MATHEMATICS (MATH)

The Mathematics Department offers a variety of entry-level courses. The prerequisite for each is a minimum of two years of high school algebra and one year of high school geometry. The courses are independent of each other, and students may take any or all of them, depending on their needs. The entry-level course for students majoring in mathematics is MATH 1910 Calculus I. For students who lack the necessary preparation for Calculus I, MATH 1730 (or MATH 1710 and 1720) is usually the entry-level course. The prerequisites for this course are two years of high school algebra, one year of high school geometry and at least 12 weeks of high school trigonometry (or equivalent). In courses listed as a sequence the first course is a prerequisite to the second. A grade of C or better is required in all prerequisite courses.

NOTE: Students cannot receive credit for a 1000-level mathematics course if that course is a prerequisite for any mathematics course that has been completed with a grade of C or better.

uMATH 1010. Introduction to Contemporary Mathematical Ideas. Lec. 3. Credit 3.
Mathematics as applied to real-life problems selected from such topics as preference schemes for voting, fair division and apportionment methods, routing and scheduling problems, analysis of graphs, growth, and symmetry and counting problems.

MATH (CSC, PHYS) 1020. First-Year Connections. Rec. 2. Credit 1.
This course is intended as a bridge course for students entering TTU from high school. The course is designed to strengthen the student’s connection to TTU, the College of Arts and Sciences, and the appropriate department (CSC, MATH, or PHYS) by focusing on the enhancement of skills needed for academic success. This course engages the student in meaningful academic and non-academic out-of-the-classroom activities, as learning occurs both in and out of the classroom. It emphasizes critical thinking, the formation of academic and social goals and support groups, and time-management and study skills.

uMATH 1130.  College Algebra.  Lec. 3.  Credit 3.
Review of algebra and coordinate geometry; functions; polynomial, rational, exponential, and logarithmic functions; systems of equations; binomial formula; counting (multiplication principle, permutations, and combinations); and conics.  Credit towards graduation will not be given for MATH 1130 and MATH 1710 or for MATH 1130 and MATH 1730.

uMATH 1410. Survey of Elementary Mathematics I. Lec. 3. Credit 3.
Prerequisite: Admission is restricted to students majoring in Elementary Education. Introduction to sets and operations on sets, properties and operations on whole numbers, and integers, rational and real numbers.

MATH 1420. Survey of Elementary Mathematics II. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 1410. Admission is restricted to students majoring in Elementary Education. Introduction to elements of probability and statistics and basic concepts of Euclidean geometry including congruence, similarity, measurements, areas, and volumes.

uMATH 1530. Elementary Probability and Statistics. Lec. 3. Credit 3.
Descriptive statistics including measures of central location and variation, frequency distributions, histograms, and frequency polygons. Probability relating to elementary sample spaces, events, conditional probability, discrete and continuous type random variables, mathematical expectation, and the normal probability. Inferential statistics relating to the confidence intervals and hypothesis tests related to the mean and proportion.

uMATH 1630. Finite Mathematics. Lec. 3. Credit 3.
Brief review of basic algebra; introduction to probability; matrix algebra and linear programming; and applications to business and economics.

uMATH 1710. Pre-calculus I. Lec. 3. Credit 3.
Review of algebra; relations and functions and their graphs, including polynomial and rational functions; conic sections; inequalities, arithmetic, and geometric sequences and series. Credit will not be given for both MATH 1710 and MATH 1730.

uMATH 1720. Pre-calculus II. Lec. 3. Credit 3.
Circular functions and radian measure, graphs of the trigonometric functions, trigonometric identities, and equations, the inverse trigonometric functions, polar coordinates. Applications involving triangles, vectors in the plane and complex numbers. Credit will not be given for both MATH 1720 and MATH 1730.

uMATH 1730. Pre-Calculus Mathematics. Lec. 5. Credit 5.
Prerequisite: Two years of high school algebra, one year of high school geometry, and 12 weeks of trigonometry. Review of algebra and trigonometry; relations and functions and their graphs, including polynomial and rational functions; conic sections; inequalities; polar coordinates; complex numbers; and advanced topics in algebra. Credit will not be given for both MATH 1730 and any of MATH 1710 and MATH 1720.

uMATH 1830. Concepts of Calculus. Lec. 3. Credit 3.
Prerequisite: ACT mathematics score of 25 or above and three years of high school mathematics, including algebra and geometry; or, special permission of the Mathematics Department; or, C or better in MATH 1130 or MATH 1710 or equivalent. A survey of limits, continuity, and the differential and integral calculus with applications in business, economics and the life sciences.

uMATH 1910. Calculus I. Lec. 4. Credit 4.
Prerequisite: ACT mathematics score of 27 or above and four years of high school mathematics, including algebra, geometry, trigonometry, and advanced or pre-calculus mathematics, or special permission of the Mathematics Department; or C or better in MATH 1730; or C or better in MATH 1720 and MATH 1710 or equivalent. Limits, continuity, derivatives and integrals of functions of one variable. Applications of differentiation and introduction to the definite integral.

MATH 1911. Calculus I Honors Seminar. Lab. 1. Credit 0.
Co-requisite: Concurrent enrollment in MATH 1910. An ACT score of 30 or higher is also recommended. Selected topics to add depth to the understanding of the material in MATH 1910. Honors students can receive honors credit for MATH 1910 by successfully completing both MATH 1910 and MATH 1911.

MATH 1920. Calculus II. Lec. 4. Credit 4.
Prerequisite: C or better in MATH 1910; or equivalent AP credit for MATH 1910. Integration techniques, applications of the definite integral, polar coordinates, parametric equations, sequences, and series.

MATH 1921. Calculus II Honors Seminar. Lab. 1. Credit 0.
Co-requisite: Concurrent enrollment in MATH 1920. A grade of A in MATH 1910 is also recommended. Selected topics to add depth to the understanding of the material in MATH 1920. Honors students can receive honors credit for MATH 1920 by successfully completing both MATH 1920 and MATH 1921.

MATH 2010. Elementary Matrix Algebra. Lec. 2. Credit 2.
Prerequisite: C or better in MATH 1920. Introduction to basic operations, determinants, inverses, systems of linear equations, bases and dimension of Euclidean spaces, linear transformations, eigenvalues, and eigenvectors.

MATH 2011. Matrix Algebra Computer Lab. Lab 1. Credit 1.
Corequisite: C or better in MATH 2010 or concurrent enrollment in MATH 2010. This lab complements matrix theory taught in MATH 2010 by providing students with the experience in applying matrix methods and modern computer software such as Matlab or Maple to solve various computational problems in mathematics, engineering, or sciences. The course will be taught in a computer laboratory. Previous knowledge of the computer software is not necessary.

MATH 2110. Calculus III. Lec. 4. Credit 4.
Prerequisite: C or better in MATH 1920; or equivalent AP credit for MATH 1910 and MATH 1920. Analytic geometry and vectors, differential calculus of functions of several variables, multiple integration, and topics from vector calculus.

MATH 2120. Differential Equations. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 1920. First order equations, linear equations of higher order, power series solutions (including Frobenius method), Laplace transforms, other topics. It is recommended but not required that students take MATH 2010 before taking MATH 2120.

MATH 2610. Discrete Structures. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 1920. Topics to be chosen from algebra of sets and relations, functions, algebras, graphs and digraphs, monoids and machines, groups and subgroups, computer arithmetic, binary codes, logic, and languages.

MATH 3000. Selected Topics in Mathematics. Lec. 1. Credit 1.
Prerequisite: C or better in MATH 1920 and consent of instructor. Lectures on and discussion of topics from upper level mathematics to be selected by the instructor in a setting with less structure than in a traditional class.

MATH 3070-3080. Statistical Methods I-II. Lec. 3-3. Credit 3-3.
Prerequisite: MATH 3070: Recommended C or better in MATH 1130; MATH 3080: C or better in MATH 3070. Introduction to parametric statistical methods with some non-parametric alternatives, sampling, probability, Type I and Type II errors, sample size estimation, confidence interval estimation, test of hypothesis using normal, Student's t, Snedecor's F, Chi-square and the binomial distributions, linear regression, analysis of variance, and data analysis utilizing statistical software.

MATH 3400. Introduction to Concepts of Mathematics. Lec. 2. Rec. 2. Credit 3.
Prerequisite: C or better in MATH 1920. A rigorous treatment of elements of logic and set theory including propositional calculus (statements, connectives, conditionals, and negation), quantifiers, sets and operations on sets, mappings, equivalence relations, and mathematical induction. Students are expected to work in an abstract setting using precise definitions and formal proofs.

MATH 3430. College Geometry. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 3400. A rigorous development of geometry from first concepts using the metric approach. Topics include constructions and hyperbolic geometry.

MATH 3470. Introductory Probability and Statistics. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 1920. Probability, random variables, discrete and continuous distributions and their simulation, elementary sampling theory, and estimation with an overall emphasis on simulation of random processes (Not allowed for mathematics majors after having taken MATH 4480.)

MATH 3510-3520. Modern Algebra I-II. Lec. 3-3. Credit 3-3.
Prerequisite: MATH 3510 - C or better in MATH 3400; MATH 3520: C or better in MATH 3510. The number system, mathematical induction, groups, rings, fields, integral domains, and mappings.

MATH 3670. Theory and Applications of Random Signals. Lec. 2. Credit 2.
Introduction to randomization, unconditional and conditional probability, independence, and concepts of random variables. Distributions and density functions, moments and moment generating functions, univariate and multivariate random variables, random process concepts, spectral characteristics of random processes, and linear systems with random inputs.

MATH 3810. Complex Variables. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 2110. Complex numbers, calculus of complex variables, analytic functions, Cauchy's Theorem, series, the Residue Theorem, and applications.

MATH 3910. Independent Study. Credit 1-3.
Prerequisite: Consent of instructor. Readings and study under the supervision of a qualified staff member.

MATH 4050 (5050). Number Theory. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 3400 or consent of instructor. Properties of integers, division algorithms, prime numbers, diophantine equations, and congruences.

MATH 4110-4120 (5110-5120). Advanced Calculus I-II. Lec. 2-2. Rec. 2-2. Credit 3-3.
Prerequisite: MATH 4110 (5110): C or better in MATH 3400 or consent of instructor; MATH 4120 (5120): C or better in MATH 4110 (5110). Rigorous treatment of functions of one and several variables, improper integrals, sequences, infinite series, uniform convergence, and applications. Students are expected to improve their ability to work in an abstract setting using precise definitions and formal proofs and to present their work in class.

MATH 4210-4220 (5210-5220). Numerical Analysis I-II. Lec. 3-3. Credit 3-3.
Prerequisite: MATH 4210 (5210): C or better in MATH 1920; MATH 4220 (5220): C or better in MATH 2120 or consent of instructor. Iterative methods for nonlinear equations, computational error analysis, convergence of iterative techniques, interpolation, numerical differentiation and integration, approximate solutions of initial-value problems, boundary-value problems, and nonlinear systems, and direct and iterative methods for linear systems.

MATH 4250-4260 (5250-5260). Advanced Ordinary Differential Equations I-II.  Lec. 3-3. Credit 3-3.
Prerequisite: MATH 4250 (5250): C or better in MATH 2110 and MATH 2120; MATH 4260 (5260): C or better in MATH 4250 (5250). Systems of ordinary differential equations, matrix methods, approximate solutions, stability theory, basic theory of nonlinear equations and differential systems, trajectories, phase space stability, and construction of liapunov functions.

MATH 4310-4320 (5310-5320). Introduction to Topology I-II. Lec. 3-3. Credit 3-3.
Prerequisite: MATH 4310 (5310): C or better in MATH 3400; MATH 4320 (5320): C or better in MATH 4310 (5310). Topological spaces, continuity, connectedness, compactness, separation axioms, function spaces, and fundamental groups.

MATH 4350 (5350). Introductory Combinatorics. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 3400 or consent of instructor. Topics to be covered include permutations, combinations, multisets, partitions, recurrence relations, generating functions, and the principle of inclusion-exclusion.

MATH 4360 (5360). Graph Theory. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 3400 or consent of instructor. Fundamental concepts of undirected and directed graphs, trees, connectivity, traversability, colorability, network flows, and matching theory.

MATH 4410 (5410). Differential Geometry. Lec. 3. Credit 3.
Prerequisites: C or better in MATH 2110, 2010 and 3400. Geometry of curves and surfaces in three dimensional space. Calculus on surfaces, curvature and Riemannian geometry.

MATH 4470-4480 (5470-5480). Probability and Statistics I-II. Lec. 3-3. Credit 3-3.
Prerequisite: MATH 4470: C or better in MATH 2110; MATH 4480: C or better in MATH 4470. Mathematical foundations of elementary statistical methods, application and theory, probability in discrete and continuous distribution, correlation and regression, sampling distributions, and significance tests.

MATH 4510 (5510). Advanced Mathematics for Engineers. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 2110 and MATH 2120. Fourier series, Sturm-Liouville problems, orthogonal functions, Legendre polynomials, Bessel functions, separable partial differential equations (e.g. heat, wave and Laplace equations), and other topics.

MATH 4530-4540 (5530-5540). Linear Algebra I-II. Lec. 3-3. Credit 3-3.
Prerequisite: MATH 4530 (5530): C or better in MATH 2010 and MATH 3400; MATH 4540 (5540): C or better in MATH 4530 (5530). A theoretical study of vector spaces, bases and dimensions, subspaces, linear transformations, dual spaces, eigenvalues and eigenvectors, inner product spaces, spectral theory, duality, and quadratic and bilinear forms.

MATH 4610 (5610). History of Mathematics I. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 3400. The development of mathematics and its relation to the development of civilization prior to the beginnings of calculus.

MATH 4620 (5620). History of Mathematics II. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 3400. History of mathematics from the beginnings of calculus through the modern times.

MATH 4710 (5710). Vector Analysis. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 2110. The algebra and the differential and integral calculus of vectors, and applications to geometry and mechanics.

MATH 4750 (5750). Category Theory of Sets. Lec. 3. Credit 3.
Prerequisites: C or better in MATH 3400 (or consent of instructor for MATH 5750). Abstract sets and mappings, categories, sums, universal property, monomorphisms and parts, finite inverse limits, colimits, epimorphisms, the Axiom of Choice, mapping sets and exponentials, covariant and contravariant functoriality of function spaces, Cantor's diagonal argument, powers sets, variable sets, models of additional variation, and selected applications.

MATH 4850 (5850). Computational Algebraic Geometry I. Lec. 3. Credit 3.
Prerequisites: C or better in MATH 2010 and C or better in MATH 3400 or equivalent (or consent of instructor for MATH 5850). Additional recommended prerequisite: MATH 3510 or any other 4000/5000 level mathematics course in which proofs are required. Affine varieties and polynomial ideals, Groebner bases, elimination theory, Hilbert’s Nullstellensatz, Zariski closure, and decomposition into irreducible varieties.

MATH 4860 (5860). Computational Algebraic Geometry II. Lec. 3. Credit 3.
Prerequisite: C or better in MATH 4850 (5850). Polynomial and rational functions on a variety, projective varieties, the dimension of a variety, selected applications in robotics, automatic theorem proving, and invariant theory of finite groups.

MATH 4910-4920 (5910-5920). Directed Readings. Credit 1-3.
Prerequisite: Consent of instructor. These courses provide an opportunity for individual reading and study under the supervision of a qualified staff member.

MATH 4950 (5950). Topics in Mathematics. Lec. 3. Credit 3.
Prerequisite: Consent of instructor. A formal course in any area where there is no other course offering. May be taken more than once provided that the topic is different.

MATH 4970. Senior Seminar. Lec. 1. Credit 1.
Prerequisite: Senior standing. Preparation of papers at an advanced level in mathematics to be presented both in writing and orally.

MATH 4991, 4992, 4993. Mathematical Research. Credit 1, 2, 3.
Prerequisite: C or better in MATH 1920 and consent of instructor. This course introduces students to the process of performing research. By reading papers the students will learn how to define open and significant problems, set up a research plan and, if applicable, define relevant experiments. Students will be required to give presentations on either their own or other people's research. These courses can be taken for credit more than once.

Course descriptions for 6000-level courses are contained in the Graduate Catalog.