Program Director
Dr. G. Jay Kerns
620 Cafaro Hall
(330) 941-3310
gkerns@ysu.edu
Program Description
The Department of Mathematics and Statistics offers the M.S. degree in mathematics both traditionally and online. Options for this degree include:
- predoctoral studies,
- applied mathematics,
- computer science,
- secondary mathematics,
- statistics, and
- actuarial science.
Graduate faculty members have a broad range of research interests in both pure and applied areas. The curriculum stresses theoretical as well as computational mathematics and is flexible enough to key a student’s program to individual interests and abilities. Receiving a well-rounded education in mathematics, graduates can pursue a Ph.D., secure a position in government or industry, or further a teaching career.
The Department of Mathematics and Statistics also offers a Master of Science in Data Science and Statistics, a Graduate Certificate in Mathematics, and a Graduate Certificate in Data Analytics.
Admission Requirements
In addition to the minimum College of Graduate Studies admission requirements, students must also have the following:
| COURSE | TITLE | S.H. |
|---|---|---|
| A cumulative undergraduate cumulative grade point average of at least 3.0 (on a 4.0 scale) in all undergraduate mathematics an statistics courses. | ||
| A completed sequence in standard calculus comparable to: | ||
| MATH 1571 | Calculus 1 | 4 |
| MATH 1572 | Calculus 2 | 4 |
| MATH 2673 | Calculus 3 | 4 |
| Previous courses in discrete structures and linear algebra comparable to: | ||
| MATH 3715 | Discrete Mathematics | 3 |
| MATH 3720 | Linear Algebra and Matrix Theory | 3 |
| Previous courses in abstract algebra and real analysis comparable to: | ||
| MATH 5821 | Topics in Abstract Algebra | 4 |
| MATH 5851 | Topics in Analysis | 4 |
Students not satisfying all of the above may be admitted with provisional status subject to the approval of the graduate program director and the graduate dean. Students may need to complete prerequisite examinations to demonstrate readiness for the core courses. If students do not pass the prerequisite examination, students must complete the prerequisite courses in the earliest available semester. The prerequisite courses are not included in the 30-semester hour minimum requirement.
Graduate Faculty
Jozsi Z. Jalics, Ph.D., Professor
Computational neuroscience; mathematical biology; dynamical systems; partial differential equations
G. Jay Kerns, Ph.D., Professor
Signed measures; infinite divisibility; exchangeability in probability and statistics; applications of stochastic processes
Lucy Xiaojing Kerns, Ph.D., Associate Professor
Simultaneous confidence bands; minimum effective doses; benchmark dose methodology
Thomas L. Madsen, Ph.D., Associate Professor
Abstract algebra; group theory; representation theory
Nguyet Thi Nguyen, Ph.D., Associate Professor
Financial models; Monte Carlo simulation; actuarial science
Anita C. O'Mellan, Ph.D., Professor
Graph theory; combinatorics; early childhood mathematics education
Alicia Prieto Langarica, Ph.D., Professor
Mathematical biology; agent-based modeling
Thomas Smotzer, Ph.D., Professor
Real analysis; measure theory; operator theory
Jamal K. Tartir, Ph.D., Professor
Set-theoretic topology
Padraic ("Paddy") W. Taylor, Ph.D., Associate Professor
Multipoint Boundary Value Problems
Thomas P. Wakefield, Ph.D., Professor, Chair
Character theory; actuarial science
- Students entering without a prior course in abstract algebra must include MATH 5821 Topics in Abstract Algebra in their program, to be taken in the earliest available semester, and students entering without a prior course in theoretical analysis must include MATH 5851 Topics in Analysis in their program, to be taken in the earliest available semester. Students may need to complete prerequisite examinations in algebra and/or analysis to demonstrate readiness for the core courses. If students do not pass the prerequisite examination, students must complete the prerequisite courses in the earliest available semester. These courses are not included in the 30-semester-hour minimum requirement.
- A minimum of 30 semester hours of credit excluding MATH 5821 Topics in Abstract Algebra and MATH 5851 Topics in Analysis
- A cumulative grade point average of at least 3.0.
- The student’s combined undergraduate and graduate programs must include a mathematics core comprising the following courses or their equivalent:
Course List COURSE TITLE S.H. Topics in Abstract Algebra (if needed, taken in the earliest available semester (Does not count toward master's degree)) Topics in Analysis (if needed, taken in the earliest available semester (Does not count toward master's degree)) MATH 6926 Advanced Linear Algebra 3 MATH 6947 Methods of Applied Mathematics 3 MATH 6952 Analysis of Real Variable Functions 3 Choose one of the following: 3 Mathematical Project or STEM 6990STEM Graduate Internships 18 Hours of Electives in MATH/STAT/DATX at the 5800 or higher with at least one course at the 6900-level. 18 Total Semester Hours 30
- Before completing 12 semester hours, the student must submit the entire degree program for approval and evaluation by the Graduate Executive Committee in the Department of Mathematics and Statistics. At least 15 hours of the student's approved program must be at the 6900 level. Subsequent revisions to this program must be approved by the Graduate Executive Committee.
- MATH 6999 Thesis is highly recommended. An abstract of a proposed thesis must be submitted for approval prior to registering for the course.
- Satisfactory performance on two oral examinations of graduate coursework in addition to presentation of project, internship presentation, or defense of thesis. The subject matter for the oral examinations must be approved by the Graduate Executive Committee.
Students with particular interests or career goals are advised to choose elective courses based upon the recommendations below.
Predoctoral Studies in Mathematics and/or Applied Mathematics
| COURSE | TITLE | S.H. |
|---|---|---|
| MATH 6922 | Advanced Topics in Group and Ring Theory | 3 |
| MATH 6975 | Complex Analysis 1 | 3 |
| MATH 6980 | Topology 1 | 3 |
| STAT 6940 | Advanced Data Analysis | 3 |
| MATH 6955 | Advanced Differential Equations | 3 |
| STAT 6943 | Mathematical Statistics 1 | 3 |
Statistics
| COURSE | TITLE | S.H. |
|---|---|---|
| STAT 6940 | Advanced Data Analysis | 3 |
| STAT 6948 | Linear Models | 3 |
| STAT 6943 | Mathematical Statistics 1 | 3 |
| STAT 6944 | Mathematical Statistics 2 | 3 |
Actuarial Science
| COURSE | TITLE | S.H. |
|---|---|---|
| STAT 5802 | Mathematical Interest Theory | 3 |
| STAT 6943 | Mathematical Statistics 1 | 3 |
| STAT 6944 | Mathematical Statistics 2 | 3 |
Applied Mathematics
| COURSE | TITLE | S.H. |
|---|---|---|
| MATH 5860 | Numerical Analysis 1 | 3 |
| MATH 6955 | Advanced Differential Equations | 3 |
| MATH 6957 | Partial Differential Equations | 3 |
| STAT 6940 | Advanced Data Analysis | 3 |
| STAT 6943 | Mathematical Statistics 1 | 3 |
Secondary/Community College Mathematics
| COURSE | TITLE | S.H. |
|---|---|---|
| STAT 6943 | Mathematical Statistics 1 | 3 |
| STAT 6940 | Advanced Data Analysis | 3 |
| MATH 6922 | Advanced Topics in Group and Ring Theory | 3 |
| MATH 6975 | Complex Analysis 1 | 3 |
| MATH 6980 | Topology 1 | 3 |
| Those students seeking certification should consult an advisor in the Department of Teacher Education. | ||
Computer Science
Students in coursework in computer science in addition to mathematics should plan their graduate program in consultation with advisors in both the Department of Mathematics and Statistics and the School of Computer Science, Information and Engineering Technology.
Accelerated MS Mathematics
Undergraduate students can apply for admission into the accelerated program for the MS in Mathematics after completing 78 semester hours with a GPA of 3.3 or higher. After being admitted into the program, students can take a maximum of nine semester hours of graduate coursework that can count toward both an bachelor's and master's degree from the Department of Mathematics and Statistics. The courses chosen to count for both undergraduate and graduate coursework must be approved by the Graduate Executive Committee within the Department upon admission into the program. An additional three hours of graduate coursework can be completed as an undergraduate and used exclusively for graduate credit.
Learning Outcomes
Students will develop and demonstrate the ability to reason mathematically by constructing mathematical proofs and recognizing and analyzing accurate numerical data in appropriate core courses. Students will learn that truth in mathematics is verified by careful argument, and will demonstrate the ability to make conjectures and form hypotheses, test the accuracy of their work, and effectively solve problems.
Students will learn to identify fundamental concepts of mathematics as applied to science and other areas of mathematics, and to interconnect the roles of pure and applied mathematics.
Students will demonstrate that they can communicate mathematical ideas effectively, both orally and in writing, by completing a graduate project or thesis involving an investigative mathematical project, together with oral and written examinations.
Students in cooperative doctoral programs will demonstrate their ability to create significant, original mathematics.
Graduate Courses
MATH 5821 Topics in Abstract Algebra 4 s.h.
A course in abstract algebra aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3721 and MATH 5821.
Prereq.: Permission of graduate coordinator or department chair.
MATH 5822 Abstract Algebra 2 3 s.h.
A continuation of MATH 3721 with special emphasis on fields. Additional topics in pure or applied algebra.
Prereq.: MATH 3721 or equivalent.
MATH 5823 Abstract Algebra 3 3 s.h.
This course introduces advanced topics in field theory. Topics may include principal ideal domains, irreducibility, quotient rings, algebraic extensions, finite fields, splitting fields, and the Galois group.
Prereq.: MATH 4822.
MATH 5828 Number Theory 3 s.h.
A study of congruences, Diophantine equations, quadratic residues, special number theory functions, and selected applications.
Prereq.: MATH 3721.
MATH 5832 Euclidean Transformations 3 s.h.
General properties of functions and transformations; isometries and transformations of the Euclidean plane; the complex plane, its geometry and subfields; transformational, analytical, and vector approaches to Euclidean geometry; connections to other branches of mathematics and applications.
Prereq.: MATH 3720 and MATH 4830.
MATH 5835 Introduction to Combinatorics and Graph Theory 3 s.h.
The pigeonhole principle; permutations, combinations, the binomial theorem; the inclusion-exclusion principle; recurrence relations; graphs and digraphs, paths and cycles, trees, bipartite graphs and matchings.
Prereq.: C or better in either MATH 3715 or CSCI 3710 and C or better in MATH 3720.
MATH 5843 Theory of Probability 3 s.h.
The mathematical foundation of probability theory including the study of discrete and continuous distributions. Other topics selected from limit theorems, generating functions, applications. Credit will not be given for MATH 5843 and STAT 5843.
Prereq.: STAT 3743 and MATH 2673.
MATH 5845 Operations Research 3 s.h.
An introduction to operations research with emphasis on mathematical methods. Topics may include: linear programming, sensitivity analysis, duality theory, transportation problems, assignment problems, transshipment problems, and network problems.
Prereq.: MATH 3715 and MATH 3720.
MATH 5849 Computational Methods for Problems in the Physical Sciences 3 s.h.
Use of contemporary computational approaches to conduct research in the physical sciences using Matlab and supercomputers. Algorithm development and formal exercise tasks may vary depending on the stage of the course, student abilities, and the topic under consideration. Provides application of the techniques discussed in the class to real world situations.
Prereq.: MATH 3705 and PHYS 2610.
Cross-Listed: CSCI 5849 and PHYS 5849.
MATH 5851 Topics in Analysis 4 s.h.
A course in analysis aimed at developing a broad understanding of the subject. Credit will not be given for both MATH 3751 and MATH 5851.
Prereq.: Permission of graduate coordinator or department chair.
MATH 5855 Ordinary Differential Equations 3 s.h.
A second course in differential equations with emphasis on nonlinear problems and qualitative methods or on boundary value problems. Topics are chosen from: proofs of fundamental theorems, phase plane analysis, limit cycles and the Poincare-Bendixon theorem, biological models, stability via Liapunov functions, asymptotic methods, and boundary value problems.
Prereq.: MATH 3705 and MATH 3720.
MATH 5857 Partial Differential Equations 3 s.h.
Introduction to partial differential equations (PDE) including solution techniques and applications. Classifications of the basic types of PDE's (hyperbolic, parabolic and elliptic) and dependence on boundary and initial conditions. Topics include Fourier series, integral transforms (Fourier, Laplace), and applications in vibrations, electricity, heat transfer, fluids or other selected topics.
Prereq.: MATH 3705 and MATH 3720.
MATH 5860 Numerical Analysis 1 3 s.h.
The theory and techniques of numerical computation. The solution of a single equation, interpolation methods, numerical differentiation and integration, direct methods for solving linear systems.
Prereq.: MATH 3720 and CSIS 2610 and MATH 2673, MATH 2673H, or MATH 2686H.
MATH 5861 Numerical Analysis 2 3 s.h.
Numerical methods of initial-value problems, eigenvalue problems, iterative methods for linear and nonlinear systems of equations, and methods involving least squares, orthogonal polynomials, and fast Fourier transforms.
Prereq.: MATH 5860 or equivalent.
MATH 5880 Introduction to Topology 3 s.h.
An introduction to the basic concepts of general topology: compactness, connectedness, and continuity in topological spaces.
Prereq.: MATH 3721 and MATH 3751.
MATH 5884 Mathematical Logic 3 s.h.
An introduction to the study of theories in formalized languages and to the theory of models.
Prereq.: MATH 3721 or PHIL 3719.
MATH 5895 Selected Topics in Mathematics 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895A Special Topics Physics of Gravity and Curvature 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895B Selected Topics in Mathematics Advanced Topics in Graph Theory 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MA
MATH 5895C ST Advanced Engineering Math 2 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895D Selected Topics Measure Theory 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH
MATH 5895E Selected Topics Analysis for Teachers 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MAT
MATH 5895F Selected Topics Computational Methods for Problems in Physical Sciences 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH
MATH 5895I Selected Topics in Mathematics Survey of Pure Mathematics 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895J Selected Topics Advanced Topics in Graph Theory 2 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895M Selected Topics in Mathematics Algebra 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751.
MATH 5895P Special Topics Discrete Math 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895Q Special Topics Topology 2 3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or 3751.
MATH 5895S Selected Topics in Representation Theory 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895V Selected Topics in Mathematics Lie Groups and Algebras 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895W Selected Topics in Mathematics Topology 2 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 5895Z Selected Topics in Mathematics Advanced Engineering Mathematics 1 2-3 s.h.
The study of a standard mathematical topic in depth or the development of a special area of mathematics. May be repeated twice.
Prereq.: 24 s.h. of mathematics applicable to the mathematics major including either MATH 3721 or MATH 3751.
MATH 6900 Mathematics Workshop 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U.
Prereq.: Permission of graduate coordinator.
MATH 6900A Workshop Teaching Math Grade 9 to 10 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900B Workshop Integrating Technologies 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900C Workshop Teaching Math Grade 5 to 6 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900D Workshop Teaching Math Grade 3 to 4 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900E Workshop Teaching Math 2 Gr 3 to 4 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900F Workshop Teaching Math 2 Gr 5 to 6 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900G Workshop Teaching Math 2 Gr 7 to 8 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900I Workshop Teaching Math 2 Gr 9 to 10 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900J Workshop Cncpt App Tch Math 3 Gr 3 4 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900K Workshop Cncpt App Tch Math 3 Gr 5 6 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900L Workshop Cncpt App Tch Math 3 Gr 7 8 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900M Cncpt App Tchng Math 3 Gr 9 10 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900N Workshop TI-Nspire 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900O Workshop TI-Nspire and SMART Boards 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900P Workshop Creativity and Innovation 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900Q Workshop Integrate Mult Technologies 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6900R Workshop CCSS Problem Solving and More 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. 1-6 s.h.
Prereq.: Permission of graduate coordinator.
MATH 6901 Mathematics Workshop 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U.
Prereq.: Permission of graduate coordinator.
MATH 6901A Mathematics Workshop Leveraging Technology for ACT Success 1-6 s.h.
Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U.
MATH 6905 College Teaching of Mathematics 1 s.h.
Intensive preparation for teaching lower-level mathematics courses, featuring formal instruction and orientation on teaching issues, evaluated presentations, mentored classroom instruction, and weekly teaching seminars. Topics include course design, policies, syllabi, grading; classroom teaching problems; orientation in Mathematics Assistance Center, specific lower-level mathematics courses, online tutorial services. Required of graduate assistants in the Department of Mathematics and Statistics and to be taken each semester the student is a graduate assistant. Grading is S/U. Does not count toward credit in the program.
MATH 6910 Advanced Engineering Mathematics 1 3 s.h.
Theory and solution techniques used in engineering applications. Topics include brief review of ordinary differential equations and linear algebra; vector calculus, integral theorems, complex analysis, series, residue theory, potential theory, special functions, integral transforms, partial differential equations and applications in mathematical modeling.
Prereq.: MATH 3705.
MATH 6911 Advanced Engineering Mathematics 2 3 s.h.
Theory and solution techniques used in engineering applications. Topics include brief review of ordinary differential equations and linear algebra; vector calculus, integral theorems, complex analysis, series, residue theory, potential theory, special functions, integral transforms, partial differential equations and applications in mathematical modeling.
Prereq.: MATH 6910.
MATH 6915 Mathematical Foundations 3 s.h.
Order-theoretic and monadic foundations of mathematics: ordered structures; topologies; powerset operators of a function; applications to continuity, compactness, algebra, logic, and calculus.
Prereq.: MATH 3721 Abstract Algebra I and MATH 3751 Real Analysis I, or permission of graduate coordinator.
MATH 6920 Advanced Topics in Algebra 3 s.h.
A continuation of MATH 5821 with special emphasis on groups acting on sets, Sylow's Theorem and its applications, ring homomorphisms, ideals, and polynomial rings. Credit will not be given for MATH 5822 and 6920.
Prereq.: MATH 3721 or 5821.
MATH 6922 Advanced Topics in Group and Ring Theory 3 s.h.
A continuation of MATH 5821 with special emphasis on groups acting on sets, Sylow's Theorem and its applications, ring homomorphisms, ideals, and polynomial rings. Credit will not be given for MATH 4822 and MATH 6922.
Prereq.: MATH 3721 or MATH 5821.
MATH 6923 Advanced Topics in Field Theory 3 s.h.
This course introduces the major results in advanced field theory. These results include splitting fields, algebraic extensions, finite extensions, cyclotomic polynomials, and finite fields. Credit will not be given for MATH 4823 and MATH 6923.
Prereq.: MATH 4822 or MATH 6922.
MATH 6925 Advanced Numerical Analysis 3 s.h.
Eigenvalue-eigenvector analysis, boundary value problems, and approximation methods for partial differential equations, and additional topics.
Prereq.: MATH 3720 Linear Algebra and Matrix Theory, MATH 3760 Numerical Analysis I, knowledge of high-level programming language, and either MATH 5852 or 5861, or permission of graduate coordinator.
MATH 6926 Advanced Linear Algebra 3 s.h.
This advanced linear algebra course will include a study of abstract vector spaces and linear transformations, among other topics. Applications of linear algebra may be included.
Prereq.: MATH 3721 or MATH 5821 or satisfactory score on a Departmental prerequisite examination.
MATH 6933 Geometry 3 s.h.
General theory of incidence structures and modern geometric theories.
Prereq.: MATH 3721 Abstract Algebra I and either MATH 4830 Foundations of Geometry or MATH 5835.
MATH 6936 Advanced Topics and Research in Graph Theory 3 s.h.
This is a research-based course in graph theory that builds upon knowledge learned in MATH 5835. The research process of a mathematician will be introduced and exercised while exploring advanced topics in graph theory and making discoveries through independent research.
Prereq.: MATH 5835.
MATH 6937 Graph Theory 3 s.h.
Advanced study of graph theory, graph algorithms, and applications of graph theory. Topics may include Ramsey theory, extremal graph theory, flows and networks, planarity, graph colorings, and combinatorial optimization.
Prereq.: MATH 5835.
MATH 6938 Combinatorics 3 s.h.
Advanced study of combinatorial models. Topics may include extremal set theory, matroids, inversion formulae, counting techniques, generating functions, difference sets, combinatorial designs, and incidence structures.
Prereq.: MATH 3721 Abstract Algebra I and MATH 5835.
MATH 6945 Stochastic Processes 3 s.h.
Identical to STAT 6945.
MATH 6947 Methods of Applied Mathematics 3 s.h.
This course surveys topics in applied mathematics and may include scaling, perturbation methods, stationary phase analysis, multi-scale asymptotics, transform methods, Green's functions, discrete models, the calculus of variations, or optimization.
Prereq.: Graduate Standing.
MATH 6948 Linear Models 3 s.h.
A study of linear statistical models of the relationship between analysis of variance and regression and the assumptions underlying the analysis of variance.
Prereq.: MATH 3720 Linear Algebra and Matrix Theory and either MATH/STAT 5844 or 6944, or permission of graduate coordinator.
MATH 6952 Analysis of Real Variable Functions 3 s.h.
This course covers topics in the analysis of functions, mainly of several variables, and may include uniform convergence of sequences of functions and some consequences, functions on n-space, derivatives in vector spaces, and results such as the mean value theorem, Taylor's formula, inverse mapping theorem, and the implicit mapping theorem.
Prereq.: MATH 3751 or MATH 5851 or satisfactory score on a Departmental prerequisite examination.
MATH 6955 Advanced Differential Equations 3 s.h.
Proofs of existence and uniqueness of nonautonomous, nonlinear equations. Additional topics may include advanced linear systems, partial differential equations, and integral equations.
Prereq.: MATH 3720 and MATH 3705 or permission of graduate coordinator.
MATH 6957 Partial Differential Equations 3 s.h.
An introduction to partial differential equations (PDE) and their applications. The classification of the basic types of linear partial differential equations, development of how boundary and initial conditions affect solutions, exploration, and application of solution techniques for PDEs and explosions in orthogonal functions will be presented.
Prereq.: MATH 3705 and MATH 3720 or equivalent .
MATH 6966 Abstract Analysis II 3 s.h.
Leb'sgue integration and measure on the real line. General measure theory and functional analysis, including the Radon-Nikodym theorem, the Fubini theorem, the Hahn-Banach theorem, the closed graph and open mapping theorems, and weak topology.
Prereq.: MATH 6965, or permission of graduate coordinator.
MATH 6975 Complex Analysis 1 3 s.h.
Analytic and meromorphic functions of a complex variable, contour integration, the Cauchy-Goursat theorem, Taylor and Laurent series, residues and poles, conformal mapping. Credit will not be given for both MATH 4875 and MATH 6975.
Prereq.: MATH 3751 or permission of graduate coordinator.
MATH 6976 Complex Analysis II 3 s.h.
The Cauchy theorem, the Weierstrass, Mittag-Lefler, Picard, and Riemann theorems, Riemann surfaces, harmonic functions.
Prereq.: MATH 5875 or 6975, or permission of graduate coordinator.
MATH 6980 Topology 1 3 s.h.
Basic concepts of topological spaces and mappings between them, including compactness, connectedness, and continuity. Credit will not be given for both MATH 4880 and MATH 6980.
Prereq.: MATH 3721 Abstract Algebra I and MATH 3751 Real Analysis I, or permission of graduate coordinator.
MATH 6981 Topology 2 3 s.h.
Separation, metrization, compactification. Additional topics will be selected from point-set topology, fuzzy topology, algebraic topology, combinatorial topology, topological algebra.
Prereq.: MATH 4880 or MATH 6980, or permission of graduate coordinator.
MATH 6984 Mathematical Logic I 3 s.h.
Syntax and semantics of propositional and first-order calculi with applications. Credit will not be given for both MATH 5884 and 6984.
Prereq.: MATH 3721 Abstract Algebra I or MATH 3751 Real Analysis I or PHIL 3719 Symbolic Logic, or permission of graduate coordinator.
MATH 6985 Mathematical Logic II 3 s.h.
Topics may include elements of recursive function theory, Godel's incompleteness theorem, decision problems for theories, order-theoretic models, fuzzy semantics.
Prereq.: One of MATH 2683 or 6915, and one of 5884 or 6984; or permission of graduate coordinator.
MATH 6989 Doctoral Qualifier Problems 3 s.h.
Intense review of undergraduate and graduate level linear algebra, abstract algebra, analysis, complex variable, and topology with emphasis on sample problems from qualifying exams at regional doctorate institutions.
Prereq.: Permission of graduate coordinator.
MATH 6990 Independent Study 1-3 s.h.
Study under the supervision of a staff member. May be repeated.
Prereq.: Consent of graduate coordinator.
MATH 6995 Special Topics 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995D Selected Topics Measure Theory 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995E ST Math Modeling for Teachers 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995F Special Topics Analysis 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995G Special Topics Discrete Mathematics 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995I Special Topics: Survey of Pure Mathematics 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995M Special Topics Algebra For Teachers 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995P Special Topics Advanced Topics in Graph Theory 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995Q Special Topics History of Mathematics 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995S Special Topics in Representation Theory 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995T Special Topics Advanced Topics in Graph Theory 2 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995U ST: Advanced Topic in Geometry 1-3 s.h.
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Prereq.: Permission of graduate coordinator and department chair.
MATH 6995V Special Topics Lie Groups and Algebras 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995W Special Topics Applied Time Series Analysis and Forecasting 1-3 s.h.
Specialized topics selected by the staff. May be repeated up to 12 semester hours.
Prereq.: Permission of graduate coordinator and department chair.
MATH 6995Y Special Topics: Biostatistics 1-3 s.h.
MATH 6995Z ST Functions of Real Variable 3 s.h.
MATH 6996 Mathematical Project 1-3 s.h.
Individual research project culminating in a written report or paper, though not as broad in scope as a thesis. May be repeated once if the second project is in a different area of mathematics.
MATH 6999 Thesis 3 s.h.
A student may register for six semester hours in one semester or for three semester hours in each of two semesters.
MATH 7005 Advanced Topics in Categorical Topology 3 s.h.
Content varies with each offering. Implements ideas from MATH 6915, MATH 6980, MATH 6981, and studies categorical methods in topology and related concrete categories. Emphasis on current literature and open questions. May be repeated with approval of graduate coordinator.
Prereq.: MATH 6915, MATH 6980, MATH 6981, or equivalent, or permission of the graduate coordinator.
MATH 7015 Advanced Topics in Foundations of Topology 3 s.h.
Content varies with each offering, implements ideas from MATH 6915, MATH 6980, MATH 6981, and studies foundations of topology from a variety of viewpoints (algebraic, categorical, logical, order theoretic, powerset theoretic, set theoretic, etc.). Emphasis on current literature and open questions. May be repeated with approval of graduate coordinator.
Prereq.: MATH 6915, MATH 6980, MATH 6981, or equivalent, or permission of graduate coordinator.
MATH 7025 Advanced Topics in General Topology 3 s.h.
Content varies with each offering, implements ideas from MATH 6915, MATH 6980, MATH 6981, and studies various topics in point-set topology. Emphasis on current literature and open questions. May be repeated with approval of graduate coordinator.
Prereq.: MATH 6980, MATH 6981, or equivalent, or permission of graduate coordinator.
MATH 7035 Advanced Topics in Lattice-Valued Topology 3 s.h.
Content varies with each offering. Implements ideas from MATH 6915, MATH 6980, MATH 6981, and studies topology from the standpoint of lattice-valued (fuzzy) subsets. Emphasis on current literature and open questions. May be repeated with approval of graduate coordinator.
Prereq.: MATH 6915, MATH 6980, MATH 6981, or equivalent, or permission of the graduate coordinator.
MATH 7045 Advanced Topics in Topological Analysis 3 s.h.
Content varies with each offering. Implements ideas from MATH 6915, MATH 6980, MATH 6981, and studies the overlap between topology and abstract analysis (topological games, topological groups, separate versus joint continuity, etc.). Emphasis on current literature and open questions. May be repeated with approval of graduate coordinator.
Prereq.: MATH 6915, MATH 6980, MATH 6981, or equivalent, or permission of graduate coordinator.
MATH 7055 Seminar in Topology and Abstract Analysis 3 s.h.
Content varies with each offering. Implements ideas from MATH 6915, MATH 6980, MATH 6981, and focuses on current research activities of seminar participants. Student registrants are expected to make at least one major presentation each month of the term. May be repeated with approval of graduate coordinator.
Prereq.: Permission of graduate coordinator.