MTH - Mathematics
An introduction to the theory, practical applications and algorithms of nonlinear programming. Prerequisites:
MTH 233.
Credits
3(3-0)
Properties of integers, congruences, greatest common divisors and prime factorization, applications of number theory to computer science and/or cryptology. Prerequisite:
MTH 332.
Credits
3(3-0)
Groups, rings, integral domains, fields, and fundamental homomorphism theorems. Prerequisite:
MTH 332 or graduate status.
Credits
3(3-0)
Vector spaces, subspaces, bases and dimensions; linear transformations, their algebra, their representation by matrices, and linear functionals; eigenvalues, triangularizable and diagonalizable transformations; inner product spaces. Prerequisite:
MTH 523.
Credits
3(3-0)
Representation theory of finite groups, Specht modules, combinatorics of Young tableaux, and symmetric functions. Prerequisite:
MTH 525.
Credits
3(3-0)
Rigorous development of calculus for functions of one variable. The real number system, sequences, limits, continuity, differentiation, integration, exponential and logarithmic functions, series, uniform convergence. Credits will not count towards MA or Ph.D. degree requirements in mathematics. Prerequisites:
MTH 233, 332; or graduate status.
Credits
3(3-0)
Continuation of
MTH 532. Rigorous development of calculus of several variables. Limits, continuity, differentiation, integration, implicit and inverse function theorems, differential forms. Prerequisite:
MTH 532.
Credits
3(3-0)
Initial-boundary value (linear, nonlinear) problems, orthogonal functions, differential operators, numerical techniques, introduction to partial differential equations, applications to biology, chemistry, engineering, medicine, and physics. Prerequisites:
MTH 233, 334.
Credits
3(3-0)
Sets, functions, metric spaces, topological spaces, homeomorphisms, compactness and connectedness, quotient spaces. Prerequisite:
MTH 332 or graduate status.
Credits
3(3-0)
Problem-solving, set theory, logic, number theory, algebra, consumer mathematics and mathematical systems. Credit will not apply toward a master's degree in mathematics. Prerequisites:
MTH 254 and 351.
Credits
3(3-0)
History of mathematical developments of western and non-western cultures for use in grades K-8. Credit will not apply toward a master's degree in mathematics. Prerequisites:
MTH 254, 351.
Credits
3(3-0)
This course explores how popular culture (such as television, comics, movies, music and books) portrays mathematicians and mathematics as a discipline. This course is intended for elementary education mathematics majors and minors or in-service teachers. Prerequisite:
MTH 256.
Credits
3(3-0)
History of arithmetic, algebra, geometry, calculus. Prerequisites:
MTH 332 or
MTH 341, or graduate status.
Credits
3(3-0)
Introduction to the basic principles of combinatorics and graph theory with applications to problems of nonmathematical origin. Prerequisites:
MTH 523.
Credits
3(3-0)
Mathematical theory and applications of mathematical programming. Linear programming duality, integer programming, mixed integer programming, and dynamic programming. Prerequisites:
MTH 133.
Credits
3(3-0)
Continuation of
MTH 586. Theory and application of stochastic models in operations research. Inventory models, queuing theory. Markov chains, stochastic programming. Prerequisites: STA 382,
MTH 586.
Credits
3(3-0)
Problem-solving techniques demonstrated through solutions of the Putnam Examination problems. Designed particularly for those students interested in participating in the Putnam Examination. Prerequisite:
MTH 233; permission of instructor.
Credits
1-3(Spec)
Subject matter not included in regular mathematics education course. May be taken for credit more than once, total credit not to exceed 6 hours. Specific topics and pre/co-requisites will be announced in Course Search and Registration. May not be counted toward a major or minor in mathematics except for students pursuing a B.S. in Ed. degree. Pre/Co- requisites: See Course Search and Registration.
Credits
1-6(Spec)
Subject matter not included in regular course. May be taken for credit more than once, total credit not to exceed 6 hours. Pre/Co-requisite: See Course Search and Registration.
Credits
1-6(Spec)
The in-depth study of a topic in mathematics under the direction of a faculty member. Prerequisite: Permission of instructor.
Credits
1-6(Spec)
A non-credit course intended for students who have completed all program credits but still need to use university resources to complete their degree requirements.
Credits
1(1-0)
Isomorphism theorems for groups, group actions, Sylow theorems, product of groups, structure theory of rings, ideals, Euclidean domains, principal ideal domains, and unique factorization domains. Prerequisite:
MTH 523, Recommended:
MTH 525.
Credits
3(3-0)
Modules, free modules, tensor products of modules, exact sequences of modules, modules over a principal ideal domain, field theory, and Galois theory. Prerequisites:
MTH 525, 623.
Credits
3(3-0)
Lie algebras, semisimplicity, representation of Lie algebras, weights and roots, universal enveloping algebras, character and dimension formulas. Prerequisite:
MTH 625. Recommended:
MTH 527.
Credits
3(3-0)
Development of integration theory with introduction to Lebesgue measure and integral on the real line. Elementary theory of normed spaces, bounded linear operators and linear functionals with applications. Prerequisite:
MTH 532.
Credits
3(3-0)
A study of functional analysis. Consideration of Banach spaces, metric spaces, and compact spaces. General measure and integration theory. Prerequisite:
MTH 632.
Credits
3(3-0)
Study of Fourier Series, convergence, summability, Fourier Transforms, distributions. Applications of fast Fourier Transform to Heat and Wave Equation. Signal Processing, Fourier Optics. Prerequisites:
MTH 532.
Credits
3(3-0)
Complex numbers, holomorphic functions, elementary functions, Cauchy's theorem and Integral formula, Taylor and Laurent series, residue theorem and its applications, Rouché's theorem. Prerequisite:
MTH 532.
Credits
3(3-0)
Conformal mapping, Möbius transformations, harmonic functions, Dirichlet problem, entire and meromorphic functions, analytic continuation, Riemann surfaces, applications of complex analysis. Prerequisite: MTH 636.
Credits
3(3-0)
Numerical solution of one-variable nonlinear equations, numerical linear algebra, approximation theory, eigenvalue-eigenvector computation, numerical differentiation and integration, initial value problems for ordinary differential equations. Prerequisite:
MTH 532. Pre/Co-requisite:
MTH 533.
Credits
3(3-0)
Advanced topics in geometry, foundations, non-Euclidean geometry. Prerequisite:
MTH 341.
Credits
3(3-0)
Differential geometry of curves and surfaces. Curvature, maps between surfaces, vector fields and differential forms, Stokes' Theorem, Euler Characteristic, Gauss-Bonnet Theorem, manifolds, Riemannian metrics. Prerequisites:
MTH 532 or 545.
Credits
3(3-0)
Homotopy and the fundamental group. Free products, van Kampen's theorem, covering spaces, universal covers, and deck transformations. Homology, cohomology, exact sequences, and higher homotopy groups. Prerequisites:
MTH 545, 623.
Credits
3(3-0)
The history, concepts, and learning of measurement systems. The metric system and laboratory activities are emphasized. Prerequisite: teaching experience.
Credits
3(3-0)
Use of instructional technology for teaching and learning mathematics and an introduction to related research literature in mathematics and mathematics education. Prerequisite: MTH 566.
Credits
3(3-0)
History of the development of modern mathematics from 1700 into the 20th century. Prerequisites:
MTH 525, 532.
Credits
3(3-0)
Rigorous study of graph theory, connectivity, coloring, flows, and Ramsey theory. Prerequisite:
MTH 578. Pre/Co-requisite:
MTH 525.
Credits
3(3-0)
Seminars focused on current issues in mathematics education. May be taken for credit more than once, total credit not to exceed four hours. Three credits needed before it counts as an elective on any graduate degree in mathematics. Prerequisite: Permission of an instructor.
Credits
1-4(Spec)
One hour seminars in subfields of mathematics and its applications; 3 credits needed before it counts as elective on graduate degrees in mathematics. Prerequisites: Graduate standing in mathematics and permission of instructor.
Credits
1-4(Spec)
Consideration of subject matter not included in regular courses. May be taken for credit more than once, total credit not to exceed 6 hours. Prerequisites: graduate standing; additional instructor prerequisites will be announced in the Course Search and Registration.
Credits
1-6(Spec)
Consideration of subject matter not included in regular courses. May be taken for credit more than once; total credit not to exceed six hours. Pre/Co-requisites: See Course Search and Registration.
Credits
1-6(Spec)
Open to graduate students in mathematics. May be taken for credit more than once; total credit not to exceed 9 hours. Prerequisite: permission of the instructor.
Credits
1-9(Spec)
Plan B paper is normally an expository paper or research project on an area or problem related to but in addition to material covered in a course, written under the direction of graduate faculty. Each Plan B project is 1 credit hour. May be taken for credit more than once. Total credit not to exceed 2 hours. CR/NC only. Prerequisites: permission of advisor.
Credits
1-2(Spec)
Advanced topics in the area of algebra that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisite:
MTH 623; permission of instructor. Recommended:
MTH 525, 625.
Credits
3-9(Spec)
Advanced topics in the area of applied mathematics that are not covered in the regularly offered courses. Specific topics are determined by the instructor. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisites:
MTH 534 or 632 or 634; permission of instructor. Recommended:
MTH 534, 632, 634, 638.
Credits
3-9(Spec)
Fundamentals of topological vector spaces, normed spaces, Banach and Hilbert spaces, functionals on such spaces, operators on Banach and Hilbert spaces, spectral theorems, Banach algebras. Prerequisites:
MTH 632, 636.
Credits
3(3-0)
Solutions of partial differential equations by analytic and numerical techniques using standard methods, including Fourier series and Laplace transforms, perturbation, finite elements and finite differences. Prerequisites:
MTH 334 and
MTH 636.
Credits
3(3-0)
Topics in the area of analysis that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisites:
MTH 632 or 636; permission of instructor. Recommended:
MTH 533, 632, 636, 732.
Credits
3-9(Spec)
Advanced topics in the area of geometry that are not covered in the regularly offered courses. To be taken as a three-credit course and may be repeated for a maximum of nine credit hours. Prerequisites:
MTH 644; permission of instructor. Recommended:
MTH 533, 645.
Credits
3-9(Spec)
Methods in teaching undergraduate mathematics including technology use, cooperative learning, inquiry, and guided discovery. Students will create activities and discuss issues surrounding undergraduate instruction. Prerequisite: Completion of 12 hours of graduate level mathematics at CMU and admission to one of the graduate programs in the Department of Mathematics.
Credits
3(3-0)
Introduction to understanding and interpreting mathematics education research at the undergraduate level. Prerequisite:
MTH 761.
Credits
3(3-0)
Advanced perspectives in collegiate mathematics education as it relates to the areas of teaching, learning, and curriculum. Prerequisites:
MTH 762 and
EDU 614.
Credits
3(3-0)
Introduction to the methods of qualitative research in mathematics education including research design, development of protocols, fieldwork, collecting and analyzing data, and techniques of interviewing. Prerequisite:
MTH 763.
Credits
3(3-0)
Teaching of approved undergraduate mathematics or statistics courses. Students will conduct their teaching internship under the supervision of a graduate faculty member. CR/NC only. Prerequisites:
MTH 761; successful completion of all qualifying examinations.
Credits
3-6(Spec)
Use of a review of literature to focus research questions and to develop a research proposal. Each student develops a proposal for his/her dissertation research. Prerequisites:
MTH 764.
Credits
3(3-0)
Conduct a pilot study to collect and analyze data. The students will then develop conclusions and implications of the study. Prerequisites:
MTH 767. Pre/Co-requisite:
PSY 611.
Credits
3(3-0)
Advanced topics in the area of combinatorics that are not covered in the regularly offered courses. To be taken as a three credit course and may be repeated for a maximum of nine credit hours. Prerequisite:
MTH 578; permission of instructor. Recommended:
MTH 525, 623, 678.
Credits
3-9(Spec)
In-depth doctoral practicum project supervised by a faculty member or internship experience in an external agency supervised by a faculty member and a professional supervisor. CR/NR only. Prerequisites: Successful completion of all required Ph.D. qualifying examinations; permission of the faculty supervisor.
Credits
3-6(Spec)
Consideration of subject matter not included in regular courses. May be taken for credit more than once; total credit not to exceed 6 hours. Prerequisite: completion of 30 hours of coursework required for the Doctoral program.
Credits
1-6(Spec)
Open to doctoral students in mathematics. May be taken for credit more than once; total credit not to exceed 9 hours. Prerequisites: 30 hours of coursework toward the doctoral program; permission of the instructor.
Credits
1-9(Spec)
Master's thesis research. CR/NC only. Prerequisites: Graduate status and permission of thesis advisor.
Credits
1-6(Spec)
Doctoral dissertation research. CR/NC only. Prerequisites: Completion of all Ph.D. qualifying exam requirements; permission of dissertation advisor.
Credits
1-30(Spec)