Mathematics
Coordinator: Rochelle (Shelly) Leibowitz
Department home page: http://www.wheatoncollege.edu/Acad/Mathematics/
The Mathematics and Computer Science Department offers students a commitment to combining our knowledge with cutting-edge technologies, initiating majors into the lush and varied realms of mathematics. You will leave Wheaton with the fundamentals, heightened powers of analysis and logic and a firm grasp on the first stage of your career. A bachelor's degree in mathematics is a key which unlocks hundreds of different doors, ranging from law school to systems analysis to a career in business to graduate study in mathematics.
Major
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The mathematics major consists of a minimum of 11 courses. Normally, the courses will be:
Math 101 Calculus I
or Math 102 Calculus I with Economic Applications
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 Solving," may be used to fulfill one of the additional 200-level 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 student teaching during spring of the senior year can substitute an additional 300-level course for the Senior Seminar with departmental approval.
Courses beyond Math 104 used to fulfill the major requirements may not be taken on a pass/fail basis. To major in mathematics, a student needs at least a C+ for the average of her/his "Calculus I" and "Calculus II" grades.
Minors
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Mathematics Minor
The mathematics minor requires five courses:
Math 101 Calculus I
or Math 102 Calculus I with Economic Applications
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
Discipline-specific advanced course
At least one 300-level course that incorporates statistical methods in a discipline-specific context. One course 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 Developmental Psychology
Psy 348 Laboratory in Animal Communication and Cognition
Chem 331 Aqueous Equiibria
Soc 302 Research Methods in Sociology
Mathematical foundation
One course chosen from:
Comp 115 Robots, Games, and Problem Solving
Math 101 Calculus I
Math 102 Calculus I with Economic Applications
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.
Courses
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. The universe is perceived and understood by observing changes and the derivative is the premier intellectual tool for grasping and precisely describing change. Topics include techniques of differentiation, the graphical relationship between a function and its derivatives, and the Fundamental Theorem of Calculus. Applications may include carbon dating archeological finds, modeling population growth and optimization. No previous experience with calculus is assumed.
(Madani Naidjate)
102. Calculus I with Economic Applications
The mathematical content is very similar to that of Math 101, but the natural connections between the techniques from Calculus I and microeconomics are emphasized. For example, the derivative from calculus is applied to the marginal analysis and optimization that are approached graphically in microeconomics.
(Janice Sklensky)
Connections:
Conx 20004 The Calculus of Microeconomics
104. Calculus II
Taking the Fundamental Theorem of Calculus as a starting point, Calculus II explores the solution of definite integrals, and their applications, by both analytic and computational methods. These ideas provide a gateway to improper integrals and the careful study of infinite series. Additional topics include techniques of integration, numeric integration, volumes of revolution and Taylor series.
(Janice Sklensky, Harrison Straley)
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, non-Euclidean geometry and the fourth dimension, tessellations, and fractals.
(Janice Sklensky)
Connections:
Conx 20025 The Math in Art and the Art of 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 not-knowing. 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 co-requisite 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 two-course Connections requirement. However, a student may enroll in only The Edge of Reason.
(Bill Goldbloom Bloch)
Connections:
Conx 20031 Science FACTion
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.
(Rochelle (Shelly) Leibowitz)
Connections:
Conx 20011 Communication through Art and Mathematics
133. Concepts of Mathematics
Required of elementary education minors. 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.
(Rochelle (Shelly) Leibowitz, Harrison Straley)
Connections:
Conx 23015 Learning to Learn in Math and Science
141. Introductory Statistics
Strongly recommended for social science students. This course aims to answer several profound questions: Given the impossibility of collecting complete data, how do we accurately answer questions about a large population of people, industrial products or mechanical devices? How do we test interesting hypotheses which apply to a large group? On each space flight, the Challenger had a one in 15 chance of a failure of a critical part--how do we understand a statement such as this? The notions of confidence intervals, hypothesis testing and probability provide a framework for answering these and other questions. May not be counted toward the mathematics major.
151. Accelerated Statistics
Strongly recommended for science and graduate school - bound social science students. This course covers all the questions and tools of Math 141, plus a deeper look at probability, tests of significance, regression and ANOVA. May not be counted toward the mathematics major.
(Michael Kahn)
Connections:
Conx 20063 Ecology: A Statistical Approach
Conx 20044 Mathematics of Chemical Analysis
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 crypto-systems, such as the government, industry and Internet standards: the public-key RSA, the DES and the Rijndael codes.
(Bill Goldbloom Bloch)
Connections:
Conx 20038 Top Secret
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.
(Rochelle (Shelly) Leibowitz)
Connections:
Conx 20018 Communicating Information
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 long-term behavior of the mathematical models given by differential equations.
(Bill Goldbloom Bloch, Rachelle C. DeCoste)
216. Computational Molecular Biology
Mathematical models and computer algorithms played a role in sequencing the human genome and continue to play a role as biologists deal with enormous amounts of data that need to be processed and analyzed. This course deals with the theory (but not computer programming) of the computational techniques used in molecular biology.
(Rochelle (Shelly) Leibowitz)
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 Gibbard-Satterthwaite Theorem concerning the manipulation of elections, Arrow's Impossibility Theorem, measures of voting power, the theory of apportionment, and nonpolitical applications of consensus theory.
(Tommy Ratliff)
Connections:
Conx 20002 Voting Theory, Math and Congress
221. Linear Algebra
How might you draw a three-dimensional image on a two-dimensional 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 high-dimensional 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.
Connections:
Conx 20045 Mathematical Tools for Chemistry
236. Multivariable Calculus
This course is a continuation of the rich field of ideas touched upon in Calculus II and extends the ideas of the derivative, the integral and optimization to functions that depend on several variables. Topics include vector-valued functions, multiple integrals, alternate coordinate systems, the gradient, vector calculus and Green's Theorem.
Connections:
Conx 20045 Mathematical Tools for Chemistry
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.
(Michael Kahn)
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 problem-solving, interpretation, quantifying uncertainty, mathematical principles and written statistical reports. Topics: ordinary, logistic, poisson regression, remedial methods, experimental design and resampling methods.
(Michael Kahn)
285. Mathematical and Statistical Consulting
Teams of students explore current problems of interest acquired from area businesses and government agencies. The student groups construct and determine appropriate techniques for investigating and solving clients' problems. Each group meets clients regularly to provide progress report. Results of investigations are delivered by way of scholarly report and professional presentation to the sponsoring organization.
(Michael Kahn, Tommy Ratliff)
298. Experimental Course
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.
(Bill Goldbloom Bloch, Tommy Ratliff)
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 well-crafted proofs.
(Janice Sklensky)
327. Graph Theory
A graph is a mathematical structure consisting of dots and lines. Graphs serve as mathematical models for many real-world 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.
(Rochelle (Shelly) Leibowitz)
331. Geometry
A comparison of Euclidean and non-Euclidean 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.
(Tommy Ratliff)
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.
(Michael Kahn)
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.
(Rochelle (Shelly) Leibowitz)
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.
(Bill Goldbloom Bloch, Rachelle C. DeCoste)
381. Combinatorics
A study of graph theory and general counting methods such as combinations, permutations, generating functions, recurrence relations, principle of inclusion-exclusion. Offered at the discretion of the department.
(Rochelle (Shelly) Leibowitz)
398. Experimental Course
Topology
Topology is the study of abstract spaces: What kinds of properties must be true in a space that is characterized by, for example, a sense of distance or separateness? How can different spaces be related to each other by functions? Can we conceive of a definition of dimension that refer to our Euclidean intuitions? Can we classify all the different kinds of spaces that are, for example, two dimensional, finite, and boundaryless? What about non-orientable spaces, or those with holes or that are broken up into multiple pieces? If you allow shifts of perspective and unloopings of twists, is it possible to classify the different kinds of knotty tangles that may be constructed from a rope?
Perhaps it is not surprising that physicists, chemists, and biologists are able to take results from topology and apply them to their respective fields. It is surprising, though, that economists do as well!
This course will touch on many of these topics and will change the way you look at the world. (Prerequisites: Math 211, mathematical maturity, or permission of the instructor.)
399. Independent Study
An individual or small-group 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.
401. Seminar
A seminar featuring historical and/or contemporary topics in mathematics. Roundtable discussions, student-led presentations and writing are featured.