Mathematics

Faculty/Staff

Gerald Springer, Chair; Paulos Berhane, Jonathan Duarte, Lawrence Turner

Adjunct: Richard DeLong, George Parry

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.

Programs

  • B.A. Mathematics
  • B.S. Mathematics
  • B.S. Mathematical Physics
  • B.S. Mathematics - Secondary Certification
  • Minor in Mathematics, Mathematics - Secondary Certification

Mathematics, B.A.

MATH 181 Calculus I 4
MATH 201 Research Methods in Mathematics 1
MATH 282 Calculus II 4
MATH 283 Calculus III 4
MATH 321 Differential Equations 3
MATH 341 Geometry 3
MATH 361 Introduction to Linear Algebra 3
MATH 431 Modern Algebra 3
MATH 471 Advanced Calculus 3
MATH 485 Portfolio 1
MATH Electives  upper division 6
Total: 35

Mathematics, B.S.

MATH 181 Calculus I 4
MATH 201 Research Methods in Mathematics 1
MATH 282 Calculus II 4
MATH 283 Calculus III 4
MATH 321 Differential Equations 3
MATH 341 Geometry 3
MATH 361 Introduction to Linear Algebra 3
MATH 431 Modern Algebra 3
MATH 461 Number Theory 3
MATH 471 Advanced Calculus 3
MATH 485 Portfolio 1
MATH Electives - upper division 6
Total: 38

Required cognate:

CSIS 110 Principles of Computer Programming I 3
or equivalent

Minor in Mathematics

MATH 181 Calculus I 4
MATH 282 Calculus II 4
MATH 283 Calculus III 4
MATH Electives  upper division 6
Total: 18

Mathematical Physics, B.S.

MATH 181 Calculus I 4
MATH 201 Research Methods in Mathematics 1
MATH 282 Calculus II 4
MATH 283 Calculus III 4
MATH 321 Differential Equations 3
MATH 361 Introduction to Linear Algebra 3
MATH 381 Complex Variables 3
MATH 411 Numerical Analysis 3
MATH 431 Modern Algebra or
MATH 471 Advanced Calculus 3
MATH 455 Probability Theory 3
MATH 485 Portfolio 1
PHYS 121 General Physics I 4
PHYS 122 General Physics II 4
PHYS 221 General Physics with Calculus I 1
PHYS 222 General Physics with Calculus II 1
PHYS 311 Modern Physics 3
PHYS 322 Classical Mechanics 3
PHYS 351 Electromagnetic Fields 3
PHYS 411 Quantum Mechanics 3
Total: 54

Required cognates:

CHEM 111 General Chemistry I 4
CHEM 112 General Chemistry II 4
CSIS 110 Principles of Computer Programming I 3
or equivalent

Teaching Certification Program

The following mathematics major and minor are for teaching certification only. Requirements for certification are listed in the Education section of this Bulletin.

You must make formal application for admittance to the Teacher Education Program. Applications are available at the Education Department office.

Mathematics - Secondary Teaching Area - B.S.

MATH 181 Calculus I 4
MATH 201 Research Methods in Mathematics 1
MATH 241 Introduction to Probability and Statistics 3
MATH 282 Calculus II 4
MATH 283 Calculus III 4
MATH 321 Differential Equations 3
MATH 341 Geometry 3
MATH 361 Introduction to Linear Algebra 3
MATH 431 Modern Algebra 3
MATH 485 Portfolio 1
MATH Electives  upper division 9
Total: 38

Minor in Mathematics - Secondary Certification

MATH 121 Precalculus 3
MATH 181 Calculus I 4
MATH 241 Introduction to Probability and Statistics 3
MATH 282 Calculus II 4
MATH 341 Geometry 3
MATH 361 Introduction to Linear Algebra 3
MATH Electives  upper division 6
Total: 26

Courses

MATH 013 - Algebra (3 hours)

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 meets five days a week. This course must be taken with a lab concurrently.  This course does not apply toward general education or graduation requirements.  (Fall, Spring)

MATH 110 - College Algebra (3 hours)

Prerequisite:  SAT mathematics score of at least 500 or an ACT mathematics score of at least 21 or MATH 013 with a C– or higher or permission of the department

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)

MATH 121 - Precalculus (3 hours)

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 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)

MATH 181 - Calculus I (4 hours)

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)

MATH 201 - Research Methods in Mathematics (1 hour)

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)

MATH 241 - Introduction to Probability and Statistics (3 hours)

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 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, Χ2 distribution, analysis of variance, correlation, and linear regression. (Fall, Spring)

MATH 282 - Calculus II (4 hours)

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)

MATH 283 - Calculus III (4 hours)

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)

MATH 291 - Selected Topics (1 hour)

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.

MATH 321 - Differential Equations (3 hours)

Prerequisite: MATH 283

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

MATH 341 - Geometry (3 hours)

Prerequisite: MATH 282

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

MATH 361 - Introduction to Linear Algebra (3 hours)

Prerequisite or corequisite: MATH 283

An introduction to vector spaces and matrix theory over the field of real numbers. (Spring, odd years)

MATH 381 - Complex Variables (3 hours)

Prerequisite: MATH 283

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

MATH 411 - Numerical Analysis with Application (3 hours)

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)

MATH 431 - Modern Algebra (3 hours)

Prerequisite: MATH 361

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

MATH 455 - Probability Theory (3 hours)

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)

MATH 461 - Number Theory (3 hours)

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)

MATH 471 - Advanced Calculus (3 hours)

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)

MATH 485 - Portfolio (1 hour)

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

MATH 491 - Selected Topics (1-3 hours)

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.