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Actuarial concentration in mathematics. This
program may be pursued under either the BA or BS 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, Econ30223 and #con 30233
as well as Acct20153, 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.
Secondary Teaching Certification. Students
seeking certification for teaching Mathematics at the secondary school level
should be advised by both the departmental secondary certification advisor and
a secondary certification advisor in the School of Education. Specific requirements
for Mathematics as a teaching field follow: For a single teaching field in Mathematics
the B.S. program above should include in the 12 advanced hours Math 50303 and
Math 50703. For two teaching fields, one of which is Mathematics, the B.A. requirements
should include Math 30803 and Math 50303 among the advanced hours.
Mathematics Specialization for Elementary
Education. This specialization requires 19 hours of mathematics including
Math 10524, 20053, 20063, and 9 additional semester hours. At least 6 of the
9 semester hours must be advanced hours and should be selected in consultation
with the departmental elementary certification mathematics advisor.
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.
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. 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 Desc 20153.
Credit is not allowed for both Math 10283 and Math 10524.
Pass/No Credit Option. Mathematics courses to be applied to a major in
mathematics may not be taken Pass/No Credit.
The following is a complete list of courses offered by this department. Go
to Class Search on Registrar's Page to see which courses are being taught this
semester.
Courses of Instruction
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.
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.
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. Note:
credit will not be given for both Math 10043 and Desc 20153.
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.
10053 PRECALCULUS. Prerequisite: Math 10023 or two years of high school
algebra and one year of geometry. A conceptual introduction to functions
with particular emphasis on topics needed for calculus. Study of linear, exponential,
logarithmic, polynomial, and rational functions. Note: This course does not
satisfy the UCR in mathematics.
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.
10143 DISCRETE MATHEMATICS II. Prerequisite: Math 10123. Continuation
of Math 10123.
10283 APPLIED CALCULUS. Prerequisite: Math 10053 or two years of high
school algebra and one year of geometry. The elements of calculus, with
applications to business and economics. Note: credit will not be given for both
Math 10283 and Math 10524.
10524 CALCULUS I. Prerequisite: Math 10053 and Math 10052 or equivalents.
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.
20053 FUNDAMENTALS OF MODERN MATHEMATICS. Topics will be selected from:
an introduction to mathematical reasoning, logic, sets, relations and functions,
development of the real number system, systems of enumeration, change of base,
elementary number theory, finance. Note: may not be counted toward a major or
minor in mathematics. Also, this course does not satisfy the UCR in mathematics.
20063 TOPICS IN MODERN MATHEMATICS. Prerequisite: Math 20053.
Topics will be selected from: probability, elementary statistics, introductory
geometry, congruence, constructions, the Cartesian coordinate system, systems
of measurement, geometric transformations. Note: may not be counted toward a
major or minor in mathematics. Also, this course does not satisfy the UCR in
mathematics.
20524 CALCULUS II. Prerequisite: Math 10524. Techniques of integration
and applications. Infinite series. Differential equations as time permits.
20970 SPECIAL TOPICS. (1 - 3 semester hours).
30000 HONORS SEMINAR. Prerequisite: Math 30224 or permission of
the instructor. (1 - 3 semester hours).
30133 SYMBOLIC LOGIC I. (PHIL 30133). An introduction to the scope and
limits of modern logic. The nature of logical systems and various areas of logic.
Alternative proof procedures in propositional logic and predicate logic.
30143 SYMBOLIC LOGIC II. (PHIL 30143). Prerequisite: Math/Phil 30133.
A continuation of Math/Phil 30133, with an emphasis in predicate logic, nonstandard
logics, and metalogic.
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.
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.
30603 INTEREST THEORY. Prerequisite: Math 20534. 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.
30613 DIFFERENTIAL EQUATIONS. Prerequisite: Math 20524. Solution
techniques for ordinary differential equations. Systems of differential equations.
Mathematical modeling and applications.
30803 PROBABILITY AND STATISTICS I. Prerequisite: Math 10524.
Probability theory. Permutations, combinations, elementary probability, and
the binomial theorem. Frequency distributions, mean and standard deviation.
30853 STATISTICS. Prerequisite: Math 20524 and Math 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.
40000 UNDERGRADUATE RESEARCH. Prerequisite: twelve semester hours
of mathematics. (1 - 3 semester hours).
40353 TOPOLOGY. Prerequisite: Math 30224 and Math 30524. Topological
spaces, bases, connectedness, compactness. Continuous functions and homeomorphisms.
Separation properties. Product and quotient spaces. Metric spaces.
40603 ACTUARIAL MATHEMATICS. Prerequisites: Math 30524 and Math 30803.
Applications of calculus, probability and statistics, emphasizing problems in
risk management and insurance.
40663 NUMERICAL ANALYSIS. Prerequisite: Math 20524, Math 30613, and
competence in a high-level programming language. Interpolation. Solution
of nonlinear equations. Numerical integration and differentiation. Approximate
solutions to ordinary differential equations.
40970 SPECIAL TOPICS. Prerequisite: Math 30524 or permission of the
instructor. (1 - 6 semester hours).
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.
50253 ABSTRACT ALGEBRA I. Prerequisite: Math 10123 and Math 30224.
Introduction to groups and rings. Homomorphisms, isomorphisms, subgroups, and
ideals. Quotient and product structures.
50263 ABSTRACT ALGEBRA II. Prerequisite: Math 50253. A continuation
of Math 50253. Introduction to field extensions and Galois theory. Advanced
topics in groups and rings.
50303 STUDIES IN GEOMETRY AND TOPOLOGY. Prerequisite: twelve semester
hours of mathematics or permission of the instructor. Analytic geometry
of euclidean space, topology of euclidean space and surfaces, metrics, non-euclidean
geometry.
50323 DIFFERENTIAL GEOMETRY. Prerequisite: Math 30224 and Math 30524.
Calculus on euclidean space. Geometry of curves and surfaces. Connections
and curvature.
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.
50503 REAL ANALYSIS I. Prerequisite: Math 10123, Math 30224, and Math
30524. A rigorous development of elementary limit processes. Continuity,
sequences, series, differentiation, integration.
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.
50613 PARTIAL DIFFERENTIAL EQUATIONS. Prerequisite: Math 30613. Basic
theory of hyperbolic, parabolic, and elliptic partial differential equations.
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.
50633 APPLIED MATHEMATICS II. Prerequisite: Math 50623. Continuation
of Math 50623.
50703 NUMBER THEORY. Prerequisite: Math 10123 and Math 30224. Properties
of the integers. Divisibility, prime numbers, modular arithmetic, Chinese Remainder
Theorem, Diophantine equations.
