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.
|000||MSC: W201||TuTh 8:30am - 9:45am||Michal Karonski||max 50|
|001||MSC: W302||MWF 9:35am - 10:25am||Annika Poerschke|
|002||MSC: W201||TuTh 10:00am - 11:15am||Michal Karonski|
|003||MSC: W304||MWF 10:40am - 11:30am||Colton Magnant|
|004||MSC: W303||MWF 12:50pm - 1:40pm||Fred 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.
|000||MSC: W303||MWF 10:40am - 11:30am||Silke Gehrke||max 27|
|001||MSC: W303||MWF 11:45am - 12:35pm||Daniel Martin||max 27|
|002||MSC: W303||MWF 2:00pm - 2:50pm||Andrzej Dudek||max 27|
|003||MSC: W303||MWF 9:35am - 10:25am||Tobias 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.
|000||MSC: W301||MWF 8:30am - 9:20am||Benjamin Shemmer|
|001||MSC: W301||MWF 9:35am - 10:25am||Chang Mo Bang|
|002||MSC: W301||MWF 10:40am - 11:30am||Chang Mo Bang|
|003||MSC: W301||MWF 11:45am - 12:35pm||Ray Lamb|
|004||MSC: W201||MWF 12:50pm - 1:40pm||Ray Lamb|
|005||MSC: W301||MWF 2:00pm - 2:50pm||Julianne 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.
|000||MSC: W306||MWF 9:35am - 10:25am||Edward 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.
|000||MSC: W301||TuTh 8:30am - 9:45am||Audrey Malagon|
|001||MSC: W304||TuTh 10:00am - 11:15am||Ken Keating|
|002||MSC: W306||TuTh 11:30am - 12:45pm||Kinnari Amin|
|003||MSC: W301||TuTh 1:00pm - 2:15pm||Christian 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).
|001||MSC: W306||TuTh 2:30pm - 3:45pm||Robert 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
|000||MSC: W302||TuTh 10:00am - 11:15am||Aaron Abrams||max 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.
|000||MSC: W303||TuTh 11:30am - 12:45pm||Vladimir Oliker|
|001||MSC: W303||TuTh 1:00pm - 2:15pm||Eldad 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.
|000||MSC: W304||TuTh 1:00pm - 2:15pm||Steve 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.
|000||MSC: W306||MWF 11:45am - 12:35pm||Edward Goetze|
|001||MSC: W201||TuTh 11:30am - 12:45pm||Robert 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.
|000||MSC: E406||MWF 11:45am - 12:35pm||William Mahavier|
|001||MSC: W302||TuTh 2:30pm - 3:45pm||Steve 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.
|000||MSC: W304||TuTh 11:30am - 12:45pm||Shanshuang 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.
|000||MSC: E408||TuTh 11:30am - 12:45pm||Eric 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.
|000||MSC: E406||TuTh 2:30pm - 3:45pm||Eldad 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.
|000||MSC: W302||MWF 11:45am - 12:35pm||David 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.
|000||MSC: W302||MWF 10:40am - 11:30am||David 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.
|000||MSC: E406||MWF 10:40am - 11:30am||Emily 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.
|000||MSC: W301||TuTh 11:30am - 12:45pm||Skip Garibaldi|
|MATH 495WR: Honors||Credits: 4||− Description||− Sections|
|MATH 497R: Directed Study||Credits: 4||− Description||− Sections|