MathematicsOffered by the Mathematics department.
Understand the central role of mathematics in the modern world.
We have a very friendly, supportive community of students and faculty who believe that mathematics is both beautiful and applicable and is one of pillars that supports Wheaton’s mission as a liberal arts college. You will learn to think like a mathematician at Wheaton, and this will serve you well no matter where your future takes you.
In addition to the traditional courses in pure mathematics, such as Calculus, Linear Algebra, and Real Analysis, we also offer a set of courses that highlight recent developments in mathematics, including sophomorelevel courses in Data Analysis, Voting Theory, and Cryptography.
We know that our students have a wide range of interests, so we have intentionally structured our program with enough flexibility that you can easily study abroad and have the space to explore other academic pursuits as well. Our recent Math majors have taken full advantage of these opportunities. Some completed a second major in a discipline you may expect, such as Physics, Economics, Secondary Education, and Computer Science, but others have a second major in an area you may find surprising, such as Psychology, Philosophy, Hispanic Studies, English and French Studies.
We pride ourselves on working closely with our students to help each one find the path that is the best fit for them. This is reflected in the many different directions our majors have taken after graduation. Some have pursued graduate school in pure mathematics, applied mathematics, or statistics, and others have chosen careers in business, finance, high school teaching, epidemiology, medicine, law, or technology fields, to name just a few.
We have beauiful spaces for our students and faculty to collaborate that are filled with chalkboards and whiteboards, including an outdoor classroom. Please stop by to visit us on the first floor of the Science Center!
For more information, contact Michael Kahn, CoChair, Department of Mathematics and Computer Science.
Major requirements for students who enter Wheaton Fall 2015 and beyond
The major in mathematics consists of 10 or 11 courses. The required courses are:
MATH 101 Calculus I
MATH 104 Calculus II
MATH 211 Discrete Mathematics
MATH 221 Linear Algebra
MATH 151 Accelerated Statistics
or MATH 342 Mathematical Statistics
MATH 301 Real Analysis
or MATH 321 Abstract Algebra
MATH 401 Seminar
Two additional courses at the 300level (MATH 342 may be one of these)
Two additional electives chosen from:
– any 200level Mathematics course
– any 300level Mathematics course
The department recommends that at least five courses be completed by the end of the second year. Students who are considering attending graduate school in mathematics are strongly encouraged to take both MATH 301 Real Analysis and MATH 321 Abstract Algebra.
For those students who place out of Calculus, the major consists of a minimum of 10 courses. Any additional course(s) needed to meet the minimum requirement will be determined in consultation with the student’s advisor and the Math Program coordinator. Students who are unable to take MATH 401 Seminar may substitute a 300level course chosen in consultation with their advisor and the Math Program coordinator.
To major in mathematics, a student needs at least a C+ for the average of their Calculus I and Calculus II grades. No course used to fulfill the major requirements may be taken on a pass/fail basis. At least one 300level course must be taken at Wheaton.
Mathematics majors are encouraged to take either COMP 115 Robots, Games and Problem Solving and COMP 116 Data Structures or PHYS 228 Scientific Computing.
Major Requirements for students who entered Wheaton prior to Fall 2015
The mathematics major consists of a minimum of 11 courses. Normally, the courses will be:
MATH 101 Calculus I
MATH 104 Calculus II
MATH 211 Discrete Mathematics
MATH 221 Linear Algebra
MATH 301 Real Analysis
or MATH 321 Abstract Algebra
MATH 401 Seminar
Five additional courses at the 200 or 300 level, at least two of which are at the 300 level. COMP 115 Robots, Games and Problem Solvingmay be used to fulfill one of the additional 200level courses.
The department recommends that at least five courses be completed by the end of the second year. For those students who place out of calculus, the major consists of a minimum of 10 courses. Any additional course(s) needed to meet the minimum requirement will be determined in consultation with the department.
Students who are considering attending graduate school in mathematics are strongly encouraged to take both MATH 301 Real Analysis and MATH 321 Abstract Algebra. Students who are education minors and are studentteaching during spring of the senior year can substitute an additional 300level course for the Senior Seminar with departmental approval.
No course used to fulfill the major requirements may be taken on a pass/fail basis. To major in mathematics, a student needs at least a C+ for the average of her or his Calculus I and Calculus II grades.
Minor requirements
Mathematics minor
The mathematics minor requires five courses:
MATH 101 Calculus I
MATH 104 Calculus II
MATH 221 Linear Algebra
or MATH 236 Multivariable Calculus
One additional course at the 300 level
One additional course at the 200 or 300 level
Statistics minor
The minor consists of a minimum of five courses, only one of which may be counted both for the minor and for the student’s major.
Required courses
MATH 141 Introductory Statistics
or MATH 151 Accelerated Statistics
and MATH 251 Methods of Data Analysis
Disciplinespecific advanced course
At least one 300level course that incorporates statistical methods in a disciplinespecific context, chosen from:
ECON 330 Applied Econometrics
MATH 342 Mathematical Statistics
PSY 340 Laboratory in Social Psychology
PSY 343 Laboratory in Cognitive Psychology
PSY 345 Laboratory in Child Development
PSY 348 Laboratory in Animal Communication and Cognition
SOC 302 Research Methods in Sociology
Mathematical foundation
One course, chosen from:
COMP 115 Robots, Games and Problem Solving
MATH 101 Calculus I
MATH 221 Linear Algebra
MATH 241 Theory of Probability
Elective
One additional course chosen from either of the two lists above, or an independent study (399) with approval of the minor’s coordinator.

Mathematics
MATH 098 – Experimental Course
From time to time, departments design a new course to be offered either on a onetime basis or an experimental basis before deciding whether to make it a regular part of the curriculum. Refer to the course schedule for current listings.

Mathematics
MATH 099 – Independent Study
An opportunity to do independent work in a particular area not included in the regular courses.

Mathematics
MATH 101 – Calculus I
Calculus is the elegant language developed to model changes in nature and to formally discuss notions of the infinite and the infinitesimal. Topics include techniques of differentiation, the graphical relationship between a function and its derivatives, applications of the derivative, the Fundamental Theorem of Calculus, and integration by usubstitution. No previous experience with calculus is assumed.

Mathematics
MATH 104 – Calculus II
Calculus II continues the study of integral calculus begun in Calculus I. In addition to the core single variable topics of techniques of integration, applications of the integral, improper integrals, and Taylor series, this course includes the multivariable topics of partial derivatives, optimization of multivariable functions and multiple integrals.

Mathematics
MATH 122 – Math in Art
This course investigates mathematics in the context of some of its myriad connections with the art and architecture of various cultures past and present. Possible mathematical topics include systems of proportion, the development of the Golden Ratio by the ancient Greeks and its connection to Fibonacci numbers, the geometry of perspective, classifying different symmetries, nonEuclidean geometry and the fourth dimension, tessellations, and fractals.

Mathematics
MATH 123 – The Edge of Reason
Consciousness has been memorably described as a flashlight trying to illuminate itself. (Perhaps art is the human activity that best understands the surrounding darkness?) The Edge of Reason is the boundary between light and dark: the mathematics at the border between knowing and notknowing. In this course, we’ll use logic and reason to grapple with ideas and concepts that are literally beyond the reach of human imagination. The Edge of Reason is for anyone interested in understanding the mental models our minds make. While people who enjoy math are encouraged to take the course, the only prerequisites are an open mind, a big mouth and an inquiring spirit. The payoffs are keener analytical abilities, a new way of looking at reality, a penchant for expressing the inexpressible and the ability to tolerate sleep deprivation. An intertwined corequisite is Eng 243 taught by Michael Drout at the same time, on alternating days. This is a yearlong course consisting of one class each semester. By taking both semesters, students will attain the QA and AH designations and also fulfill a twocourse Connections requirement. However, a student may enroll in only The Edge of Reason.

Mathematics
MATH 125 – The Shape of Space
The geometry behind objects in everyday life and the shape of our universe will be investigated. Topics include: symmetry, tilings, patterns, planes, spheres, and higher dimensional surfaces. By adopting the perspective of a bug on a surface, different geometries will be experienced, allowing the students to consider the shape of our universe.

Mathematics
MATH 126 – Math and Pop Culture
Introduces mathematical ideas, by first seeing them mentioned, or used, in a script/text. Examples: Proof, by David Auburn; Breaking the Code, by Hugh Whitemore; Arcadia, by Tom Stoppard; The Simpsons and Numb3rs. Each work at least mentions mathematics, some even provide details. In most cases, the work is not really about, nor does the story depend on, the mathematics. In other cases, the mathematics is crucial to the story. We take the mathematical ideas and learn about the mathematical details, understand them for their own sake and how the ideas fit the original work. Mathematical topics: proof, cryptography, number theory, probability/data analysis. Satisfies QA requirement. No prerequisites.

Mathematics
MATH 127 – Colorful Mathematics
The mathematics behind coloring, drawing and design will be investigated and the art of coloring, drawing and design will aid in the study of other math topics. Topics include: African unicursal tracings, coloring maps, coloring graphs, symmetry, border patterns and tessellations.

Mathematics
MATH 133 – Concepts of Mathematics
Required of early childhood and elementary education majors. Mathematical topics that appear in everyday life, with emphasis on problem solving and logical reasoning. Topics include ratios and proportion, alternate bases, number theory, geometry, graph theory and probability.

Mathematics
MATH 141 – Introductory Statistics
An introduction to the language, methods and applications of Statistics. Data from numerous fields are used to show the many uses of basic statistical practice, with use of statistical software. Topics include: data summary, graphical techniques, elementary probability, sampling distributions, central limit theorem, inferential procedures such as confidence intervals and hypothesis testing for means and proportions, chisquare test, simple and multiple linear regression, and analysis of variance (ANOVA).

Mathematics
MATH 151 – Accelerated Statistics
An introduction to the language, methods, theory and applications of Statistics. Data from numerous fields are used to show the many uses of basic statistical practice. Includes an introduction to R for basic computer programming, though no prior programming required. Topics include: data summary, graphical techniques, elementary probability, sampling distributions, central limit theorem, inferential procedures such as confidence intervals and hypothesis testing for means and proportions, chisquare test, simple and multiple linear regression, and oneway and twoway analysis of variance (ANOVA).

Mathematics
MATH 198 – Experimental Course
From time to time, departments design a new course to be offered either on a onetime basis or an experimental basis before deciding whether to make it a regular part of the curriculum. Refer to the course schedule for current listings.

Mathematics
MATH 199 – Independent Study
An individual or smallgroup study in mathematics under the direction of an approved advisor. An individual or small group intensively studies a subfield of mathematics not normally taught. An independent study provides an opportunity to go beyond the usual undergraduate curriculum and deeply explore and engage an area of interest. Students are also expected to assume a greater responsibility, in the form of leading discussions and working examples.

Mathematics
MATH 202 – Cryptography
We live in an ocean of information and secrets, surrounded by codes and ciphers. Actions as prosaic as making a call on a cellphone, logging onto a computer, purchasing an item over the Internet, inserting an ATM card at the bank or using a satellite dish for TV reception all involve the digitizing and encrypting of information. Companies with proprietary data and countries with classified information: all kinds of organizations need a way to encode and decrypt their secrets to keep them hidden from prying eyes. This course will develop from scratch the theoretical mathematics necessary to understand current sophisticated cryptosystems, such as the government, industry and Internet standards: the publickey RSA, the DES and the Rijndael codes.

Mathematics
MATH 211 – Discrete Mathematics
Combining the iron rules of logic with an artist’s sensitivity is part of the aesthetics of a mathematical proof. Discrete mathematics is the first course that asks students to create their own rigorous proofs of mathematical truths. Relations and functions, sets, Boolean algebra, combinatorics, graph theory and algorithms are the raw items used to develop this skill.

Mathematics
MATH 212 – Differential Equations
Since the time of Newton, some physical processes of the universe have been accurately modeled by differential equations. Recent advances in mathematics and the invention of computers have allowed the extension of these ideas to complex and chaotic systems. This course uses qualitative, analytic and numeric approaches to understand the longterm behavior of the mathematical models given by differential equations.

Mathematics
MATH 217 – Voting Theory
This course examines the underlying mathematical structures and symmetries of elections to explain why different voting procedures can give dramatically different outcomes even if no one changes their vote. Other topics may include the GibbardSatterthwaite Theorem concerning the manipulation of elections, Arrow’s Impossibility Theorem, measures of voting power, the theory of apportionment, and nonpolitical applications of consensus theory.

Mathematics
MATH 221 – Linear Algebra
How might you draw a 3D image on a 2D screen and then “rotate” it? What are the basic notions behind Google’s original, stupefyingly efficient search engine? After measuring the interacting components of a nation’s economy, can one find an equilibrium? Starting with a simple graph of two lines and their equations, we develop a theory for systems of linear equations that answers questions like those posed here. This theory leads to the study of matrices, vectors, linear transformations and geometric properties for all of the above. We learn what “perpendicular” means in highdimensional spaces and what “stable” means when transforming one linear space into another. Topics also include: matrix algebra, determinants, eigenspaces, orthogonal projections and a theory of vector spaces.

Mathematics
MATH 236 – Multivariable Calculus
This course is a continuation of the rich field of multivariable calculus begun in Calculus II with an emphasis placed on vector calculus. Topics include vectorvalued functions, alternate coordinate systems, vector fields, line integrals, surface integrals, Green’s Theorem and Stokes’ Theorem.

Mathematics
MATH 241 – Theory of Probability
This course is an introduction to mathematical models of random phenomena and process, including games of chance. Topics include combinatorial analysis, elementary probability measures, conditional probability, random variables, special distributions, expectations, generating functions and limit theorems.

Mathematics
MATH 251 – Methods of Data Analysis
Second course in statistics for scientific, business and policy decision problems. Case studies are used to examine methods for fitting and assessing models. Emphasis is on problemsolving, interpretation, quantifying uncertainty, mathematical principles and written statistical reports. Topics: ordinary, logistic, Poisson regression, remedial methods, experimental design and resampling methods.

Mathematics
MATH 266 – Operations Research
An introduction to methods in Operations Research (OR). OR is concerned with modeling/analyzing complex decision problems, such as those in business, medicine transportation, telecommunications and finance. Develop techniques to optimize the efficiency of operating processes. Topics include: linear and nonlinear programming, simplex method, duality theory/applications, transportation problems, dynamic programming.

Mathematics
MATH 298 – Experimental Course
From time to time, departments design a new course to be offered either on a onetime basis or an experimental basis before deciding whether to make it a regular part of the curriculum. Refer to the course schedule for current listings.

Mathematics
MATH 299 – Independent Study
An individual or smallgroup study in mathematics under the direction of an approved advisor. An individual or small group intensively studies a subfield of mathematics not normally taught. An independent study provides an opportunity to go beyond the usual undergraduate curriculum and deeply explore and engage an area of interest. Students are also expected to assume a greater responsibility, in the form of leading discussions and working examples.

Mathematics
MATH 301 – Real Analysis
This course takes a rigorous approach to functions of a single real variable to explore many of the subtleties concerning continuous and differentiable functions that are taken for granted in introductory calculus. Much more than simply an advanced treatment of topics from calculus, this course uses beautiful and deep results about topics such as the Cantor set, Fourier series and continuous functions to motivate the rigorous approach.

Mathematics
MATH 302 – Advanced Cryptography
This course is a continuation of Mathematics 202 – Cryptography (MATH 202), Cryptography, that will explore more mathematically sophisticated topics. Possible topics include elliptic curve cryptography, latticebased cryptography, primality testing, the computational complexity of various cryptographics systems, and the relationship between cryptography and privacy in digital communication.

Mathematics
MATH 321 – Abstract Algebra
This course is an introduction to the study of abstract algebra. We begin with sets, and operations on those sets, that satisfy just a few basic properties and deduce many more properties, creating an impressive body of knowledge from just these few initial ideas. We use this approach to focus on structures known as groups. Symmetry, permutation groups, isomorphisms and homorphisms, cosets and factor groups will be covered, as well as an introduction to rings, domains and fields. A secondary focus will be developing the student’s ability to write rigorous and wellcrafted proofs.

Mathematics
MATH 327 – Graph Theory
A graph is a mathematical structure consisting of dots and lines. Graphs serve as mathematical models for many realworld applications: for example, scheduling committee meetings, routing of campus tours and assigning students to dorm rooms. In this course, we study both the theory and the utility of graphs. Offered at the discretion of the department.

Mathematics
MATH 331 – Geometry
A comparison of Euclidean and nonEuclidean geometries with an emphasis on understanding the underlying structures that explain these geometries’ fundamental differences. At the instructor’s discretion, the geometries of the Euclidean plane and Euclidean manifolds will be compared with spherical and hyperbolic geometries.

Mathematics
MATH 342 – Mathematical Statistics
This course covers mathematical theory of fundamental statistical techniques and applications of the theory. Topics: estimation and associated likelihood statements regarding parameters, hypothesis testing theory and construction, ANOVA, regression, Bayesian and resampling methods for inference.

Mathematics
MATH 351 – Number Theory
Divisibility properties of the integers, prime and composite numbers, modular arithmetic, congruence equations, Diophantine equations, the distribution of primes and discussion of some famous unsolved problems. Offered at the discretion of the department.

Mathematics
MATH 361 – Complex Analysis
Complex numbers first arose naturally during the algorithmic process of finding roots of cubic polynomials. Extending the ideas of calculus to complex numbers continues to bring forth beautiful ideas such as the Mandelbrot Set and powerful applications to quantum mechanics. This course will take primarily the geometric perspective in understanding the many surprising and elegant theorems of complex analysis. Offered at the discretion of the department.

Mathematics
MATH 381 – Combinatorics
A study of graph theory and general counting methods such as combinations, permutations, generating functions, recurrence relations, principle of inclusionexclusion. Offered at the discretion of the department.

Mathematics
MATH 398 – Advanced Topics in Math
From time to time, departments design a new course to be offered either on a onetime basis or an experimental basis before deciding whether to make it a regular part of the curriculum. Refer to the course schedule for current listings.

Mathematics
MATH 399 – Independent Study
An individual or smallgroup study in mathematics under the direction of an approved advisor. An individual or small group intensively studies a subfield of mathematics not normally taught. An independent study provides an opportunity to go beyond the usual undergraduate curriculum and deeply explore and engage an area of interest. Students are also expected to assume a greater responsibility, in the form of leading discussions and working examples.

Mathematics
MATH 401 – Seminar
A seminar featuring historical and/or contemporary topics in mathematics. Roundtable discussions, studentled presentations and writing are featured.

Mathematics
MATH 499 – Independent Research
Offered to selected majors at the invitation of the department.

Mathematics
MATH 500 – Individual Research
Selected majors are invited by the department to pursue individual research in preparation for writing an Honors Thesis.