Mathematics

Anderson, Aslan, Coskun, Davenport, Dorsett, Faulkenberry, Heath, Huse, Kreminski (head), Simonelli, Singleton, Sirakov, Staebler, Webster

Binnion Hall, Room 305, 903.886.5157

The Department of Mathematics offers the Bachelor of Science or Bachelor of Arts degree with a major in mathematics. This major prepares graduates for careers in industry, government, business, scientific and technological fields, computing and information science, actuarial work, and education. A graduate with a major in mathematics should possess the following competencies: calculus, discrete mathematics, and abstract algebra.

The Bachelor of Science or Bachelor of Arts degree with a major in mathematics with teacher certification is offered by the department. A student may select a broadfield major or select a field outside mathematics as a minor. This major prepares graduates for careers in teaching at the secondary level. A graduate with a major in mathematics should possess the following competencies: trigonometry, calculus, discrete mathematics, geometry, abstract or linear algebra, history of mathematics, and number theory.

Students seeking a bachelor's degree in the following major must complete:

(1) degree requirements for a Bachelor of Arts or Science degree and (2) University Studies requirements (refer to those sections of this catalog). In addition, courses in the major must be completed as shown below.

Major in Mathematics

Required courses in the major (33 semester hours)

Math 191, 192, 314, 331, 334, plus 15 sh (Adv) exclusive of 301, 310, 350, 351, 372, 453.

Required support courses (10 semester hours)*

CSci 151, 152 or 241 or 270; Phys 2114 or 2124

*These courses may apply on a second major or minor.

SUGGESTED CURRICULUM OUTLINE (B.S.)

Freshman                              Sophomore                                       Junior                                            Senior
Math 191, 192            Math 314, 331, 3 sh (Adv)  Math, 6 sh (Adv) excl.    Math 334 and 6 sh (Adv)
Eng 101, 102               Psci 220, 221                       of: 301, 310, 350              excl. of: 301, 310,
US Science, 4 sh         US Humanities, 3 sh           351, 372, and 453             350, 351, 372, 453
Hist 121, 122              US Vis/Perf Arts, 3 sh         Spc 111 or 245, or 348     Second Major/Minor
Csci 151; 152 or         US Soc/Behav Sci, 3 sh       Electives, 11 sh                  9 sh
241 or 270                   Second Major/Minor,         Second Major/Minor,      Electives, 12 sh
                                        3 sh                                      6 sh
                                    US PE Activity, 2 sh            Phys 211 or 212
                                                                                
_________________ ___________________        ___________________     _____________________
       30 sh                                30 sh                            30 sh                                   30 sh

Total Semester Hours: 120

See Guide for Initial Enrollment in Mathematics on following pages.

Second Major in Mathematics

A student who elects a second major in mathematics must complete a minimum of 24 sh including Mathematics 191, 192, 314, and 12 sh chosen from 315, 317, 321, 331, 334, 335, 401, 426, 436, 437, 438, 440, and 453. Selection of courses should be determined by the student's interests. More than eight courses is strongly recommended, especially for those students who plan to do graduate study in mathematics. Please consult mathematics staff members for advice.

Minor in Mathematics

A student in the College of Arts and Sciences who elects a minor in mathematics must complete a minimum of 18 sh including Mathematics 191, 192, and ten semester hours advanced.

Mathematics 301, 350, 351, 361, 362, and 372 may not be used to satisfy mathematics requirements for a major or minor in non-education programs.

Teacher Education Programs

Students seeking a bachelor's degree in any of the following teacher education programs must complete: (1) degree requirements for a Bachelor of Arts or Science degree (refer to the bachelor's degree requirements section of this catalog), (2) University Studies requirements, (refer to that section of this catalog), (3) requirements for admission to and retention in the Teacher Education Program (refer to the Center for Educator Certification and Academic Services section of this catalog), (4) professional development courses (refer to the appropriate departmental section in this catalog, i.e. Department of Elementary Education or Department of Secondary and Higher Education). In addition, courses in the major must be completed as shown below.

Major in Mathematics

Secondary Teacher Certification

Required courses in the this major (36 semester hours)

Math 191, 192, 321, 331, 334, 335, 401 or 453, 426, 437, 460, and 4 sh from 314, 315, 317, 401, 436, 438, 440, 460.

Required support courses (6 semester hours)*

Csci 151, 152 or 241 or 270.

*These courses may apply on a second major or minor.

SUGGESTED CURRICULUM OUTLINE (B.S.)

Freshman                         Sophomore                      Junior                                 Senior
Math 191, 192                 Math 321, 331, 335         Math 334, 426, 401 or      Math 437, 460 and 4 sh from
Eng 101, 102                    US Humanities, 3 sh       453                                     314, 315, 317, 401,
Hist 121, 122                   Psci 220, 221                   Psy 300                              436, 438, 440
Csci 151; 152 or              US Science, 8 sh*            Spc 111 or 245 or 348       SHEd 302, 401,  
    241 or 270                    US PE Activity, 2 sh       SHEd 300, SpEd 346 or    404, 405
US Vis/Perf Arts, 3 sh     SHEd 200                        475; US Soc/Behav Sci,   Elective, 2 sh 
 Elective, 3 sh                   *-Phys211 or 212           3 sh; ETec 424; Rdg 370
__________________       ___________________  ___________________     _____________________
        32 sh                                   31 sh                              30 sh                                   27 sh

Total Semester Hours: 120

*Students who have credit for this course in high school may take an approved advanced course in its place.

Specialization in Mathematics for Interdisciplinary Studies Major (4-8 Mathematics Teacher Certification)

Students desiring to teach in elementary school should select the interdisciplinary studies major with an academic specialization.

The programs are designed with emphasis on solving problems which arise from real life settings. The development of skills of mathematics and the correct application of mathematical principles and methods are essential to this process. This curriculum is planned with these objectives in mind.

Required courses in the specialization (18 semester hours)

Math 141, 301, 350, 351, 361, 362, 372, 380, 453: and 3 sh from Math 142, 191, 321

Other requirements

Refer to the Department of Elementary Education's section of this catalog.

Guide for Initial Enrollment in Mathematics

The Texas Higher Education Coordinating Board has ruled that a mathematics course taught in a college or university may count toward the baccalaureate degree requirements only if it has a prerequisite of high school Algebra II. Generally, students not taking Algebra II high school will need remediation in college. A diagnostic test will be given to each entering student for initial placement in mathematics courses. (See "Basic Skills Requirements.")

Mathematics Courses (Math)

131. Intermediate Algebra. Three semester hours.

May not be used to satisfy any mathematics or degree requirements. Basic algebraic operations, equations and inequalities, polynomials, functions, rational expressions, exponents and radicals, quadratic equations, graphing and geometry in the plane, sequences and series. This course is to prepare students for further study at the level of college mathematics.

141. (MATH 1314) College Algebra. Three semester hours.

Quadratic equations; solutions of equations in several unknowns; ratio and proportion; variation; arithmetic and geometric progressions; the binomial theorem; permutations and combinations; elementary theory of equations.

142. (MATH 1316) Pre-Calculus. Three semester hours.

Trigonometric functions and their graphs; radian measurement; solution of triangles; identities; logarithmic and exponential functions; trigonometric equations; applications of trigonometry; conic sections and their graphs. Prerequisite: High school geometry and two years of high school algebra or Math 141.

175. (MATH 1324) Mathematics for Business Applications. Three semester hours.

Linear equations, quadratic equations, functions, inequalities, mathematics of finance, linear programming, matrices and determinants, systems of linear equations, probability. Applications to management, economics, and business.

176. (MATH 1325) Mathematics for Business Applications II. Three semester hours.

The derivative, graphing and optimizations, exponential and logarithmic functions, integration. Applications to management, economics, and business. Prerequisite: Math 141 or 175.

179. Mathematics: Applications and Philosophy. Three semester hours.

Applications of mathematics which may include graph theory, linear programming, statistics, probability, coding theory and conic sections; logic; topics from the history of mathematics; the mathematical method and philosophy; mathematical writings.

191. (MATH 2313) Calculus I. Four semester hours.

Limits; continuity; derivatives; curve sketching; applications of the derivative; the definite integral; derivatives and integrals of the logarithmic, exponential and trigonometric functions; and use of computer technology. Prerequisites: Two years of High School algebra and trigonometry or Math 142.

192. (MATH 2313) Calculus II. Four semester hours.

Techniques of integration; applications of the integral; improper integrals; limits involving indeterminate forms; sequences and series; some exposure to multiple integrals; and use of computer technology. Prerequisite: Math 191.

198. Computer Algebra Systems for Calculus Applications. One semester hour (2 lab).

This course will introduce the student to use of computer algebra systems for solution of problems found in first year calculus courses. Suggested for concurrent enrollment in Math 191, 192, or 314. 

301. Introductory Geometry. Three semester hours.

Topics from plane and solid Euclidean geometry, including the properties of parallels, perpendiculars, triangles, and circles along with perimeter and formulas for area of place regions and for the surface area and volume of solids. Prerequisite: Math 141.

314. Calculus III. Four semester hours.

Continuation of infinite series; vector-valued functions; partial derivatives; multiple integrals; three-dimensional geometry; Green's Theorem; Stroke's Theorem. Prerequisite: Math 192.

315. Differential Equations. Three semester hours.

First order equations, second order linear equations, power series solutions, Laplace Transformations, and application. Prerequisite: Math 225.

317. Numerical Analysis. Three semester hours.

Computer algebra systems will be introduced. Topics include methods for approximate solutions of equations in one variable, polynomial approximation methods, numerical calculus, numerical solutions to ordinary differential equations, linear systems of equations, and difference equations. Prerequisite: Csci 151 and 152. Co-requisite: Math 192.

321. College Geometry. Three semester hours.

A study of advanced topics in Euclidean plane geometry and an introduction to non-Euclidean geometry. Emphasis will be placed on the axiomatic method. Prerequisite: Math 331.
 

331. Discrete Mathematics. Three semester hours.

Mathematical models, mathematical reasoning, sets, binary relations, counting and algorithm analysis, infinite sets. Prerequisites: Csci 151 and Math 192.

334. Introduction to Abstract Algebra. Three semester hours.

Properties of the integers, permutations, groups, rings, integral domains and fields. Prerequisites: Math 331.

335. Linear Algebra. Three semester hours.

Vector spaces; linear transformations; matrices; determinants; systems of linear equations; equivalence relations on matrices; characteristic vectors, operators. Prerequisites: Math 331.

350. Topics in Mathematics for Elementary Teachers I. Three semester hours.

Topics include problem solving and reasoning, sets, numeration, the four fundamental operations of arithmetic, number theory, intergers, fractions, decimals, mental arithmetic and estimation. Students should already have substantial skills in these areas. The course focuses on underlying concepts and multiple techniques of explaining the concepts in addition to extended problem-solving. Prerequisites: Math 141.

351. Topics in Mathematics for Elementary Teachers II. Three semester hours.
Topics include ratio and proportion, percents, statistics, probability, geometry and measurement. Students should already have substantial skills in these areas. Problem solving undergrids all of these topics. The course focuses on underlying concepts and multiple techniques of explaining the concepts. Prerequisite: Math 350

372. Mathematics Structures and Applications. Three semester hours.

A study of the algebraic processes, polynomials, equations, inequalities, functions, graphs, and mathematics of finance. Prerequisites: Math 141.

397. Special Topics. One to four semester hours.

Organized class. May be repeated when topics vary.

398. Advanced Computer Algebra Systems Applications. One semester hour (2 lab).

This course will introduce the student to the use of computer algebra systems for solution of problems found in advanced mathematics courses. Prerequisites: Math 192 or Junior standing.

401. Introduction to Mathematical Statistics. Three semester hours.

Classical probability theory; discrete and continuous random variables; distribution functions; expectation; law of large numbers; central limit theorem; applications. Prerequisites: Math 192.

426. History of Mathematics. Three semester hours.

Selected topics in the history of mathematics; the growth of algebra, trigonometry, geometry, and the calculus; the contribution of different cultures; selected biographies of mathematicians. Prerequisites: Math 192 or consent of Instructor.

436. Introduction to Analysis. Three semester hours.

Sequences; limits; functions continuity; differentiation; integration. Prerequisites: Math 192 and 331.

437. Elementary Number Theory. Three semester hours.

Mathematical induction, divisibility, prime numbers, congruencies, factorization, arithmetic functions, quadratic reciprocity, primitive roots, diophantine equations. Prerequisite: Math 331.

438. Complex Analysis. Three semester hours.

The complex numbers; elementary functions and their mapping; complex limits and power series; analytic functions; conformal mapping and boundary value problems; Contour integrals; Cauchy's Theorem; Taylor and Laurent expansions; residues; Liouville's Theorem. Prerequisites: Math 314.

440. Introduction to Topology. Three semester hours.

Topological spaces, topology of the real line, metric spaces, connectedness, compactness, separation axioms, mappings continuity, homeomorphisms, product spaces. Prerequisite: Math 331

453. Essentials of Statistics. Three semester hours.

Techniques of statistical applications concerning descriptive statistics, test of hypothesis, regression and analysis of variance. Prerequisite: One course in college mathematics.

460. Technology and Topics in Mathematics for Secondary Teachers. Three semester hours.

Exploration of problems in algebra, trigonometry, analytic geometry, calculus, Euclidean geometry, probability, statistics and discrete mathematics using technology. The course is intended as a capstone study for prospective secondary teachers of mathematics. Graphing calculators and computers will be employed to illustrate and encourage conjecturing and problem solving with an emphasis on applications. In addition, a brief survey will be made of major documents and resources pertinent to secondary mathematics teachers, such as the NCTM standards. Prerequisite: Math 331 or consent of instructor.

489. Independent Study. One to four semester hours.

Individualized instruction/research at an advanced level in a specialized content area under the direction of a faculty member. May be repeated when the topic varies. Prerequisite: consent of department head.

497. Special Topics. One to four semester hours.

Organized class. May be repeated when the topics vary. Prerequisite: consent of department head.

Note: For graduate courses, see Graduate Catalog.