## Department of Mathematics and Statistics Undergraduate 300/400 level Course Offerings for 2024-2025

**MTH 301-Introduction to Number theory.** Pre-reqs: A grade of “C” or better in MTH220. This course introduces fundamentals of number theory, including Euclid’s algorithm, the Chinese Remainder Theorem, prime factorization, Fermat’s theorem, quadratic residues, and primitive roots. Applications include coding theory and cryptography. Contact: Prof. Soprunov, i.soprunov@csuohio.edu

**MTH 311-Introduction to Numerical Analysis** Pre-reqs: C or better and at least 6 credits chosen from the following six courses: MTH 220, MTH 281, MTH 283, MTH 284, MTH 286 and MTH 288. Course covers numerical methods for solving nonlinear equations, systems of linear equations, interpolation problems, integration problems, and differential equations. Contact: Prof. Hoover, a.p.hoover@csuohio.edu

**MTH 333-Geometry.** Pre-reqs: C or better in MTH220 and MTH288 (or MTH284). Proofs-based, rigorous development of familiar results of Euclidean geometry. A sample of non-Euclidean geometry; transformation geometry; vectors in geometry; some of the ways in which geometry is important in contemporary settings such as machine vision and GPS. Contact: Prof. Lupton, g.lupton@csuohio.edu

**MTH 358-Abstract Algebra. **Pre-reqs: A grade of “C” or better in MTH220 and MTH288. This course is an introduction to group theory. Topics include modular arithmetic, groups of symmetries, permutations, Lagrange’s theorem, classification of finite abelian groups, and group actions. Contact: Prof. Soprunov, i.soprunov@csuohio.edu

**MTH 386 – Differential Equations**. Prerequisites: A grade of “C” or better in MTH 281 or MTH 283, MTH 288 or MTH 284, and MTH 286 or permission of instructor. Series solutions of second-order linear equations, qualitative behavior of linear and almost linear systems of first-order differential equations, boundary value problems, introduction to partial differential equations. Course includes use of a computer algebra system, such as Python or MATLAB. Contact: Prof. Hoover, a.p.hoover@csuohio.edu. **Note: Students can use the permit request form to request permission if they have completed MTH 286 or ESC 250.**

**MTH 401-Mathematical Modeling.** Pre-reqs: C or better in MTH286 and MTH288 (or MTH284); and at least one mathematics course numbered 300 or above, or departmental approval. This course will develop the intuition for building mathematical models that unravel the mysteries of life—from phase transitions to pattern formation to oscillations. We will develop the theory needed to build, analyze, and simulate classical difference and differential equation-based models with applications to biology, physics, epidemiology, economics, and more. Contact: Prof. Ryan, s.d.ryan@csuohio.edu

**MTH 415-Real Analysis.** Pre-reqs: A grade of “C” or better in MTH 281 or MTH 283, a grade of “C” or better in at least one mathematics course numbered 300 or above, or departmental approval. This course gives a rigorous introduction to the real numbers. Topics include sequences and series, basic topology of the real numbers, functional limits and continuity, the derivative, sequences and series of functions. Contact: Prof. Martins, l.martins@csuohio.edu

**MTH 416-Complex Analysis.** Pre-reqs: A grade of “C” or better in MTH281 (or MTH283), a grade of “C” or better in a least one mathematics course numbered 300 or above. This course introduces fundamentals of complex analysis, including analytic and harmonic functions, Taylor and Laurent series, integration, and residue theory. Contact: Prof. Soprunov, i.soprunov@csuohio.edu

**MTH 487-Dynamical Systems.** Pre-reqs: C or better in MTH286 and MTH288 (or MTH284); and at least one mathematics course numbered 300 or above, or departmental approval. Why is it difficult to make a long-term weather forecast? How could enrichment of a prey species lead to the extinction of their predator species? Why do epidemics of measles exhibit annual, biennial or triennial cycles? If you are interested in questions of this kind, then do not miss this course on dynamical systems: the study of systems that evolve over time. The theory of dynamical systems has applications in a multitude of fields such as biology, physics, chemistry, engineering, meteorology, astronomy, economics, and epidemiology. Topics to be covered include linear systems, classification of equilibrium points, limit cycles, Poincaré-Bendixson theorem, chaos, strange attractors. Course includes use of a computer algebra system such as MATLAB. Contact: Prof. Gao, d.gao51@csuohio.edu

**MTH 493-Boundary Value Problems.** Pre-reqs: C or better in MTH 286 and at least one mathematics course numbered 300 or above or departmental approval We will begin the course with boundary value problems (BVPs), the shooting method to numerically solve BVPs, orthogonality of solutions, and Fourier series. We will use these tools to analytically solve classical PDEs like reaction-diffusion equations in Chemistry, and Laplace’s equation and the wave equation from Physics. We will also look briefly at integro-differential equations, an important tool for modeling certain phenomena. Contact: Prof. Srinivasan, p.srinivasan35@csuohio.edu