# Mathematics

## Courses

MATH105Quantitative Reasoning and Statistical Analysis An introduction to some of the quantitative techniques used to clarify ordinary experience and to some of the statistical ideas used to shape public policy and human sciences, with emphasis on the concepts involved in producing, organizing, and drawing conclusions from data. Does not count toward the major or minor. Not open to students who already have credit from ANSO-212, MATH-260, or MATH-261.

MATH110Calculus I with Review, Part 1 MATH 110 and 111 cover in two terms the material covered in Mathematics 112. In addition, topics from precalculus mathematics are reviewed and practiced as needed. Precalculus topics include: algebra and analytic geometry; linear, quadratic, polynomial and rational functions; and trigonometric functions. Enrollment is restricted to those who were advised to take Math 110-111 on the basis of the department's placement examination. The two-term Math 110-111 sequence serves as an alternate prerequisite for all college courses requiring MATH 112. Prerequisite: Placement into MATH-110 required

MATH111Calculus I with Review, Part 2 This course continues the study of calculus begun in MATH 110. Review of precalculus mathematics continues as needed. Prerequisite: Take MATH-110 All course prerequisites must be met with a minimum grade of C-.

MATH112Calculus I Differential calculus of single-variable functions: limits, derivatives, differentiation rules, related rates, optimization. An emphasis on problem solving using the tools of differential calculus with application to the natural and social sciences. Prerequisite: Math Placement Exam Required

MATH113Calculus II Integral calculus of single-variable functions: the fundamental theorem of calculus, techniques of integration, infinite sequences and series. An emphasis on problem solving using the tools of integral calculus with application to the natural and social sciences. Prerequisite: MATH-112 All course prerequisites must be met with a minimum grade of C-.

MATH214Calculus III Series, vectors in two and three dimensions, and integral and differential calculus of functions of several variables. Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.

MATH240Linear Algebra and Vectors Study of vector spaces, matrices, determinants, linear transformations, systems of equations and eigenvalues. Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.

MATH250Discrete Mathematics Introduction to formal structures and mathematical reasoning. Graphs, sets, logic, induction, structure of mathematical proof, counting, relations, and algebraic structures. Prerequisite: MATH-112 and one computer science course. All course prerequisites must be met with a minimum grade of C-.

MATH260Applied Statistics I Introduction to statistics including methods of data collection and description, correlation and regression, chance, and statistical inference. The course makes extensive use of technology and is designed for students in the behavioral, biological, and social sciences. Does not count towards the major or minor in mathematics. Not open to students who already have credit from MATH-261

MATH261Biostatistics Introduction to statistics with particular attention to applications in biology and health sciences. Topics include sampling methods, design of experiments, exploratory data analysis, estimation, tests of significance, ANOVA, and correlation and regression analysis. BIOL 112 and 123 highly recommended. Does not count towards the major or minor in mathematics. Not open to students who already have credit from MATH-260

MATH/PHYS270Nonlinear Dynamics and Chaos Dynamical systems are mathematical objects used to model phenomena of natural and social phenomena whose state changes over time. Nonlinear dynamical systems are able to show complicated temporal, spatial, and spatiotemporal behavior. They include oscillatory and chaotic behaviors and spatial structures including fractals. Students will learn the basic mathematical concepts and methods used to describe dynamical systems. Applications will cover many scientific disciplines, including physics, chemistry, biology, economics, and other social sciences. Appropriate for Math or Physics Majors. Either MATH 305 or this course, but not both, may be counted towards the major in mathematics.

MATH280Differential Equations and Numerical Methods Introduction to key concepts underlying analytical methods for the solution of ordinary differential equations and first-order systems studied together with techniques for constructing approximate numerical solutions. Prerequisite: MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.

MATH295Special Topics Living under the data deluge of the early 21st century, our challenge is no longer finding data, but instead transforming it into a format useful for addressing important questions. To that end, this course will focus on the use of the R statistics language and environment to access, visualize, transform and model data. Specific topics may include data scraping, data wrangling, graphical displays, reproducible research reports, and methods for modeling data including supervised and unsupervised learning.Prerequisite: MATH-260 or MATH-261 or COMP-210 or with instructor permission.

MATH/COMP300Automata, Formal Languages, and Computability Study of automata as mathematical models of computation; of formal languages, which play a central role in the specification and translation of programming languages; and of the fundamental capabilities and limitations of computers.Prerequisite: MATH-250 or MATH-330, and 1 COMP course All course prerequisites must be met with a minimum grade of C-.

MATH/IDSY305/PHYS 482Dynamic Models in Social Science The study of why mathematical and computational methods are important in understanding social phenomena, and how different social phenomena can be described by proper mathematical models. Specifically, applications of the theory of dynamical systems will be presented. Designed for math/science and social science students. Either MATH/PHYS 270 or this course, but not both, may be counted towards the major in mathematics.Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.

MATH310Complex and Vector Variables Generalizations of differentiation and integration to spaces of higher dimension: divergence, curl, and the classical integration theorems of multivariable calculus. Introduction to analytic functions of a complex variable, including Laurent series, Cauchy's formula, and conformal mapping. Prerequisite: MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.

MATH316Topics in Number Theory Study of classical number theory including distribution of primes, congruences, the Euler Phi function, and quadratic reciprocity. This course will also focus on developing proof writing skills.Prerequisite: MATH-214 and MATH-240 with a C- or better

MATH318Topics in Topology An introduction to topological spaces including the study of connectedness, metric spaces, and compactness. This course will also focus on developing proof writing skills.Prerequisite: MATH-214 MATH-240; All course prerequisites must be met with a minimum grade of C-.

MATH320Real Analysis I Introduction to basic topological concepts in metric spaces followed by rigorous development of classical real analysis including sequences and series of functions, continuity, differentiability, and Reimann-Stieltjes integration. This course is among the most theoretical in our curriculum. Before enrolling, students are strongly encouraged to complete MATH 250, MATH 310, MATH 314, or MATH 318.Prerequisite: MATH-310, MATH-316, or MATH-318 All course prerequisites must be met with a minimum grade of C-.

MATH330Abstract Algebra I Study of modern abstract algebra including groups, rings, fields, and other algebraic structures together with advanced topics of linear algebra. This course is among the most theoretical in our curriculum. Before enrolling, students are strongly encouraged to complete MATH 250, MATH 310, MATH 314, or MATH 318.Prerequisite: MATH-310, MATH-316, or MATH-318 All course prerequisites must be met with a minimum grade of C-.

MATH360Applied Statistics II This course uses real data case studies to review descriptive statistics and to explore statistical inference for means, proportions, and transformations; analysis of variance; and regression. Statistical software is used throughout. The course is recommended both for students planning to do graduate coursework in the behavioral, biological, and social sciences and for mathematics majors seeking a comprehensive introduction to statistical methods.Prerequisite: 200-level math course. All course prerequisites must be met with a minimum grade of C-.

MATH362Probability Study of mathematical theory of probability. Topics include data analysis, discrete and continuous sample spaces, combinatorial problems, random variables, probability densities and distributions, expected value, moment-generating functions, functions of a random variable, sampling distributions, and the central limit theorem. Prerequisite: MATH-113 All course prerequisites must be met with a minimum grade of C-.

MATH365Mathematical Statistics Study of statistical inference. Topics include sampling theory, point and interval estimations, hypothesis testing, and regression. Stochastic processes, analysis of variance, simple experimental design, and nonparametric statistics may also be included. Prerequisite: MATH-362 All course prerequisites must be met with a minimum grade of C-.

MATH420Real Analysis II Continuation of MATH 320.Prerequisite: MATH-320 All course prerequisites must be met with a minimum grade of C-.

MATH430Abstract Algebra II Continuation of MATH 330. Prerequisite: MATH-330 All course prerequisites must be met with a minimum grade of C-.

MATH450Topics in Pure and Applied Mathematics Readings in pure and applied mathematics. Content varies from year to year. Possible topics include: set theory, number theory, geometry, topology.Prerequisite: 1 COMP course and MATH-250 or MATH-316 or MATH-330 All course prerequisites must be met with a minimum grade of C-.

MATH450/COMP 483Special Topics: Cryptography This course provides a mathematics-based introduction to cryptography. Students will study the algorithms and security of various symmetric-key and public-key cryptosystems, and will write programs to implement several different cryptographic algorithms. Students will also gain some awareness of the social, ethical, and political issues related to cryptography.Prerequisite: COMP-108 or COMP-110 and MATH-250 or MATH-316 or MATH-330 All course prerequisites must be met with a minimum grade of C-.

MATH490Senior Seminar In this course we will explore some of the meta-themes of mathematics. In particular, we will examine how themes such as continuity and approximation are evident - or not - in various branches of mathematics. We will also reflect on such topics as the role of proof in mathematics versus the role of intuition, and what literacy in mathematics means.

MATH593Senior Individualized Project Each program or department sets its own requirements for Senior Individualized Projects done in that department, including the range of acceptable projects, the required background of students doing projects, the format of the SIP, and the expected scope and depth of projects. See the Kalamazoo Curriculum -> Senior Individualized Project section of the Academic Catalog for more details.Prerequisite: Permission of department and SIP supervisor required.