# Undergraduate classes, Spring 2009, Mathematics

Note: All courses taken towards the major or minor must be taken on a letter grade basis, not pass/fail.
 MATH 107: Intro. Probability and Statistics Credits: 4 − Description − Sections
Content: Elementary methods for calculating probabilities along with the construction of statistical models. Illustrations from the social sciences and natural sciences. A major goal is to enable the student to draw the correct conclusions to statistical questions, avoiding some of the pitfalls and fallacies encountered.
000MSC: W302TuTh 8:30am - 9:45amSilke Gehrkemax 28
001MSC: W304TuTh 11:30am - 12:45pmTobias Grafmax 28
002MSC: W302MWF 12:50pm - 1:40pmSean Thomasmax 28
003MSC: W302TuTh 1:00pm - 2:15pmHasan Paltamax 28
005MSC: W302TuTh 2:30pm - 3:45pmKinnari Aminmax 28
 MATH 111: Calculus I Credits: 4 − Description − Sections
Content: Introduction to the derivative and limits, including motivation; differentiation of functions; the chain rule; applications of differentiation including max-min problems and related rate problems; antiderivatives and the definite integral.
000MSC: W304MWF 9:35am - 10:25amCatherine Cromptonmax 28
001MSC: W304MWF 10:40am - 11:30amRaya Horeshmax 28
002MSC: W304MWF 11:45am - 12:35pmZhuojun T. Magnantmax 28
003MSC: W304MWF 12:50pm - 1:40pmFeng Chenmax 28
 MATH 112: Calculus II Credits: 4 − Description − Sections
Content: Exponential and logarithmic functions; trigonometric and inverse trigonometric functions; techniques of integration; numerical methods of integration; improper integrals; infinite sequences and series; polar coordinates.
Prerequisites: Math 111, Math 115 or placement.
000MSC: W302MWF 9:35am - 10:25amChang Mo Bangmax 30
001MSC: W302MWF 10:40am - 11:30amChang Mo Bangmax 30
002MSC: W301MWF 11:45am - 12:35pmRay Lambmax 30
003MSC: W201MWF 12:50pm - 1:40pmRay Lambmax 30
004MSC: W302MWF 2:00pm - 2:50pmAnastasia Svishchevamax 28
005MSC: W201MWF 3:00pm - 3:50pmJake McMillenmax 28
006MSC: W306MWF 2:00pm - 2:50pmBenjamin Shemmermax 28
 MATH 116: Life Sciences Calculus II Credits: 4 − Description − Sections
Content: Second semester calculus with an emphasis on applications to biology. Topics covered include brief introductions the multivariable calculus and matrix topics needed to study systems of differential equations used for modeling in the life sciences. Introduction to probability and inferential statistics, including hypothesis testing.
Particulars: There will be regular written assignments, three midterm exams and a final exam. Students intending to take Math 211 or Math 212 should meet with the instructor for advice -- Math 112 is often better preparation for these courses than Math 116.
Prerequisites: Math 115 or AP Calculus placement. Students with AP credit are strongly advised to meet with the instructor before the beginning of the term.
000MSC: W201MWF 9:35am - 10:25amDwight Duffusmax 40
002MSC: W201MWF 11:45am - 12:35pmLior Horesh / Audrey Malagonmax 50
LA1MSC: W303M 3:00pm - 3:50pmDwight Duffusmax 20
LA2MSC: W303M 5:00pm - 5:50pmLior Horeshmax 25
LB1MSC: W303Tu 9:00am - 9:50amLior Horeshmax 25
LC1MSC: W303W 8:30am - 9:20amDwight Duffusmax 20
 MATH 119: Calculus with Business Applications Credits: 4 − Description − Sections
Content: An introduction to differential and integral calculus with applications in Business and Economics. Topics include limits, derivatives, applications of the derivative, exponential and logarithm functions, integration, and applications of integrals. There will be an emphasis on modeling and word problems.
Particulars: Math 119 is a beginning calculus course designed for students who plan to enter the School of Business.
000MSC: W303MWF 9:35am - 10:25amVerena Kuhlemannmax 28
001MSC: W303MWF 10:40am - 11:30amSang June Leemax 28
002MSC: W303MWF 11:45am - 12:35pmJodi Blackmax 28
003MSC: W303MWF 12:50pm - 1:40pmPaul Wraynomax 28
004MSC: W303MWF 2:00pm - 2:50pmPraphat Fernandesmax 28
005MSC: W304MWF 3:00pm - 3:50pmAlexis Aposporidismax 28
 MATH 190: Freshman Seminar: Theory of Knots Credits: 4 − Description − Sections
Content: Knots are familiar objects. We use them to tie our shoes, wrap our packages, and moor our boats. Yet they are also quite mysterious: if you have two tangled up ropes, for instance, can you tell if they are tied in the same knot? This course will introduce some of the mathematical techniques people have developed to study knots, partially in an attempt to answer this very question. We will also study connections between knot theory and topology, and try to understand what mathematical knots might have to do with the shape of the universe.
Particulars: Text: The Knot Book, by Colin Adams
000MSC: W306TuTh 10:00am - 11:15amAaron Abramsmax 16
 MATH 190: Freshman Seminar: Sports, Games and Gambling Credits: 4 − Description − Sections
Content: The course is designed to build the laws of probability, statistics and game theory through the models of well known games and sports. Fundamental laws of probability will be developed and applied to games such as poker, blackjack, backgammon, lotteries and more. Fundamental combinatorial counting techniques will be employed to determine outcomes (permutations and combinations). Card tricks based on mathematical principles will be demonstrated in order to learn basic ideas of information encoding. Deeper fundamentals will be introduced using more involved examples. In developing these theories, laws of fair judging can also be investigated. Games will be employed to develop winning strategies or determine when a win is not possible.
Particulars: Class participation will be a major component of the course. Small group learning will also be employed, both for in class experiments and for some assignments. Students will be encouraged to work together in class to test experiments and raise conjectures. They will present their ideas to the rest of class. General writing techniques will also be employed. Formal and informal writing will be assigned, both to individuals and groups. Communication of ideas at all levels will be stressed throughout the course.
001MSC: E406MWF 2:00pm - 2:50pmRon Gouldmax 16
 MATH 211: Multivariable Calculus Credits: 4 − Description − Sections
Content: Vectors and 3-space, functions of several variables, multiple integration, vector fields, line integrals.
Prerequisites: Math 112 or Math 112s or Math 112Z.
000MSC: W201TuTh 10:00am - 11:15amCarol Coxmax 36
001MSC: W201TuTh 1:00pm - 2:15pmCarol Coxmax 36
 MATH 212: Differential Equations Credits: 4 − Description − Sections
Content: First and second-order differential equations, systems of differential equations, power series solutions, applications.
Particulars: Primary emphasis will be placed on developing techniques for the solution of differential equations. Some time will be spent on theory and applications.
Prerequisites: Math 112 or Math 112s or Math 112Z.
000MSC: W301MWF 10:40am - 11:30amPeter Komjathmax 30
001MSC: W302MWF 11:45am - 12:35pmPeter Komjathmax 30
 MATH 221: Linear Algebra Credits: 4 − Description − Sections
Content: A study of systems of linear equations, matrices, determinants, linear transformations, eigenvalues and eigenvectors.
Particulars: This course is required for most degrees in mathematics, computer science and math-economics. Math 221 is also a prerequisite for several other courses required for these degrees. Students who have completed Math 250 and desire a more abstract treatment of linear algebra, should consider enrolling in Math 321 instead of Math 221.
Prerequisites: Math 112 or Math 112s or Math 112Z.
001MSC: W303TuTh 11:30am - 12:45pmRobert Rothmax 34
002MSC: W301MWF 2:00pm - 2:50pmLuca Gerardo Giordamax 34
 MATH 250S: Foundations of Mathematics Credits: 4 − Description − Sections
Content: This course provides the bridge from calculus to more abstract mathematics courses. It is a small seminar intended to develop the student's ability to work with fundamental logical and mathematical concepts. Emphasis will be placed on the careful and precise expression of ideas. The students and the instructor will construct proofs of theorems and present them in class.
Particulars: Students planning a degree in Mathematics should complete Math 250 by the end of their sophomore year.
Prerequisites: Math 112 or Math 112s or Math 112Z or consent of instructor.
001MSC: E408TuTh 11:30am - 12:45pmSteve Battersonmax 16
002MSC: W306TuTh 2:30pm - 3:45pmRobert Rothmax 16
 MATH 321: Abstract Vector Spaces Credits: 4 − Description − Sections
Content: This course will begin with the theory of vector spaces. We will examine matrices and linear transformations and then develop their relationship. All of this builds toward the study of eigenvalues, diagonalization, and Jordan canonical form. Emphasis will be placed on rigorous proof and intuition, rather than computation.
Particulars: This course is required for the B.S. degree in Mathematics. Math 221 is no longer a prerequisite for Math 321. However, since Math 321 will assume familiarity with matrices, some students might benefit from enrolling in Math 221 prior to Math 321.
Prerequisites: Math 250.
000MSC: W201MWF 8:30am - 9:20amDwight Duffusmax 30
 MATH 346: Intro. to Optimization Theory Credits: 4 − Description − Sections
Content: Topics include: Modeling and optimization analysis, simplex method, duality, transportation problems, elements of probability theory and game theory.
Prerequisites: Math 221 (or 321) and CS 170 or consent of instructor. *Strongly recommended*: Math 211.
000MSC: W306TuTh 11:30am - 12:45pmVladimir Olikermax 25
 MATH 351: Partial Differential Equations Credits: 4 − Description − Sections
Content: PDE's and their origin, classification of PDE's, analytical methods for the solutions of PDE's, qualitative properties of the solutions, eigenvalue problems and introduction to numerical methods. At the end of the course students should know to use PDE's for simple models, classify PDE's and solve some simple PDE's.
Prerequisites: Math 211, Math 221.
000MSC: W306TuTh 8:30am - 9:45amEldad Habermax 25
 MATH 362: Probability & Statistics II Credits: 4 − Description − Sections
Content: The mathematical theory of statistical inference. Heavy use will be made of the theory of probability developed in Mathematics 361.
Prerequisites: Math 361.
000MSC: W306MWF 10:40am - 11:30amDavid Borthwickmax 28
 MATH 412: Real Analysis II Credits: 4 − Description − Sections
Content: This is a sequel to Math 411: Real Analysis I. Topics in differentiation and integration of functions on Euclidean n-space will be studied.
Particulars: Emphasis will be placed on proof and intuition rather than computation. This course is required for the BS degree in Mathematics.
Prerequisites: Math 411.
000MSC: W306MWF 9:35am - 10:25amEmily Hamiltonmax 20
 MATH 422: Abstract Algebra II Credits: 4 − Description − Sections
Content: Math 422 is a continuation of Math 421, and is primarily concerned with Ring Theory and Field Theory. Rings and fields were invented to solve problems in the theory of numbers, but now have broad applications in all parts of mathematics. Topics in Math 422 include: polynomial rings, unique factorisation, Euclidean domains, Fields (definition), splitting fields of polynomials, elements of Galois theory, finite fields.
Prerequisites: Mathematics 421
000MSC: E406TuTh 10:00am - 11:15amRaman Parimalamax 16
 MATH 425S: Mathematical Economics Credits: 4 − Description − Sections
Content: The course focuses on various models from microeconomics and on the mathematical tools used to analyze these models. The scope includes consumer behavior, theory of the firm, risk analysis, and game theory. The underlying mathematical tools come generally from constrained optimization of functions of several variables. The material studied is from the class notes and from the current literature.
Particulars: This course is required for the joint major in economics and mathematics.
Prerequisites: Econ 201 and 212; and Math 211 or permission of the instructors.
000MSC: W306TuTh 1:00pm - 2:15pmSkip Garibaldimax 8
 MATH 489R: Topics in Analysis - Computational Methods in Imaging Credits: 4 − Description − Sections
Content: This course introduces students to mathematical and computational methods used in biomedical imaging. Topics to be covered include digital image models and file formats, enhancement, convolution, Fourier transforms, filtering, segmentation, image restoration, and image reconstruction. Particular attention is given to computer implementations using MATLAB.
Prerequisites: Math 221 (Linear Algebra) and Math 315 (Numerical Analysis), or permission of the instructor.
001MSC: W304TuTh 1:00pm - 2:15pmJames Nagymax 20
 MATH 495RWR: Honors Credits: 1 - 4 − Description − Sections
000Faculty (TBA)
 MATH 497R: Directed Study Credits: 1 - 4 − Description − Sections
Content: Credit, one to four hours, as arranged with the department.
00PFaculty (TBA)