### Contact Information

Bernard Lidický

(515) 294-8136

lidicky@iastate.edu

Jason McCullough

(515) 294-8150

jmccullo@iastate.edu

## Certificate Requirements

- 13 total credits hours (12 in
**graduate courses**and 1 seminar credit) - 12 credits from MATH and STAT classes acceptable for graduate credit. These 12 credits must include at least 9 credits chosen from MATH 501, MATH 503X, MATH 507, MATH 518X, MATH 565X, MATH 581, MATH 569X, STAT 500 (see the description below.)
- For mathematics, courses will normally include MATH 501 and MATH 503X and at least one of MATH 507, MATH 569X.
- For applied mathematics, courses will normally include MATH 518X and MATH 581 and at least one of MATH 501, MATH 507.

- Seminar classes
- MATH 591 (0.5 credit, Orientation for Math. Graduate Students in the fall).
- MATH 592 (0.5 credits Orientation for Math. Graduate Students in the spring).

- GPA at least 3.00
- A grade of C or better in every course

## Classes

A listing of all courses offered by the math department are in the ISU Catalog . The postbaccalaureate students will generally take specially designed courses, that also serve gradate students and advanced undergraduate students.

Students will get individual help with choosing the right classes based on their skills and goals before the semester begins.

### Classes planned for the first year of the program

- MATH 501 Introduction to Real Analysis
*(3-0) Cr. 3. Fall*

A development of the real numbers. Study of metric spaces, completeness, compactness, sequences, and continuity of functions. Differentiation and integration of real-valued functions, sequences of functions, limits and convergence, equicontinuity.

- MATH 502 Topology (3-0)
*Cr. 3 Spring*

Introduction to general topology. Topological spaces, continuous functions, connectedness, compactness. Topics selected from countability and separation axioms, metrization, and complete metric spaces. topics in algebraic topology.

- MATH 507 Applied Linear Algebra
*(3-0) Cr. 3. Fall*

Advanced topics in applied linear algebra including eigenvalues, eigenvalue localization, singular value decomposition, symmetric and Hermitian matrices, nonnegative and stochastic matrices, matrix norms, canonical forms, matrix functions. Applications to mathematical and physical sciences, engineering, and other fields.

- STAT 500 Statistical Methods I
*(3-2) Cr. 4. Fall*

Analysis of data from designed experiments and observational studies. Randomization-based inference; inference on group means; nonparametric bootstrap; pairing/blocking and other uses of restricted randomization. Use of linear models to analyze data; least squares estimation; estimability; sampling distributions of estimators; general linear tests; inference for parameters and contrasts. Model assessment and diagnostics; remedial measures; alternative approaches based on ranks.

- Math 518X Introduction to applied mathematics and partial differential equations
*. (3-0) Cr. 3. Spring*

Basic theory of ordinary differential equations, existence and uniqueness theorems, linear systems, linearization and stability, ODE models in biology and physics, modeling with partial differential equations, dynamical systems techniques.

- Math 503X Algebra and Applications
*(3-0) Cr. 3. Spring*

Properties of groups and rings, subgroups, ideals, and quotients, homomorphisms, structure theory for finite groups. PIDs, UFDs, and Euclidean Domains. Field extensions and finite fields. Selected applications.

- Math 569X Introduction to discrete mathematics
*(3-0) Cr. 3. Spring*

Combinatorial counting, binomial theorem, estimates of factorial, inclusion-exclusion principle, permutations without fixed point, double counting, graphs, subgraphs, graph score, connectivity, triangle-free graphs, graph isomorphism, planar graphs, points in general position, H-polytope, V-polytope, cyclic polytope, Farkas lemma, linear programming and duality.

- Math 581 Numerical methods for differential equations
*(3-0) Cr. 3. Spring*

First order Euler method, high order Runge-Kutta method, and multistep method for solving ordinary differential equations. Finite difference and finite element methods for solving partial differential equations. Local truncation error, stability, and convergence for finite difference method. Numerical solution space, polynomial approximation, and error estimate for finite element method.

### Classes to be introduced later

- Math 565X Introduction to mathematical modeling
*(3-0) Cr. 3. Spring*

Development of skills in mathematical modeling through practical experience. Use of computational methods to investigate mathematical models. Students will work in groups on specific projects involving real-life problems that are accessible to their existing mathematical backgrounds, and make oral and written presentations of results.

## Mentoring

Participants will be assigned mentors from faculty as well as from graduate students. Students will be enrolled in MATH 591 and MATH 592. These are orientation classes for first year graduate students and they include professional development activities and accessible research talks by faculty.

## Teaching and Funding

Postbaccalaureate graduate students will be funded by teaching assistantships. Hence the students will lead recitations in classes such as calculus. The duties will usually include running two to three recitations per week, holding office hours, grading quizzes and exams, and proctoring exams.

The teaching assistantships come with coverage of 1/2 of the tuition and they provide sufficient $ support to cover living expenses in Ames and the other 1/2 of the tuition.

## Other Opportunities

The students in the program will participate in usual departmental life, same as other graduate students. That means attending seminars, colloquia, and other events organized in the department. Students may also participate in EDGE or MOCA.