Master of Science in Mathematics

Program Director

Dr. G. Jay Kerns
620 Lincoln Building
(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 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 1571Calculus 14
MATH 1572Calculus 24
MATH 2673Calculus 34
Previous courses in discrete structures and linear algebra comparable to:
MATH 3715Discrete Mathematics3
MATH 3720Linear Algebra and Matrix Theory3
Previous courses in abstract algebra and real analysis comparable to:
MATH 5821Topics in Abstract Algebra4
MATH 5851Topics in Analysis4

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

Eric J. Wingler, Ph.D., Professor
Real analysis; complex analysis; operator theory

  • 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
  • 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.
  • The student’s combined undergraduate and graduate programs must include a mathemat­ics core comprising the following courses or their equivalent:
    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 6926Advanced Linear Algebra3
    MATH 6947Methods of Applied Mathematics 3
    MATH 6952Analysis of Real Variable Functions 3
    Choose one of the following:3
    Mathematical Project
    STEM Graduate Internships
    18 Hours of Electives in MATH/STAT/DATX at the 5800 or higher. 18
    At least 1 course must be 6900 level.
    Total Semester Hours30
  • Satisfactory performance on written and oral examinations. The subject matter for these examinations must be approved by the Graduate Executive Committee.  Additionally, the following distribution requirements apply:
    • Written exams in MATH 6926, MATH 6947, and MATH 6952
    • Oral exam on thesis, or oral exam on a project and two courses
    • At least half of the hours of the courses examined must be at the 6900 level
  • At least 15 hours of the student's approved program must be at the 6900 level. 
  • MATH 6999 Thesis is highly recommended
  • 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. Subsequent revisions to this program must be approved by the Graduate Executive Committee. An abstract of a proposed thesis must be submitted for approval prior to registering for the course.
  • Students must participate in an exit interview during the semester in which they plan on graduating. The exit interview will be conducted with one or more members of the Graduate Executive Committee and must be scheduled by the student prior to the thesis or project presentation.

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 6922Advanced Topics in Group and Ring Theory3
MATH 6975Complex Analysis 13
MATH 6980Topology 13
STAT 6940Advanced Data Analysis3
MATH 6955Advanced Differential Equations3
STAT 6943Mathematical Statistics 13

Statistics

COURSE TITLE S.H.
STAT 6940Advanced Data Analysis3
STAT 6948Linear Models3
STAT 6943Mathematical Statistics 13
STAT 6944Mathematical Statistics 23

Actuarial Science

COURSE TITLE S.H.
STAT 5802Theory of Interest3
STAT 6943Mathematical Statistics 13
STAT 6944Mathematical Statistics 23

Applied Mathematics

COURSE TITLE S.H.
MATH 5860Numerical Analysis 13
MATH 6955Advanced Differential Equations3
MATH 6957Partial Differential Equations3
STAT 6940Advanced Data Analysis3
STAT 6943Mathematical Statistics 13

Secondary/Community College Mathematics

COURSE TITLE S.H.
STAT 6943Mathematical Statistics 13
STAT 6940Advanced Data Analysis3
MATH 6922Advanced Topics in Group and Ring Theory3
MATH 6975Complex Analysis 13
MATH 6980Topology 13
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 5825    Advanced Linear Algebra    3 s.h.

A study of abstract vector spaces, linear transformations, duality, canonical forms, the spectral theorem, and inner product spaces.
Prereq.: MATH 3721.

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 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 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: CSIS 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 5852    Real Analysis 2    3 s.h.

Uniform convergence of sequences of functions and some consequences; functions on n-space: derivatives in vector spaces, mean value theorem, Taylor's formula, inverse mapping theorem, implicit mapping theorem.
Prereq.: MATH 3720 and MATH 3751 or equivalent.

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 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 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 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 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 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 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 5852 and either MATH 3705 or MATH 4855 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 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 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 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 6995U    ST: Advanced Topic in Geometry    1-3 s.h.

.
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.