### MATH 441 : Calculus-Based Probability Theory

A study of the basic ideas of probability theory, discrete and continuous random variables, and their distributions. Offered fall, even years via Southwestern's virtual classroom from Southern Adventist University.

4

### MATH 442 : Actuarial Exam P Preparation

This course prepares students to take Exam P from the Society of Actuaries. Offered via Southwestern's virtual classroom from Union College, NE.

3

### MATH 461 : Number Theory

A study of topics including Diophantine equations, congruences, prime numbers, and applications. Emphasis is placed on proving theorems.

3

### MATH 471 : Real Analysis

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. Offered fall odd years via Southwestern's virtual classroom from Southern Adventist University.

3

### MATH 484 : Mathematics Seminar

Oral presentation of research papers or articles from the variety of topics in mathematics.

1

#### Prerequisites

Senior level standing

### MATH 485 : Portfolio

This course fulfills the requirement for a capstone/portfolio completion course.

1

### MATH 498 : Individual Study Topics

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.

1 - 3

#### Prerequisites

Approval by the department chair

### MATH 499 : Directed Group Study Topics

Provides academic departments an opportunity to offer courses in specialized or experimental areas, either lower or upper division, not listed in the undergraduate Bulletin.  . May be repeated for a total of 3 credits.

1 - 3

#### Prerequisites

Approval by department chair