Department of Mathematics and Statistics

Professor Ronald M. Anderson, Chairperson.

Horn Professor and ESA Distinguished Professor Martin; Professors E. Allen, L. Allen, Barnard, Bennett, Chanda, Dayawansa, Duran, Ford, Gilliam, Gustafson, Harris, Lewis, McLaughlin, Mansouri, Newman, Pearce, Ruymgaart, Schovanec, Strauss, Tarwater, and Victory; Associate Professors Byerly, Cordero, Drager, Gornet, Kellogg, Lee, Mitra, Moreland, M. Shubov, V. Shubov, Sun, Wang, Weinberg, White, Yang, and Zhang; Assistant Professors Avalos, Dunyak, Korchagin, and Seaquist; Visiting Assistant Professors Draayer and Ji.

This department supervises the following degree programs: MATHEMATICS, Bachelor of Arts or Bachelor of Science, Master of Arts or Master of Science, Doctor of Philosophy; STATISTICS, Master of Science. In addition, the department supervises programs leading to minors in mathematics and to teacher certification in mathematics at the elementary and secondary levels.

Flexibility of elective courses in mathematics is designed to allow the student to prepare to enter the industrial job market, to enter graduate school or professional school, or to begin a teaching career. Recent Tech mathematics graduates have been employed by companies in aerospace (N.A.S.A., defense), electronics (computers, telecommunications), finance (banks, brokerage, insurance), government (federal agencies, offices, laboratories), petroleum (geophysical, oil), and transportation (airlines, trucking). Some graduates have entered law school or medical school, while many have pursued graduate degrees at various universities.

The curricula leading to the Bachelor of Arts or Bachelor of Science degrees follow the general patterns described in the Arts and Sciences section of this catalog. Immediately upon declaring a major in mathematics, students should consult with the department's Director of Undergraduate Studies for the design and approval of their individual mathematics degree programs. A typical program includes proficiency in calculus at the level of MATH 2350, plus MATH 2360, 3354, 3360, 4350 and at least two of MATH 4343, 4351, 4354, and 4360. In addition, candidates for the B.A. degree must take at least 6 additional hours of approved electives in mathematics at the 3000-level and above, while candidates for the B.S. degree must take at least 12 additional hours of approved electives in mathematics at the 3000-level and above.

For a major in mathematics, a minimum of 30 to 39 hours of mathematics is required, depending on where the student can start in calculus and which degree the student seeks. Also, a student must have a grade of C or better in each mathematics course counted toward the degree.

Candidates for the B.S. degree must choose their minor from the following: atmospheric science, biology, botany, chemistry, chemical engineering, civil engineering, computer science, economics, electrical engineering, exercise and sport sciences, geosciences, industrial engineering, mechanical engineering, microbiology, petroleum engineering, physics, or zoology. A minor must include 18 semester hours, 6 of which must be advanced, in the minor department. Courses counted for the minor must be approved by the minor department.

In addition to the minor, candidates for the B.S. degree must complete a full year (8 hours) in a laboratory science (biology, botany, chemistry, geosciences, microbiology, physical geography, physics, or zoology).

The Department of Mathematics and Statistics also participates with the Department of Computer Science to offer a Dual Degree Program in Mathematics and Computer Science. This is a five year program. See the Computer Science portion of the catalog for the curriculum, culminating in a B.S. degree in Mathematics from the College of Arts and Sciences, and a B.S. degree in Computer Science from the College of Engineering.

A minor in mathematics requires 18 semester hours, at least 6 of which must be at the 3000-level or above and must be approved by the Director of Undergraduate Studies. The minor sequence is MATH 1351, 1352, 2350, and 2360 plus 6 semester hours of approved courses at the 3000-level or above. Students cannot receive minor credit for both MATH 3350 and 3354. Students must receive a grade of at least C in all courses counted toward a minor in mathematics.

For the minor and major in mathematics at least one half of the upper level mathematics courses must be taken in the Department of Mathematics and Statistics at Texas Tech University. This residency requirement will be waived by the department only in very exceptional circumstances.

Teacher Education. The Department of Mathematics and Statistics cooperates with the College of Education in offering plans for teacher certification in mathematics at both the elementary and the secondary school levels. The student preparing to teach in the secondary school may select mathematics as a teaching field and complete the program for teacher certification in mathematics. The student preparing to teach in the elementary school may select mathematics as an area of academic specialization in elementary education. The student should consult the Department of Mathematics and Statistics concerning teacher certification. A student must have a grade of C or better in each mathematics course counted toward elementary or secondary education certification.

The courses offered in mathematics for students intending to prepare themselves for elementary teaching are MATH 1320, 2370, 2371, 3370, 3371, 4370, and 4371.

The minimum requirements for the teaching field in mathematics (option II) at the secondary level are:

(1) MATH 1351 and 1352 (See Guide for Initial Enrollment in Mathematics) and MATH 2350, 2360, 4331 and 4342;

(2) 6 additional hours to be chosen from MATH 3354, 3360, 3430, 4350, 4362.

Mathematics Placement. Placement for students into entry-level mathematics courses (0301-2322) is based on either appropriate previous prerequisite collegiate mathematics credit or the results of the departmentally administered Mathematics Placement Examination (MPE). The MPE will be given on the first day of each summer orientation for students enrolling in the fall and during the open registration periods prior to each semester and term. Students without appropriate prerequisite collegiate mathematics credit will be placed into entry-level courses based on the results of the MPE. Students may retake the MPE if necessary. Students who have scored at least 610 on the SATM or at least 26 on the ACTM may enroll in any entry-level mathematics course independent of whether they have the appropriate previous prerequisite collegiate mathematics credit or the appropriate MPE score. However, they are encouraged to take the MPE during an orientation session to provide them with a current assessment of their mathematics skills for advisement purposes.

Students having 6 hours or less of basic mathematics requirements in their degree program may wish to satisfy the requirements by choosing from among these courses: MATH 1320, 1321, 1330, 1331, 1350, 1351, 1352, 2300.

The following list describes the mathematics courses most frequently taken by freshmen:

·MATH 0301 and 0302 are remedial courses and do not carry any degree credit.
Students earning a grade of A or B in MATH 0302 will be eligible to enroll in MATH 1320, 1330, or 1550.

·MATH 1320 College Algebra

·MATH 1330 Introductory Mathematical Analysis

·MATH 1321 Trigonometry

·MATH 1350 Analytical Geometry

·MATH 1351 Calculus I

·MATH 1550 Precalculus

NOTE: Satisfactory score on the placement exam is required for entrance to all above courses. TASP students who have not passed the mathematics section of the TASP Test may not enroll in MATH 1320 or 1321 until they have successfully completed their prescribed program of TASP mathematics skills development. See course listings for descriptions and prerequisites for the courses listed above.

Courses in Mathematics. (MATH)

0301. Essential Mathematics (3:3:0). A developmental course for students with weak preparation in fundamental mathematics, high school algebra, and geometry. MATH 0301 counts in the student's semester load and is recorded on the transcript, but the hours do not count as part of the minimum number of hours required for graduation in any degree program of the University. Grades are awarded for the semester, but they are not computed in the student's grade point average. This course counts for TASP math skills development provided the student has met with an advisor in the TASP Skills Development Office in 72 Holden Hall.

0302. Intermediate Algebra (3:3:0). Prerequisite: Score on the Mathematics Placement Examination of 2 or higher or a grade of B or better in MATH 0301. A developmental course for students with weak preparation in algebra or who need a review of high school algebra before enrolling in MATH 1320 or higher. MATH 0302 counts in the student's semester load and is recorded on the transcript, but the hours do not count as part of the minimum number of hours required for graduation in any degree program of the University. Grades are awarded for the semester, but they are not computed in the student's grade point average. This course counts for TASP math skills development provided the student has met with an advisor in the TASP Skills Development Office in 72 Holden Hall.

1320. College Algebra (3:3:0). Prerequisite: Score on the mathematics placement examination of 3 or higher or a grade of B or better in MATH 0302. Inequalities; determinants; theory of equations; binomial theorem; progressions; mathematical induction. [MATH 1314]

1321. Trigonometry (3:3:0). Prerequisite: Score on the mathematics placement examination of 4 or higher MATH 1320, or a grade of A in MATH 0302. Trigonometric functions; radians; logarithms; solutions of triangles; identities; trigonometric equations; complex numbers; De Moivre's Theorem. [MATH 1316]

1330, 1331. Introductory Mathematical Analysis (3:3:0 each). Score on the mathematics placement examination of 3 or higher or a grade of B or better in MATH 0302. MATH 1330 contains set theory; inequalities; equations, relations; functions; vectors; matrices; linear programming; probability; progressions; mathematics of finance. MATH 1331 contains differential, integral, and multivariable calculus. [MATH 1324,1325]

1350. Analytical Geometry (3:3:0). Prerequisite: Score on the mathematics placement examination of 6 or higher and knowledge of basic trigonometry or MATH 1320 and 1321. Fundamental concepts of analytical geometry. [MATH 1348, 2312]

1351. Calculus I (3:3:0). Score on the mathematics placement examination of 7, MATH 1350, 1550, or score on MPE of 5 and MATH 1321. Differentiation of algebraic and transcendental functions, applications of the derivative, differentials, indefinite integrals, definite integrals. (Honors section offered.) [MATH 2313]

1352. Calculus II (3:3:0). Prerequisite: MATH 1351 or consent. Methods of integration, parametric equations, polar coordinates, hyperbolic functions, applications. (Honors section offered.) [MATH 2314]

1550. Precalculus (5:5:0). Prerequisite: Score on the MPE of 3 or higher. Topics from college algebra, trigonometry, and analytical geometry that are necessary prerequisites for calculus I.

2300. Statistical Methods (3:3:0). Prerequisite: Score on MPE of 4 or higher or MATH 1320 or equivalent. Methods of analyzing data; statistical concepts and models; estimation; tests of significance; introduction to analysis of variance, linear regression, and correlation. [MATH 1342]

2322. Analytical Geometry and Calculus for Engineering Technology I (3:3:0). Prerequisite: Score on MPE of 6 or higher or MATH 1320 and 1321. This course is intended for students of engineering technology. It covers selected topics in analytical geometry and stresses the geometric and physical aspects of calculus.

2323. Calculus for Engineering Technology II (3:3:0). Prerequisite: MATH 2322. This course is a continuation of MATH 2322.

2350. Calculus III (3:3:0). Prerequisite: MATH 1352. Partial differentiation; functions of several variables; multiple integrals, line integrals, surface integrals, Stokes Theorem. (Honors section offered.) [MATH 2315]

2360. Linear Algebra (3:3:0). Prerequisite: MATH 1352. Finite-dimensional vector spaces; linear transformations and matrices; eigenvalues and eigenvectors. [MATH 2318]

2370. Elementary Analysis I (3:3:0). Prerequisite: MATH 1320, and sophomore standing. Analytic geometry and the real number system with applications. Not for engineering, science, or mathematics majors.

2371. Elementary Analysis II (3:3:0). Prerequisite: MATH 1350 or 2370. Elementary differential and integral calculus with application. Not for engineering, science, or mathematics majors.

3322. Higher Mathematics for Engineering Technology (3:3:0). Prerequisite: MATH 2323. Topics include differential equations, Laplace transform, Fourier series, and vector and matrix algebra.

3342. Mathematical Statistics for Engineers and Scientists (3:3:0). Prerequisite: MATH 2350. Descriptive statistics; elementary probability; random variables and distributions; mean; variance; parameter estimation; hypothesis testing; regression; analysis of variance. MATH 3342 and 4332 cannot both be counted toward a mathematics major or minor.

3350. Higher Mathematics for Engineers and Scientists I (3:3:0). Prerequisite: MATH 2350 or concurrent registration with departmental consent. Ordinary differential equations. Laplace transforms. Other selected topics.

3351. Higher Mathematics for Engineers and Scientists II (3:3:0). Prerequisite: MATH 3350 or 3354. Partial differential equations and numerical methods.

3354. Differential Equations I (3:3:0). Prerequisite: MATH 2350 and 2360. Solutions of ordinary differential equations; geometric and physical applications. MATH 3350 and 3354 may not both be counted toward a mathematics major or minor.

3360. Foundations of Algebra I (3:3:0). Prerequisite: MATH 2360. Fundamental concepts of abstract algebra.

3370. Elementary Geometry (3:3:0). Prerequisite: MATH 2370 and junior standing. Congruence and measures of plane and solid figures; similarity; areas; volumes; and a brief introduction to concepts in probability and statistics.

3371. Elements of Finite Mathematics (3:3:0). Prerequisite: MATH 1331, 1351, or 2371. Combinatorics, probability theory. Bayes' Theorem, Bernoulli Trials. Probability distributions and statistics. Not for engineering, science, or mathematics majors.

3430. Computational Techniques for Science and Mathematics (4:3:2). Prerequisite: MATH 2360. Emphasis on scientific computing and problem solving techniques using state-of-the-art mathematics software packages.

4000. Selected Topics (V1-3). Prerequisite: Consent of undergraduate program director. Selected topics in upper division mathematics. May be repeated for credit.

4310. Introduction to Numerical Analysis I (3:3:0). Prerequisite: MATH 3350 or 3354, including an elementary knowledge of programming or consent of instructor; Interpolation; approximations; numerical integration and differentiation.

4312. Introduction to Numerical Analysis II (3:3:0). Prerequisite: MATH 2360, including an elementary knowledge of programming or consent of instructor. Numerical techniques in linear algebra.

4330. Mathematical Computing (3:3:0). Prerequisite: Consent of the Director of Undergraduate Programs, Department of Mathematics and Statistics. Topics from computer literacy and programming.

4331. Advanced Geometry (3:3:0). Prerequisite: MATH 2350 and 2360. Euclidean and projective geometries.

4342, 4343. Mathematical Statistics (3:3:0 each). Prerequisite: MATH 2350. Frequency functions; moments; probability; correlation and regression; testing hypotheses; small sample distributions; analysis of variance; nonparametric methods; sequential analysis. 4342 is prerequisite for 4343. MATH 3342 and 4332 cannot both be counted toward a mathematics major or minor.

4350, 4351. Advanced Calculus (3:3:0 each). Prerequisite: MATH 2360 (MATH 3360 recommended). Sets; functions; vector fields; partial derivatives; power series; theory of integration; line, surface, and multiple integrals. 4350 is prerequisite for 4351.

4354. Differential Equations II (3:3:0). Prerequisite: MATH 3354. Partial differential equations and boundary value problems.

4356. Elementary Functions of Complex Variables (3:3:0). Prerequisite: MATH 2360 (MATH 4350 is recommended). The complex number system; functions of a complex variable; differentiation; elementary functions; and contour integration.

4360. Foundations of Algebra II (3:3:0). Prerequisite: MATH 3360. Continuation of MATH 3360.

4362. Theory of Numbers (3:3:0). Prerequisite: MATH 2360 (MATH 3360 is recommended). Prime numbers; congruences; theorems of Fermat, Euler, and Wilson; residues; reciprocity law; Diophantine Equations.

4370. Elementary Problem Solving (3:3:0). Prerequisite: MATH 2371, or equivalent. Techniques of problem solving using elementary number theory.

4371. Basic Computer Literacy and Programming (3:3:0). Prerequisite: MATH 2371 or equivalent. Computer literacy, structured programming, and problem solving using elementary number theory.


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