The mission of the Mathematics Program is to foster in all our students critical habits of mind: description, analysis and interpretation. The Program is designed to prepare its majors for successful lifetime engagement with mathematics whether it be through applied work in industry or government; research in mathematics, statistics, or one of the other mathematical sciences; teaching; or applying mathematics in the physical, computing, or social sciences. For non-majors, the Program builds substantive skills in quantitative and abstract reasoning and in their application to the study of modern society.
For purposes of course placement and prerequisites, a score of 4 or 5 on the AB calculus exam (or an AB subscore of the BC calculus exam) is regarded as equivalent to successful completion of MATH 112. A score of 4 or 5 on the BC calculus exam is equivalent to MATH 113. A score of 4 or 5 on the statistics exam is equivalent to MATH 260. As the department does not offer a precalculus course, no Kalamazoo College credit is awarded for the AP precalculus exam.
Courses taken at other institutions will be awarded credit in mathematics if they meet one of the following criteria:
Students are responsible for meeting with the department chair in advance to determine whether a course offered elsewhere will transfer back as a mathematics credit.
Nine units of mathematics are required, exclusive of SIP and Computer Science or Applied Statistics Cognate. Typically up to two units from outside courses (AP, transfer, dual enrollment, or study abroad) may count towards the major or minor in mathematics. MATH 105, MATH 260 and MATH 261 do not count toward the nine units for the major. Students who wish to apply additional external units toward the major must consult with the department.
Among the courses we offer, MATH 320 and MATH 330 are at the highest level of abstraction. Before enrolling in one of these courses, students are strongly encouraged to complete MATH 310, MATH 316 or MATH318.
For students interested in graduate work in one of the mathematical sciences, additional work in MATH 280, 310, 316, 318, 320, 330, 420, 430, and 450 is appropriate. Those with a strong interest in computing should elect the minor in computer science in addition to MATH 300. For those students interested in applied work (mathematical biology, mathematical economics, operations research, etc.), election of MATH 270, 280, 310, 362, 365, and at least two courses in computer science is appropriate.
In addition to the requirements stated above, mathematics majors are required to complete the Mathematics Colloquium requirement. See the Mathematics Department for details.
Mathematics majors are required to satisfactorily complete the Sophomore Comprehensives and the Senior Comprehensives. See the Mathematics Department for details.
There are four options for the minor in mathematics, each of which requires six units of credit in mathematics. Each of these options requires the “core” courses: Single variable calculus (MATH 112 and MATH 113), Multivariable Calculus (MATH 214), and Linear Algebra (MATH 240). The other required courses for each option are as follows:
Students interested in mathematics are especially encouraged to consider the study abroad program in Budapest. The Budapest program is given in English; no prior knowledge of Hungarian is needed. It offers a number of mathematics courses as well as history, language, and literature courses. Mathematics majors have also studied mathematics in Erlangen, Quito, Perth, Aberdeen, and Lancaster. Early consultation with the department is strongly urged.
MATH
105
Quantitative 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 BUSN-160, ECON-160, ANSO-212, MATH-260, or MATH-261.
MATH
110
Calculus 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 Successful completion of the two-term Math 110-111 sequence serves as an alternate prerequisite for all college courses requiring MATH 112 and contributes one unit toward the nine units required for the math major.
Placement into MATH-110 required
MATH
111
Calculus I with Review, Part 2
This course continues the study of calculus begun in MATH 110. Review of precalculus mathematics continues as needed. Successful completion of the two-term Math 110-111 sequence serves as an alternate prerequisite for all college courses requiring MATH 112 and contributes one unit toward the nine units required for the math major.
MATH-110 All course prerequisites must be met with a minimum grade of C-.
MATH
112
Calculus 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.
Math Placement Exam Required
MATH
113
Calculus 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.
MATH-112 or MATH-111 or placement into MATH-113 All course prerequisites must be met with a minimum grade of C-.
MATH
214
Calculus III
Series, vectors in two and three dimensions, and integral and differential calculus of functions of several variables.
MATH-113 or placement into MATH-214 All course prerequisites must be met with a minimum grade of C-.
MATH
240
Linear Algebra and Vectors
Study of vector spaces, matrices, determinants, linear transformations, systems of equations and eigenvalues.
MATH-113 or placement into MATH-240 All course prerequisites must be met with a minimum grade of C-.
MATH
250
Discrete Mathematics
Introduction to formal structures and mathematical reasoning. Graphs, sets, logic, induction, structure of mathematical proof, counting, relations, and algebraic structures.
MATH-112 and one computer science course. All course prerequisites must be met with a minimum grade of C-.
MATH
260
Applied 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 BUSN-160, ECON-160, or MATH-261.
MATH
261
Biostatistics
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 BUSN-160, ECON-160, or MATH-260.
MATH
265
Introduction to Data Science
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.
MATH-260 or MATH-261 or COMP-210 or with instructor permission.
MATH
270
Nonlinear 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.
MATH
280
Ordinary Differential Equation: Analytic, Symbolic, and Numeric Techniques
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.
MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.
MATH
295
Getting to X: Math & Some of Its History
This is a course about mathematics, rather than about a branch of mathematics. We will use history as a unifying approach as we navigate ideas, in an attempt to see mathematics more broadly than our other courses usually allow. We will strive to put some of the ideas we've already encountered in context as well as introduce ourselves to new mathematical ideas.
MATH-214 and MATH-240. All course prerequisites must be met with a minimum grade of C-.
MATH
300
Automata, 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.
MATH-250 or MATH-330, and 1 unit of Computer Science. All course prerequisites must be met with a minimum grade of C-.
MATH
305
Dynamic 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.
MATH-113 All course prerequisites must be met with a minimum grade of C-.
MATH
310
Complex 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.
MATH-214 and MATH-240 All course prerequisites must be met with a minimum grade of C-.
MATH
316
Topics 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. This course is typically offered in the winter of even years.
MATH-214 and MATH-240 with a C- or better
MATH
318
Topics 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. This course is typically offered in the winter of odd years.
MATH-214 and MATH-240; All course prerequisites must be met with a minimum grade of C-.
MATH
320
Real 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. This course is typically offered in the spring of odd years.
MATH-310, MATH-316, or MATH-318 All course prerequisites must be met with a minimum grade of C-.
MATH
330
Abstract 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. This course is typically offered in the spring of even years.
MATH-310, MATH-316, or MATH-318 All course prerequisites must be met with a minimum grade of C-.
MATH
360
Applied 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.
200-level math course. All course prerequisites must be met with a minimum grade of C-.
MATH
362
Probability
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.
MATH-113 All course prerequisites must be met with a minimum grade of C-.
MATH
365
Mathematical 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.
MATH-362 All course prerequisites must be met with a minimum grade of C-.
MATH
395
Self-Selected Topics in Math
This seminar aims to develop proficiency in communicating mathematics and to provide an opportunity for students to learn about a topic of individual interest outside the usual curriculum.
MATH
420
Real Analysis II
Continuation of MATH 320 and is typically offered in the spring of even years.
MATH-320 All course prerequisites must be met with a minimum grade of C-.
MATH
430
Abstract Algebra II
Continuation of MATH 330 and is typically offered in the spring of odd years.
MATH-330 All course prerequisites must be met with a minimum grade of C-.
MATH
450
Special 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.
COMP-104, COMP-105, or COMP-150 and MATH-250 or MATH-316 or MATH-330 All course prerequisites must be met with a minimum grade of C-.
MATH
490
Senior 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.
MATH
593
Senior Integrated Project
Each program or department sets its own requirements for Senior Integrated 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 Integrated Project section of the Academic Catalog for more details.
Permission of department and SIP supervisor required.
MATH
600
Teaching Assistantship
