Program Director
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. 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 has extensive computing facilities that include microcomputers, workstations, mainframe, and access to supercomputers.
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 course in abstract algebra comparable to: | ||
| MATH 5821 | Topics in Abstract Algebra | 4 |
| MATH 5851 | Topics in Analysis | 4 |
| The Graduate Record Examination | ||
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.
Guang-Hwa (Andy) Chang, Ph.D., Professor
Biostatistics
Jozsi Z. Jalics, Ph.D., Associate 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., Assistant Professor
Simultaneous confidence bands; minimum effective doses; benchmark dose methodology
Thomas L. Madsen, Ph.D., Assistant Professor
Abstract algebra; group theory; representation theory
Nguyet Thi Nguyen, Ph.D., Assistant Professor
Financial models; Monte Carlo simulation; actuarial science
Anita C. O'Mellan, Ph.D., Professor
Graph theory; combinatorics; early childhood mathematics education
Stephen Rodabaugh, Ph.D., Professor
Foundations of topology and fuzzy logic: point-set, lattice-theoretic, and categorical methods
Thomas Smotzer, Ph.D., Professor
Real analysis; measure theory; operator theory
Angela Spalsbury, Ph.D., Professor
Functional analysis; operator theory; measure theory
Jamal K. Tartir, Ph.D., Professor
Set-theoretic topology
Thomas P. Wakefield, Ph.D., Associate Professor
Character theory; actuarial science
Eric J. Wingler, Ph.D., Professor
Real analysis; complex analysis; operator theory
George Yates, Ph.D., Professor
Applied mathematics; partial differential equations; mathematical biology; nonlinear waves
- A minimum of 33 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. These courses are not included in the 33-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 List COURSE TITLE S.H. MATH 5821 Topics in Abstract Algebra (taken in the earliest available semester) 4 MATH 5851 Topics in Analysis (taken in the earliest available semester) 4 MATH 5825 Advanced Linear Algebra 3 MATH 5852 Real Analysis 2 3 MATH 6996 Mathematical Project 1-3
- 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 5852, Math 5825 and the first course in the student's chosen course sequence
- 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 17 hours of the student's approved program must be at the 6900 level. In addition to completing the courses which make up the mathematics core, students must complete at least one course sequence for depth and at least fifteen additional hours of elective courses to satisfy the breadth requirement for the degree. The course groupings are described below.
- 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.
Course Sequences for Depth
The description of the recommended course sequences for depth will refer to the following list. The sequences offered depend upon student interest.
| COURSE | TITLE | S.H. |
|---|---|---|
| Abstract Algebra | ||
| Advanced Topics in Group and Ring Theory | ||
| Advanced Topics in Field Theory | ||
| Actuarial Mathematics | ||
| Theory of Interest | ||
| Advanced Data Analysis | ||
| Advanced Data Analysis | ||
| Linear Models | ||
| Advanced Differential Equations | ||
| Partial Differential Equations | ||
| Mathematical Statistics | ||
| Mathematical Statistics 1 | ||
| Mathematical Statistics 2 | ||
| Operations Research | ||
| Operations Research | ||
| Advanced Operations Research | ||
| Topology | ||
| Topology 1 | ||
| Topology 2 | ||
Predoctoral Studies in Mathematics and Applied Mathematics
| COURSE | TITLE | S.H. |
|---|---|---|
| Advanced Topics in Group and Ring Theory | ||
| Advanced Topics in Field Theory | ||
| Complex Analysis 1 | ||
| Real Analysis 2 | ||
| Topology 1 | ||
| Advanced Data Analysis | ||
| Advanced Differential Equations | ||
| Mathematical Statistics 1 | ||
| Numerical Analysis 2 | ||
| Operations Research | ||
| Electives | ||
| Select two or more sequences in areas of interest | ||
| Total Semester Hours | 0 | |
Statistics
| COURSE | TITLE | S.H. |
|---|---|---|
| Core Requirements | ||
| STAT 6940 | Advanced Data Analysis | 3 |
| STAT 6948 | Linear Models | 3 |
| STAT 6943 | Mathematical Statistics 1 | 3 |
| STAT 6944 | Mathematical Statistics 2 | 3 |
| Electives | ||
| Select 9 additional hours of statistics courses. | 9 | |
| Total Semester Hours | 21 | |
Actuarial Science
| COURSE | TITLE | S.H. |
|---|---|---|
| Core Requirements | ||
| STAT 5802 | Theory of Interest | 3 |
| STAT 6943 | Mathematical Statistics 1 | 3 |
| STAT 6944 | Mathematical Statistics 2 | 3 |
| Electives | ||
| Select from statistic and actuarial science course offerings | ||
| Total Semester Hours | 9 | |
Applied Mathematics
| COURSE | TITLE | S.H. |
|---|---|---|
| Core Requirements | ||
| Advanced Data Analysis | ||
| Advanced Differential Equations | ||
| Mathematical Statistics 1 | ||
| Numerical Analysis 2 | ||
| Operations Research | ||
| Depth Requirement | ||
| Select the second course in on e of the sequence | ||
| Total Semester Hours | 0 | |
Secondary/Community College Mathematics
| COURSE | TITLE | S.H. |
|---|---|---|
| Mathematical Foundations | ||
| Advanced Data Analysis | ||
| or | ||
| Mathematical Statistics 1 | ||
or STAT 6940 | Advanced Data Analysis | |
| Select one of the following: | 3 | |
| Advanced Topics in Group and Ring Theory | ||
| Advanced Topics in Field Theory | ||
| Complex Analysis 1 | ||
| Abstract Analysis 1 | ||
| Topology 1 | ||
| Advanced Topics in Group and Ring Theory | ||
| Advanced Topics in Field Theory | ||
| Those students seeking certification should consult an advisor in the school of Education. | ||
| Total Semester Hours | 3 | |
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 Department of Computer Science and Information Systems.
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 six 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.