# Undergraduate classes, Spring 2007, 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: W201TuTh 8:30am - 9:45amMichal Karonskimax 50
001MSC: W302MWF 9:35am - 10:25amAnnika Poerschke
002MSC: W201TuTh 10:00am - 11:15amMichal Karonski
003MSC: W304MWF 10:40am - 11:30amColton Magnant
004MSC: W303MWF 12:50pm - 1:40pmFred Helenius
 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: W303MWF 10:40am - 11:30amSilke Gehrkemax 27
001MSC: W303MWF 11:45am - 12:35pmDaniel Martinmax 27
002MSC: W303MWF 2:00pm - 2:50pmAndrzej Dudekmax 27
003MSC: W303MWF 9:35am - 10:25amTobias Graf
 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.
Particulars: Usually three or four exams and a final are given during the semester. Some instructors collect homework or give impromptu quizzes.
Prerequisites: Math 111, Math 115 or placement.
000MSC: W301MWF 8:30am - 9:20amBenjamin Shemmer
001MSC: W301MWF 9:35am - 10:25amChang Mo Bang
002MSC: W301MWF 10:40am - 11:30amChang Mo Bang
003MSC: W301MWF 11:45am - 12:35pmRay Lamb
004MSC: W201MWF 12:50pm - 1:40pmRay Lamb
005MSC: W301MWF 2:00pm - 2:50pmJulianne Chung
 MATH 116: Life Sciences Calculus II Credits: 4 − Description − Sections
Content: Second semester calculus with an emphasis on applications to biology. Topics covered include integration, simple differential equations, multivariable calculus, discrete probability, and statistics.
Particulars: There will be weekly quizzes or written assignments, three tests and a final exam. Students intending to take Math 211 or Math 212 should take Math 112 rather than Math 116.
Prerequisites: Math 115, Math 111, or placement.
000MSC: W306MWF 9:35am - 10:25amEdward Goetze
 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. Students will be required to have a graphing calculator. The TI83 is recommended, but a TI82 or TI85 is acceptable.
000MSC: W301TuTh 8:30am - 9:45amAudrey Malagon
001MSC: W304TuTh 10:00am - 11:15amKen Keating
002MSC: W306TuTh 11:30am - 12:45pmKinnari Amin
003MSC: W301TuTh 1:00pm - 2:15pmChristian Avart
 MATH 190: Freshman Seminar: Games and Gambling Credits: 4 − Description − Sections
Content: In this course we will learn some mathematics from the areas of probability, game theory, and combinatorial design theory by investigating topics from the world of sports, competitive games of strategy, casino games, lotteries, and the mathematical theory of games. Depending upon the interests of students in the class, possible topics include backgammon, poker, othello (and other board games), football and basketball pools, baseball statistics, evaluation of individual player performances in team sports such as basketball and hockey, and card games such as hearts, casino and blackjack (although the complexity of the game and the use of multiple deck shoes make a mathematical analysis of blackjack beyond the scope of this seminar, we can still make intelligent empirical observations about various playing and betting strategies; i.e., we can still have a good time playing the game).
001MSC: W306TuTh 2:30pm - 3:45pmRobert Roth
 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. Additionally, these studies lead to deep results about topology and geometry. We will also see various applications, like how knot theory is relevant to the study of DNA.
Particulars: Text: The Knot Book, by Colin Adams
000MSC: W302TuTh 10:00am - 11:15amAaron Abramsmax 50
 MATH 211: Multivariable Calculus Credits: 4 − Description − Sections
Content: Vectors and 3-space, functions of several variables, multiple integration, vector fields, line integrals.
Particulars: Usually 2 or 3 tests and a final examination are given.
Prerequisites: Math 112 or Math 112s or Math 112Z.
000MSC: W303TuTh 11:30am - 12:45pmVladimir Oliker
001MSC: W303TuTh 1:00pm - 2:15pmEldad Haber
 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: W304TuTh 1:00pm - 2:15pmSteve Batterson
 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.
000MSC: W306MWF 11:45am - 12:35pmEdward Goetze
001MSC: W201TuTh 11:30am - 12:45pmRobert Roth
 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.
000MSC: E406MWF 11:45am - 12:35pmWilliam Mahavier
001MSC: W302TuTh 2:30pm - 3:45pmSteve Batterson
 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 towards 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: W304TuTh 11:30am - 12:45pmShanshuang Yang
 MATH 324: Abstract Algebra II Credits: 4 − Description − Sections
Content: Math 324 is a continuation of Math 323, 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 324 include: Rings (definition and examples), quotient rings and homomorphisms, Euclidean rings, polynomial rings, fields (definition), roots of polynomials, and elements of Galois Theory. Particulars: Prerequisite: Math 323. There will be two exams during the semester and a final examination in addition to regular homework assignments.
Particulars: There will be two exams during the semester and a final examination in addition to regular homework assignments.
Prerequisites: Math 323.
000MSC: E408TuTh 11:30am - 12:45pmEric Brussel
 MATH 346: Intro. to Optimization Theory Credits: 4 − Description − Sections
Content: The course will deal with the theory of optimization and its applications. Topics include: optimization in many dimensions, optimization of functionals and variational principle, theory of constrained optimization, and applications.
Particulars: Students will learn to use Mathematica (a system for doing mathematics by computer) as an aid in problem solving.
Prerequisites: Math 221 and CS 150/170 or consent of instructor.
000MSC: E406TuTh 2:30pm - 3:45pmEldad Haber
 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: W302MWF 11:45am - 12:35pmDavid Borthwick
 MATH 362: Probability & Statistics II Credits: 4 − Description − Sections
Content: The theory and practice of statistics. Heavy use will be made of the theory of probability developed in Mathematics 361.
Prerequisites: Math 361.
000MSC: W302MWF 10:40am - 11:30amDavid Borthwick
 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: E406MWF 10:40am - 11:30amEmily Hamilton
 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, Econ 212, and Math 211 or permission of the instructors.
000MSC: W301TuTh 11:30am - 12:45pmSkip Garibaldi
 MATH 495WR: Honors Credits: 4 − Description − Sections
000Faculty (TBA)
 MATH 497R: Directed Study Credits: 4 − Description − Sections
000Faculty (TBA)