Mathematics General Information
Requirements for the B.A. with a major in Mathematics
Requirements for the B.S. with a major in Mathematics
Actuarial concentration in Mathematics
Requirements for a minor in Mathematics
Secondary and Middle School Mathematics Certification
Honors Program
Affiliations
Pass/No Credit Option
Courses of Instruction

(MATH)

Available as a major and a minor on the B.A. and B.S. degrees.

General Information

Factors which determine a student's placement include 1) high school credits presented, 2) scores achieved in the SAT, ACT, or other appropriate examination, and 3) performance in advanced placement examinations. Advanced placement, with credit, is available for Math 10052, 10053, 10524, and 20524.

For a student taking a major in mathematics (B.A. or B.S), the recommended sequence for the first four semesters is Math 10524, 20524, 30224, and 30524. In either the first or second semester the student should also complete Computer Science 10403 or Computer Science 10503. In addition, Math 10123 should be taken in one of the first four semesters.

Students planning to do graduate work in mathematics should take Math 50253, 50263, 50503, and 50513.

Students with majors in business ordinarily select from Math 10053, 10283, 10524, and 20524. Credit is not allowed for both Math 10043 and INSC 20153.

Credit is not allowed for both Math 10283 and Math 10524.

Requirements for the B.A. with a major in Mathematics

28 semester hours of mathematics with a grade of C or better, of which 19 must consist of Math 10123, 10524, 20524, 30224, and 30524. An additional 9 hours must be chosen from among Math 10143 and mathematics courses at or above the 30000-level. Also required are Computer Science 10503 or Computer Science 10403 or 10503 and Physics 20474 and 20484. A minimum of 124 semester hours is required for the degree.

Note: FOREIGN LANGUAGE REQUIREMENT. All students pursuing the Bachelor of Arts degree in the College of Science and Engineering must demonstrate competency in a foreign language equivalent to the completion of one of the following:

FREN 20063 Fourth Semester College French
GRMN 20063 Intermediate German
GREE 20063 Fouth Semester Greek (Hellenistic)
ITAL 20063 Fourth Semester college Italian
JAPN 20063 Fourth Semester College Japanese
SPAN 20203 Intermediate Spanish

Requirements for the B.S. with a major in Mathematics

40 semester hours of mathematics with a grade of C or better, of which 28 must consist of Math 10123, 10524, 20524, 30224, 30524, 30803, 50253, and 50503. An additional 12 semester hours from among Math 10143 and mathematics courses at or above the 30000-level are required. Also required are Computer Science 10503 or Computer Science 10403 or 10503 and Physics 20474 and 20484. A minimum of 132 semester hours is required for the degree.

Actuarial concentration in Mathematics

This program may be pursued under either the B.A. or B.S. option as described above. Mathematics coursework for the actuarial concentration must include Math 30603, Math 30803, Math 30853, and Math 40603. Additional required courses outside the Mathematics Department are Econ 10223, Econ 10233, Econ 30223 and Econ 30233 as well as Acct 20153, Acct 20163 and Fina 30153. Students seeking a BA degree are advised to consider a minor in Economics. All actuarial students need to work closely with an advisor to plan course schedules.

Requirements for a minor in Mathematics

18 semester hours of Mathematics with a grade of C or better, including Math 10524, 20524 and 30224, and an additional 6 semester hours from among Math 10123 and courses at or above the 30000-level. Computer Science 10403 or Computer Science 10503 is also required.

Secondary and Middle School Mathematics Certification

Students seeking certification for either grade levels 8-12 or 4-8 should be advised by both a Mathematics faculty member and an advisor in the School of Education. Secondary certification in Mathematics requirements include a major in Mathematics (BA or BS) and an Educational Studies Minor. Middle School mathematics majors pursue a BSE degree from the School of Education.

Honors Program

Mathematics majors who plan to pursue departmental honors must be members of the Honors Program. A minimum 3.5 GPA in the major is required. Course work must include at least three of Math 40353, 40663, 50253, 50263, 50323, 50403, 50503, 50513, 50613, 50623, 50633, and 50703, or substitutes approved by the department. Students should enroll in Math 30000 during their junior year and Math 40000 during the fall semester of their senior year. Departmental honors further require satisfactory presentation of thesis results to faculty.

Affiliations

TCU is an institutional member of the American Mathematical Society and of the Mathematical Association of America. The department holds a charter for Texas Alpha Chapter of Pi Mu Epsilon, a national mathematics honor society, and also participates in the sponsoring of a chapter of Sigma Xi, the honor society for research in the natural sciences.

Pass/No Credit Option

Mathematics courses to be applied to a major in mathematics may not be taken Pass/No Credit.

Courses of Instruction

MATH 10023 Fundamentals of Algebra. Operations with polynomials. Fractions and exponents. Linear and quadratic equations, with applications. Arithmetic, geometric, and binomial series. Note: This course does not satisfy the UCR in mathematics. Credit will not be given in this course to anyone who has already received credit for any other mathematics course at TCU or comparable or higher-level course at other institutions or credit through AP/CLEP exams.

MATH 10033 Topics in Mathematics. Prerequisite: MATH 10023 or two years of high school algebra and one year of geometry. A selection of topics of general interest and some degree of applicability, such as mathematical modeling, geometry, deductive reasoning, mathematics of finance, probability, and statistics.

MATH 10043 Elementary Statistics. Prerequisite: MATH 10023 or two years of high school algebra. Empirical frequency distributions, binomial and normal distributions. Regression and correlation. Statistical inference.

MATH 10052 Trigonometry. Prerequisite: MATH 10023 or two years of high school algebra and one year of geometry. The trigonometric functions, their graphs, and applications. Note: This course does not satisfy the UCR in mathematics.

MATH 10054 Precalculus with Trigonometry. Prerequisites: MATH 10023 or 2 years of high school algebra and one year of geometry. Precalculus treatment of polynomial, rational, exponential, logarithmic, and trigonometric functions with particular emphasis on topics needed for MATH 10524. Note: Credit will not be given for both MATH 10273 and MATH 10054. Note: This course does not satisfy the core mathematical reasoning requirement or the UCR in mathematics.

MATH 10123 Discrete Mathematics I. Prerequisite: MATH 10053 or two years of high school algebra. Discrete algebraic structures. Algorithms and applications to programming. Selected topics such as recursion and induction, combinatorics, binary relations, graphs and trees, language, automata.

MATH 10143 Discrete Mathematics II. Prerequisite: MATH 10123. Continuation of MATH 10123.

MATH 10273 Applied Precalculus. Prerequisites: MATH 10023 or two years of high school algebra. Precalculus treatment of polynomial, rational, exponential and logarithmic functions. Additional special applications from the mathematics of finance and probability. NOTE: Credit will not be given for both MATH 10053 and MATH 10273.

MATH 10283 Applied Calculus. Prerequisite: MATH 10273 with a grade of C or better, or MATH 10053 or MATH 10054 with a grade of C or better, or high school precalculus and a score of 600 or higher on the SAT Math exam. The elements of calculus, with applications to business and economics. Note: credit will not be given for both MATH 10283 and MATH 10524.

MATH 10524 Calculus I. Prerequisite: MATH 10054 with a grade of C or better, or MATH 10053 and MATH 10052 with a grade of C or better in both, or AP Calculus AB or BC score of 3 or better, or SAT Subject Test (SAT II), Mathematics Level 1 (1C) with a score of 560 or better, or SAT Subject Test (SATII), Mathematics Level 2 (IIC) with a score of 520 or better, or a passing grade on the Calculus Placement Test. Differential and integral calculus of elementary functions, including exponential, logarithmic, and trigonometric functions. Applications. Note: credit will not be given for both MATH 10283 and MATH 10524.

MATH 20053 Fundamentals of Modern Mathematics. Systems of enumeration, change of base. Axiomatic approach to mathematical structures. Development of the real number system. Sets, logic, and the nature of mathematical proof. Relations, including inequalities in two variables, and functions. Note: may not be counted toward a major or minor in mathematics. Also, this course does not satisfy the UCR in mathematics.

MATH 20063 Topics in Modern Mathematics. Prerequisite: MATH 20053. Logic and an introduction to mathematical reasoning. Probability and elementary statistics. Geometry. Systems of measurement. Note: may not be counted toward a major or minor in mathematics.

MATH 20524 Calculus II. Prerequisite: MATH 10524. Techniques of integration and applications. Infinite series. Differential equations as time permits.

MATH 20970 Special Topics. 1 - 3 semester hours.

MATH 30000 Honors Seminar. Prerequisite: MATH 30224 or permission of the instructor. 1 - 3 semester hours.

MATH 30133 Symbolic Logic I. An introduction to the scope and limits of modern logic. The nature of logical systems and the various areas of logic are discussed. Alternative proof- procedures in propositional logic and predicate logic are presented. (Offered as MATH or PHIL credit.)

MATH 30143 Symbolic Logic II. Prerequisite: PHIL 30133. A continuation of 30133, with an emphasis on predicate logic, nonstandard logic, and metalogic. (Offered as MATH or PHIL credit.)

MATH 30224 Linear Algebra. Prerequisite: MATH 10524 and either MATH 10123 or MATH 20524. Vector spaces, linear independence, bases, and dimension. Linear mappings, matrices, and determinants. Eigenvalues and eigenvectors, diagonalization.

MATH 30524 Calculus III. Prerequisite: MATH 20524. Vector calculus and multiple integration. Optimization and Lagrange multipliers. Vector fields and potential functions. Gradient, curl, and divergence. Line and surface integrals. The theorems of Green, Stokes, and Gauss, as time permits.

MATH 30603 Interest Theory. Prerequisite: MATH 20524. A rigorous development of the theory of interest in both discrete and continuous time. Present value, yield rates, compound interest, amortization, and cash flows. Selected financial applications to bonds and securities.

MATH 30613 Differential Equations. Prerequisite: MATH 20524. Solution techniques for ordinary differential equations. Systems of differential equations. Mathematical modeling and applications.

MATH 30623 Interest Theory II. Prerequisites: MATH 30603. Treatment of bonds and yield rates, stocks and financial markets, arbitrage, the term structure of interest rates, options and swaps, and topics in interest rate sensitivity including duration, convexity and immunization.

MATH 30803 Probability and Statistics I. Prerequisite: MATH 10524. Probability theory. Permutations, combinations, elementary probability, and the binomial theorem. Frequency distributions, mean and standard deviation.

MATH 30853 Statistics. Prerequisites: MATH 20524 and 30803. Organization and analysis of data. Descriptive statistics. Confidence intervals and hypothesis testing. As time permits, topics in regression, analysis of variance, nonparametric statistics, sampling methods.

MATH 40000 Undergraduate Research. Prerequisite: twelve semester hours of mathematics. (1-3 semester hours).

MATH 40353 Topology. Prerequisite: MATH 30224 and 30524. Topological spaces, bases, connectedness, compactness. Continuous functions and homeomorphisms. Separation properties. Product and quotient spaces. Metric spaces.

MATH 40603 Actuarial Mathematics. Prerequisites: MATH 30524 and 30803. Applications of calculus, probability, and statistics, emphasizing problems in risk management and insurance.

MATH 40663 Numerical Analysis. Prerequisite: MATH 20524, 30613, and competence in a high-level programming language. Interpolation. Solution of nonlinear equations. Numerical integration and differentiation. Approximate solutions to ordinary differential equations.

MATH 40970 Special Topics. Prerequisite: MATH 30524 or permission of the instructor. 1 - 6 semester hours.

MATH 50073 History of Mathematics. Prerequisite: Advanced standing in mathematics, or permission. The history of mathematics from the times of ancient Egypt and Mesopotamia until the advent of calculus in the seventeenth century.

MATH 50073 History of Mathematics. Prerequisite: advanced standing in mathematics or permission of the instructor. A survey of the history of mathematics from ancient times to the seventeenth century. Emphasis on topics closely related to contemporary mathematics

MATH 50253 Abstract Algebra I. Prerequisite: MATH 10123 and MATH 30224. Introduction to groups and rings. Homomorphisms, isomorphisms, subgroups, and ideals. Quotient and product structures.

MATH 50263 Abstract Algebra II. Prerequisites: MATH 50253. A continuation of MATH 50253. Introduction to field extensions and Galois Theory. Advanced topics in groups and rings.

MATH 50303 Studies: Geometry-Topology. Prerequisite: Twelve semester hours of mathematics, and permission of the instructor. Analytic geometry of euclidean space, topology of euclidean space and surfaces, metrics, non-euclidean geometry.

MATH 50303 Studies in Geometry and Topology. Prerequisite: Twelve semester hours of mathematics, and permission of the instructor. Topics include the topology of surfaces, convex sets, networks, and non-Euclidean Geometry.

MATH 50323 Differential Geometry. Prerequisite: MATH 30224 and 30524. Calculus on Euclidean space. Geometry of curves and surfaces.

MATH 50403 Complex Analysis. Prerequisite: MATH 30524. Analytic functions, harmonic functions, and the Cauchy-Riemann equations. Conformal mappings. Cauchy's integral theorem and formula, with applications. Power series and analytic continuation.

MATH 50503 Real Analysis I. Prerequisite: Math 10123, Math 30224, and Math 30524. A rigorous development of elementary limit processes. Continuity, sequences, series, differentiation, integration.

MATH 50513 Real Analysis II. Prerequisite: Math 50503. A continuation of Math 50503. Multivariable calculus, including the Implicit Function Theorem and change of variables. Other selected topics.

MATH 50613 Partial Differential Equations. Prerequisite: Math 30613. Basic theory of hyperbolic, parabolic, and elliptic partial differential equations.

MATH 50623 Applied Mathematics I. Prerequisite: Math 30224, Math 30524 and Math 30613. Selected topics, such as linear and nonlinear systems, equilibria, Fourier series, computational graph theory, optimization and linear programming, calculus of variations, complex integration.

MATH 50633 Applied Mathematics II. Prerequisite: MATH 50623. Continuation of MATH 50623.

MATH 50703 Number Theory. Prerequisite: Math 10123 and Math 30224. Properties of the integers. Divisibility, prime numbers, modular arithmetic, Chinese Remainder Theorem, Diophantine equations.

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