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. In addition, prerequisites for MATH 1730 Precalculus and MATH 1910 Calculus 1 include trigonometry. For certain pairs of courses, e.g., 1710 and 1730, credit is not given for both. The entry-level course for students planning to major in Engineering, Mathematics, Physics, or other technical areas, but who lack the necessary preparation for Calculus, is MATH 1730 Pre-calculus Mathematics. The prerequisites for this course are 2 years of high school algebra, one year of high school geometry, and at least 12 weeks of high school trigonometry (or equivalent).

For easier navigation, you can jump to 1000 level, 2000 level, 3000 level, 4000/5000 level, and 6000 level courses.
NOTE: Beginning with spring 2004, all mathematics prerequisite courses must be completed with a grade of "C" or better.
NOTE: Upper Division courses are mathematics courses with 3000 and 4000 level numbers.

Note: Links to syllabi lead to departmental syllabi in Adobe's .PDF format. Use Adobe Acrobat Reader to view and print these files

Note: Most recent changes in undergraduate courses were approved by the Executive Committee of the Graduate School on April 24, 2005. They are identified by .

Note: Most recent changes in graduate courses were approved by the Executive Committee of the Graduate School on November 9, 2004.  They are identified by .

Note: At its November 11, 2005, meeting, the University Curriculum Committee approved, effective immediately, the following new policy regarding mathematics courses:

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 MATH 1010 Introduction to Contemporary Mathematical Ideas (Lecture 3 hours, Credit 3 hours) Syllabus for 1010

Prerequisites: Minimum of two years high school algebra and one year of high school geometry.
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 1020 First-Year Connections (Recitation 2 hours, Credit 1 hour) Syllabus for 1020

Prerequisites: None
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. Cross listed as CSC 1020 and PHYS 1020. Recitation 2. Credit 1.

 

 MATH 1130 College Algebra (Lecture 3 hours, Credit 3 hours) Syllabus for 1130

Prerequisites: Minimum of two years high school algebra and one year of high school geometry.
Review of algebra and coordinate geometry; functions; polynomial, rational, exponential, and logarithmic functions; systems of equations; binomial formula; counting (multiplication principle, permutations, and combinations); conics. Credit towards graduation will not be given for MATH 1130 and MATH 1710 or for MATH 1130 and MATH 1730.

 

 MATH 1410 Survey of Elementary Mathematics I (Lecture 3 hours, Credit 3 hours) Syllabus for 1410

Prerequisites: Minimum of two years high school algebra and one year of high school geometry.
Admission is restricted to students majoring in Elementary Education.
Introduction to sets and operations on sets, properties and operations on whole numbers, integers, rational and real numbers.

 

 MATH 1420 Survey of Elementary Mathematics II (Lecture 3 hours, Credit 3 hours) Syllabus for 1420

Prerequisites: "C" or better in MATH 1410

Admission is restricted to students majoring in Elementary Education.
Introduction to elements of probability and statistics, basic concepts of Euclidean geometry including congruence, similarity, measurements, areas and volumes.

 

 MATH 1530 Elementary Probability and Statistics (Lecture 3 hours, Credit 3 hours) Syllabus for 1530

Prerequisites: Two years of high school algebra and one year of high school geometry.
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 normal probability.  Inferential statistics relating to the confidence intervals and hypothesis tests related to the mean and proportion.

 

 MATH 1630 Finite Mathematics (Lecture 3 hours, Credit 3 hours) Syllabus for 1630

Prerequisites: Two years of high school algebra and one year of high school geometry.
Brief review of basic algebra; introduction to probability; matrix algebra and linear programming; applications to business and economics.

 

 MATH 1710 Pre-calculus 1 (Lecture 3 hours, Credit 3 hours), Syllabus for 1710

Prerequisites: Two years of high school algebra and one year of high school geometry.
Review of algebra; relations and functions and their graphs, including polynomial and rational functions; conic sections; inequalities, arithmetic and geometric sequences and series.

 

 MATH 1720 Pre-calculus 2 (Lecture 3 hours, Credit 3 hours), Syllabus for 1720

Prerequisites: Two years of high school algebra and one year of high school geometry.
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.

 

 MATH 1730 Pre-Calculus Mathematics (Lecture 5 hours, Credit 5 hours), Syllabus for 1730

Prerequisites: 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; advanced topics in algebra.

 

 MATH 1830 Concepts of Calculus (Lecture 3 hours, Credit 3 hours) Syllabus for 1830

Prerequisites: 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.

 

 MATH 1910 Calculus I (Lecture 4 hours, Credit 4 hours) Syllabus for 1910

Prerequisites: 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 with applications, sequences and series.

 

 MATH 1920 Calculus II (Lecture 4 hours, Credit 4 hours) Syllabus for 1920

Prerequisites: "C" or better in MATH 1910 or equivalent AP credit for MATH 1910

Limits, continuity, derivatives and integrals of functions of one variable with applications, sequences and series.

 

 MATH 1911-1921 Calculus I Honors Seminar - Calculus II Honors Seminar (Lecture 1, Credit 0, Graded S/U) Syllabus for 1911, Syllabus for 1921

These are enrichment Calculus 1 and Calculus 2 seminars open to all students, and to be taken concurrently with MATH 1910 and MATH 1920, respectively. Recommended minimum Math ACT score is 30.  Upon completion of MATH 1911 and/or MATH 1921 students will be entitled to receive honors credit for MATH 1910 and/or MATH 1920, respectively. Each seminar is graded S/U and carries 0 academic credits.                         .

 

MATH 2010 Elementary Matrix Algebra (Lecture 2 hours, Credit 2 hours) Syllabus for 2010

Prerequisites: "C" or better in MATH 1910

Introduction to basic operations, determinants, inverses, systems of linear equations, vector spaces and dimension, linear transformations, eigenvalues and eigenvectors.

 

MATH 2011 Matrix Algebra Computer Lab (Lab 1 hour, Credit 1 hour) Syllabus for 2011

Corequisites: "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 (Lecture 4 hours, Credit 4 hours) Syllabus for 2110

Prerequisites: "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, topics from vector calculus.

 

 MATH 2120 Differential Equations (Lecture 3 hours, Credit 3 hours) Syllabus for 2120

Prerequisites: "C" or better in MATH 1920

Power series, exact equations, operators, variation of parameters, systems of equations, Laplace transform. It is recommended, but not required, that students take MATH 2010 before taking this course.

 

 MATH 2610 Discrete Structures (Lecture 3 hours, Credit 3 hours) Syllabus for 2610

Prerequisites: "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 (Lecture 1, 1 hour, Credit 1, 1 hour)

Prerequisites: "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 (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 3070, Syllabus for 3080

Prerequisites for MATH 3070: Recommended "C" or better in MATH 1130

Prerequisites for 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 hypotheses 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 (Lecture 4 hours, Credit 3 hours) Syllabus for 3400

Prerequisites: "C" or better in MATH 1920

A rigorous treatment of elements of logic and set theory including propositional calculus (statements, connectives, conditionals, negation), quantifiers, sets and operations on sets, mappings, equivalance relations, mathematical induction. Students are expected to work in an abstract setting using precise definitions and formal proofs.

 

 MATH 3430 College Geometry (Lecture 3 hours, Credit 3 hours) Syllabus for 3430

Prerequisites: "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 (Lecture 3 hours, Credit 3 hours) Syllabus for 3470

Prerequisites: "C" or better in MATH 1920

Random experiments, random variables, enumeration, discrete and continuous distributions, sampling, estimation, hypothesis testing. (Not allowed as a mathematics sequence; no credit allowed for mathematics and computer science majors after having taken MATH 4480.)

 

 MATH 3510-3520 Modern Algebra I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 3510-3520

Prerequisites for MATH 3510: "C" or better in MATH 3400

Prerequisite for MATH 3520: "C" or better in MATH 3510

The number system, mathematical induction, groups, rings, fields, integral domains and mapping.

 

 MATH 3670 Theory and Applications of Random Signals (Lecture 2 hours, Credit 2 hours) Syllabus for 3670

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 (Lecture 3 hours, Credit 3 hours) Syllabus for 3810

Prerequisites: "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)          
          Prerequisites: Consent of Instructor.  Readings and study under the supervision of a qualified staff member.

 

 MATH 4050-5050 Number Theory (Lecture 3 hours, Credit 3 hours) Syllabus for 4050-5050

Prerequisites:  "C" or better in MATH 3400 or consent of instructor.
Properties of integers, division algorithms, prime numbers, diophantine equations, congruences.

 

 MATH 4110-4120/5110-5120 Advanced Calculus I-II (Lecture 2, 2 hours, Recitation 2, 2, Credit 3, 3 hours) Syllabus for 4110-4120-5110-5120

Prerequisites for MATH 4110/5110: "C" or better in MATH 3400 or consent of instructor

Prerequisites for MATH 4120/5120: "C" or better in MATH 4110/5110

Rigorous treatment of functions of one and several variables, integral calculus of 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 (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 4210-4220-5210-5220

Prerequisites for MATH 4210/5210: "C" or better in MATH 1920 (or consent of instructor for MATH 5210)

Prerequisites for MATH 4220/5220: "C" or better in MATH 2120 or consent of instructor

Direct and iterative methods for linear systems, sparse matrices, orthogonal decompositions, least squares, algebraic eigenvalue problem, computational errors and error control, interpolation, differentiation, quadrature, and difference equations, convergence of iterative techniques, non-linear equations, differential equations, special functions.

 

 MATH 4250-4260/5250-5260 Advanced Ordinary Differential Equations I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 4250-4260-5250-5260

Prerequisites for MATH 4250/5250: "C" or better in MATH 2110 and MATH 2120 (or consent of instructor for MATH 5250)

Prerequisites for 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, construction of liapunov functions.

 

 MATH 4310-4320/5310-5320 Introduction to Topology I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 4310-4320-5310-5320

Prerequisites for MATH 4310/5310: "C" or better in MATH 3400 (or consent of instructor for MATH 5310)

Prerequisites for MATH 4320/5320: "C" or better in MATH 4310/5310

Topological spaces, continuity, connectedness, compactness, separation axioms, function spaces, and fundamental group.

 

 MATH 4350-5350 Introductory Combinatorics (Lecture 3 hours, Credit 3 hours) Syllabus for 4350-5350

Prerequisites: "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 (Lecture 3 hours, Credit 3 hours) Syllabus for 4360-5360

Prerequisites: "C" or better in MATH 3400 or consent of instructor

Fundamental concepts of undirected and directed graphs, trees, connectivity, traversability, planarity, colorability, network flows, and matching theory.

 

 MATH 4410-5410 Differential Geometry (Lecture 3 hours, Credit 3 hours) Syllabus for 4410-5410

Prerequisites: "C" or better in each MATH 2110, 2010, and 3400 (or consent of instructor for MATH 5410)

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 (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 4470-4480-5470-5480

Prerequisites for MATH 4470/5470: "C" or better in MATH 2110 or consent of instructor

Prerequisites for MATH 4480/5480: "C" or better in MATH 4470/5470

Mathematical foundations of elementary statistical methods, application and theory, probability in discrete and continuous distribution, correlation and regression, foundations of sampling theory, significance tests.

 

 MATH 4510-5510 Advanced Mathematics for Engineers (Lecture 3 hours, Credit 3 hours) Syllabus for 4510-5510

Prerequisites: "C" or better in MATH 2110 and MATH 2120

Fourier series, partial differential equations, method of Frobenius, Gamma function, Bessel functions, orthogonal polynomials, Sturm-Liouville equations plus other topics.

 

 MATH 4530-4540/5530-5540 Linear Algebra I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 4530-4540-5530-5540

Prerequisites for MATH 4530/5530: "C" or better in MATH 2010 and MATH 3400

Prerequisites for MATH 4540/5540: "C" or better in MATH 4530/5530

A study of matrices and vector spaces including basic operations, systems of linear equations, determinants, eigenvalues, functions of matrices, canonical forms, spectral decomposition, generalized inverses, bases, linear transformations, change of basis, duality, inner product spaces, quadratic and bilinear forms.

 

 MATH 4610/5610 History of Mathematics I (Lecture 3 hours, Credit 3 hours) Syllabus for 4610-5610

Prerequisites: "C" or better in MATH 3400 (or consent of instructor for MATH 5610)

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 (Lecture 3 hours, Credit 3 hours) Syllabus for 4620-5620

Prerequisites: "C" or better in MATH 3400 (or consent of instructor for MATH 5620)

History of mathematics from the beginnings of calculus through the modern times.

 

 MATH 4710/5710 Vector Analysis (Lecture 3 hours, Credit 3 hours) Syllabus for 4710-5710

Prerequisites: "C" or better in MATH 2110

The algebra and the differential and integral calculus of vectors, applications to geometry and mechanics.

 MATH 4750/5750 Category Theory of Sets (Lecture 3 hours, Credit 3 hours) Syllabus for 4750-5750

Prerequisites: "C" or better in MATH 3400 (or consent of instructor for MATH 5750)

Abstracts 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, selected applications.

 MATH 4910-4920/5910-5920 Directed Readings (Credit 3, 3 hours)

Prerequisites: 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 (Lecture 3 hours, Credit 3 hours)

Prerequisites: 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 (Credit 1, 1 hour) Syllabus for 4970

Prerequisites: 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, 1 hour; 2, 2 hours; 3, 3 hours; ) Syllabus for 4991

Prerequisites: "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. Offered on Pass/Fail basis.

 

 MATH 6010-6020 Functional Analysis (Lecture 3 hours, Credit 3 hours) Syllabus for 6010-6020

Prerequisites for MATH 6010: "C" or better in MATH 4120 or MATH 5120

Prerequisites for MATH 6020: "C" or better in MATH 6010

Metric spaces, normed and Banach spaces, inner product and Hilbert spaces. Fundamental theorems for normed and Banach spaces and their applications. Linear operators on normed and Hilbert spaces.

MATH 6070-6080 Applied Linear Statistical Methods I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 6070-6080

Prerequisites for MATH 6070: Consent of instructor

Prerequisites for MATH 6080: "C" or better in MATH 6070

Regression analysis, correlation, analysis of variance, experimental designs.

 

 MATH 6110-6120 Abstract Algebra I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 6110-6120

Prerequisites for MATH 6110: "C" or better in MATH 3520 or consent of instructor

Prerequisites for MATH 6120: "C" or better in MATH 6110

An extensive treatment of groups, semigroups, integral domains, rings and ideals, fields, and Galois fields.

 

 MATH 6150 Mathematical Modeling (Lecture 3 hours, Credit 3 hours) Syllabus for 6150

Prerequisites: Consent of instructor. Applications of mathematics to real world problems with emphasis on problem definition, research, solution, and written report presentation.

 

 MATH 6170-6180 Experimental Design I-II (Lecture 3 hours, Credit 3 hours) Syllabus for 6170-6180

Prerequisites for MATH 6170: Consent of instructor

Prerequisites for MATH 6180: "C" or better in MATH 6170

Introduction to basic concepts of experimental design, fundamental assumptions in analysis of variance, multiple comparison tests, complete randomized design, and general linear model approach to ANOVA, and various experimental designs.

 

 MATH 6210-6220 Topology I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 6210-6220

Prerequisites for MATH 6210: "C" or better in MATH 4320 or MATH 5320 or consent of instructor

Prerequisites for MATH 6220: "C" or better in MATH 6210

Topics in point-set topology, homotopy theory, triangulated spaces, homology theory, other topics in topology.

 

 MATH 6270 Mathematical Statistics (Lecture 3 hours, Credit 3 hours) Syllabus for 6270

Prerequisites: Consent of instructor

Statistical hypothesis, uniform most powerful tests, sufficient statistics, completeness, Roa-Cramer inequality, sequential probability ratio test, analysis of variance, multiple comparisons, nonparametric techniques.

 

 MATH 6310-6320 Complex Analysis I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 6310-6320

Prerequisites for MATH 6310: "C" or better in MATH 4120 or MATH 5120 or consent of instructor

Prerequisites for MATH 6320: "C" or better in MATH 6310

Complex numbers, calculus of complex variables, analytic function. Cauchy's Theorem and complex integration, power series including Taylor's and Laurent's, residue theory with applications, conformal mapping with physical applications.

 

 MATH 6370-6380 Probability Theory and Stochastic Processes I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 6370-6380

Prerequisites for MATH 6370: "C" or better in MATH 4480 or MATH 5480

Prerequisites for MATH 6380: "C" or better in MATH 6370

Probability theory of sets, random variable distribution and characteristic functions, convergence, limits and law of large numbers, convolutions, compound distribution, recurrent events, random walk models, Markov chains, homogeneous, nonhomogeneous, and queueing processes.

 

 MATH 6410-6420 Real Analysis I-II (Lecture 3, 3 hours, Credit 3, 3 hours) Syllabus for 6410-6420

Prerequisites for MATH 6410: "C" or better in MATH 4120 or MATH 5120

Prerequisites for MATH 6420: "C" or better in MATH 6410

Theory of Lebesgue measure and integration, L^p spaces, integration in locally compact spaces.

 

 MATH 6450 Advanced Theory of Computation (Lecture 3 hours, Credit 3 hours) Syllabus for 6450

Prerequisites: Consent of instructor (previous coursework involving proofs and some programming experience are needed).

A rigorous treatment of the theory of computation.  Topics such as: computable functions, the Church-Turing thesis, complexity theory, and P vs NP.

 

 MATH 6460 Computational Methods for Graphics and Modeling (Lecture 3 hours, Credit 3 hours) Syllabus for 6460

Prerequisites: Consent of the instructor (previous coursework involving proofs and some programming experience are needed).

Mathematical methods for graphics and modeling. Topics such as: 3-D transformations, ray tracing, rendering,image processing, and compression.

 

 MATH 6510 Finite Difference Solutions of Partial Differential Equations (Lecture 3 hours, Credit 3 hours) Syllabus for 6510

Prerequisites: "C" or better in MATH 4510 or MATH 5510 or consent of instructor

Approximate solutions of boundary and initial value problems using the finite difference method. Elliptic, parabolic, and hyperbolic PDE's. Numerical differentiation. Solution methods for linear systems.

 

 MATH 6520 Finite Element Solutions of Partial Differential Equations (Lecture 3 hours, Credit 3 hours) Syllabus for 6520

Prerequisites: "C" or better in MATH 4510 or MATH 5510 or consent of instructor

Mathematical foundations of the finite element method. Approximate solutions of PDE's. Polynomial interpolation. Variational techniques. Numerical integration. Solution methods for linear systems. Isoparametric technique.

 

 MATH 6530 Integral Equations and Applications (Lecture 3 hours, Credit 3 hours) Syllabus for 6530

Prerequisites: Consent of instructor

Volterra and Fredholm equations. Green function, Hilbert-Schmidt and Fredholm theories. Neumann series, iterative methods.

 

 MATH 6540 Calculus of Variations and Applications (Lecture 3 hours, Credit 3 hours) Syllabus for 6540

Prerequisites: Consent of instructor

Euler equation, constraints, Lagrange multipliers, Ritz method, applications.

 

 MATH 6610 Operational Mathematics (Lecture 3 hours, Credit 3 hours) Syllabus for 6610

Prerequisites: Consent of instructor

Integral transforms (Laplace, Fourier) inversion and convolution theorems, applications.

 

 MATH 6810 Partial Differential Equations (Lecture 3 hours, Credit 3 hours) Syllabus for 6810

Prerequisites: Consent of instructor

First and second order PDE's, wave, heat and Laplace's equations, applications to boundary and eigenvalue problems of mathematics, physics, and engineering.

 

 MATH 6900 Mathematics Seminar (Lecture 1 hour, Credit 1 or 0 hours)

 

 MATH 6910-6920 Special Topics in Mathematics (Lecture 1-3 hours, Credit 1-3 hours)

Prerequisites: Consent of instructor

Individual study of advanced mathematical topics in fields of interest under the supervision of a qualified staff member.

 

 MATH 6990 Research and Thesis (Credit 3 or 6 hours)

Syllabus for 6991

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