Undergraduate classes, Fall 2007, Mathematics

Note: All courses taken towards the major or minor must be taken on a letter grade basis, not pass/fail.
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MATH 107: Intro. Probability and StatisticsCredits: 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: W302MWF 8:30am - 9:20amSilke Gehrke
001MSC: W304MWF 9:35am - 10:25amFred Helenius
002MSC: W303TuTh 11:30am - 12:45pmPraphat Fernandes
003MSC: W306TuTh 1:00pm - 2:15pmJodi Black
004MSC: W306TuTh 2:30pm - 3:45pmAndrzej Dudek
005MSC: W302MWF 3:00pm - 3:50pmKinnari Amin
MATH 111: Calculus ICredits: 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: W301MWF 9:35am - 10:25amTobias Graf
001MSC: W302MWF 9:35am - 10:25amChang Mo Bang
002MSC: W301MWF 10:40am - 11:30amRay Lamb
003MSC: W302MWF 10:40am - 11:30amChang Mo Bang
004MSC: W201MWF 11:45am - 12:35pmHa Nguyen
005MSC: W301MWF 12:50pm - 1:40pmRay Lamb
006MSC: W306MWF 12:50pm - 1:40pmSean Thomas
007MSC: W201MWF 2:00pm - 2:50pmRay Lamb
009MSC: W304MWF 3:00pm - 3:50pmBenjamin Shemmer
010MSC: W301MWF 8:30am - 9:20amFeng Chen
MATH 112: Calculus IICredits: 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: W303MWF 2:00pm - 2:50pmYing Wai (Daniel) Fan
001MSC: W201MWF 3:00pm - 3:50pmJake McMillen
MATH 112S: Freshman Seminar: Calculus IICredits: 4− Description− Sections
Content: This section of Math 112Z is designated a freshman seminar. It is an introduction to mathematical proofs in which students learn to speak and write with the accuracy required to communicate mathematical work effectively. Course content is largely that of a calculus 2 course: Introduction of the natural logarithm via the definite integral, exponential functions, sequences and series, power series, Taylor series.
Particulars: Students are given the necessary definitions and, after some class discussion, problems will be assigned. Students will be expected to work on these problems at home and present their work at the board in class. Solutions may be sought individually or cooperatively and all will be discussed in class. Some problem solutions will be written up individually for grading. A midterm exam and a final exam will be give. Final grades are determined by examination grades, written work and class presentations, with approximately equal weight to each.
Prerequisites: A score of 4 or 5 on the AB Advanced Placement Calculus exam, and an interest in solving mathematical problems.
000MSC: E408MWF 10:40am - 11:30amWilliam Mahavier
MATH 112Z: Calculus IICredits: 4− Description− Sections
Content: A brief review of topics in Math 111 (see above) followed by a discussion of the transcendental functions, derivatives and antiderivatives of the transcendental functions, techniques of integration, infinite series, and applications of these topics.
Particulars: For freshmen only.
Prerequisites: These sections are restricted to freshmen with a score of 4 or 5 on the AB Calculus Advanced Placement Test.
000MSC: W303MWF 9:35am - 10:25amEdward Goetze
001MSC: W302TuTh 10:00am - 11:15amAaron Abrams
002MSC: W304MWF 10:40am - 11:30amShanshuang Yang
004MSC: W304MWF 11:45am - 12:35pmSteve Batterson
005MSC: W304MWF 12:50pm - 1:40pmSteve Batterson
MATH 115: Life Science Calculus ICredits: 4− Description− Sections
Content: A first semester calculus class directed at students intending to major in the life sciences. Topics will be similar to those in Math 111. In addition the course will include an introduction to the use of mathematical models for the study of organ function and population evolution. The sequel, Math 116, will include probability and statistics.
Particulars: Freshmen who have a question about their placement in mathematics should come to the Department of Mathematics and Computer Science during the orientation period for a brief interview with one of the department's faculty members. This should be done before the student's appointment with his/her academic adviser.
Prerequisites: The Biology Department encourages students considering a major in biology to consider the Math 115-116 sequence, designed specifically for life science majors. The calculus topics, examples, material on modeling and the probability & statistics component (in Math 116) are particularly appropriate for the life sciences.
000MSC: W201MWF 9:35am - 10:25amDwight Duffus
000LMSC: W303W 8:30am - 9:20amLior Horesh
001MSC: W201MWF 9:35am - 10:25amDwight Duffus
001LMSC: W303W 3:00pm - 3:50pmLior Horesh
004MSC: W201MWF 10:40am - 11:30amEdward Goetze
004LMSC: W303M 3:00pm - 3:50pmJeremiah Pack
005MSC: W201MWF 10:40am - 11:30amEdward Goetze
005LMSC: W303W 5:00pm - 5:50pmJeremiah Pack
MATH 119: Calculus with Business ApplicationsCredits: 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: E208TuTh 10:00am - 11:15amVictoria Powers
000LMSC: W306M 8:30am - 9:20amAlexis Aposporidis
001MSC: E208TuTh 10:00am - 11:15amVictoria Powers
001LMSC: W306W 8:30am - 9:20amAlexis Aposporidis
002MSC: E208TuTh 10:00am - 11:15amVictoria Powers
002LMSC: W306F 8:30am - 9:20amAlexis Aposporidis
003MSC: E208TuTh 10:00am - 11:15amVictoria Powers
003LMSC: W306M 2:00pm - 2:50pmAnastasia Svishcheva
004MSC: E208TuTh 10:00am - 11:15amVictoria Powers
004LMSC: W306W 2:00pm - 2:50pmAnastasia Svishcheva
005MSC: E208TuTh 10:00am - 11:15amVictoria Powers
005LMSC: W306F 2:00pm - 2:50pmAnastasia Svishcheva
006MSC: E208TuTh 10:00am - 11:15amVictoria Powers
006LMSC: W306M 3:00pm - 3:50pmVerena Kuhlemann
007MSC: E208TuTh 10:00am - 11:15amVictoria Powers
007LMSC: W306W 3:00pm - 3:50pmVerena Kuhlemann
008MSC: E208TuTh 10:00am - 11:15amVictoria Powers
008LMSC: W306F 3:00pm - 3:50pmVerena Kuhlemann
MATH 190: Freshman Seminar: Sports, Games and GamblingCredits: 4− Description− Sections
Content: The course is designed to build the laws of probability 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. Graph models will be developed to study certain situations in games and to trace strategies. Concepts will be developed through experimentation and conjectures made by the students. Hence, class participation will be a major component of the course. In doing this I hope to improve their basic intuition about what should be true as well as their general communication skills. 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 be encouraged to present their ideas to the rest of class. We will maintain an on-going dialogue while we develop the theorems and laws governing the models we study. 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.
Particulars: The style of this course will be halfway between a humanities and a mathematics class. Texts: The Mathematics of Games and Gambling by Edward Packel, The Mathematical Association of America New Mathematical Library, 1981.
Prerequisites: High School Algebra
001MSC: W302MWF 12:50pm - 1:40pmRon Gould
MATH 190: Freshman Seminar: Theory of KnotsCredits: 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
002MSC: W302TuTh 1:00pm - 2:15pmAaron Abrams
MATH 211: Multivariable CalculusCredits: 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: W303MWF 10:40am - 11:30amGideon Maschler
MATH 211P: Multivariable CalculusCredits: 4− Description− Sections
Content: This section of Math 211 is designed to meet the needs of physics majors, but math majors and others with strong interest are welcome. Topics include vectors and 3-space, functions of several variables, parametrized curves, vector fields, line integrals, surfaces, gradients, partial derivatives, multiple integrals in various coordinate systems, conservative fields, circulation, flux, Stokes' Theorem. Optimization (for economics) will not be covered.
Prerequisites: Math 112, Math 112s, or Math 112Z. The course is required for physics majors.
000MSC: W201TuTh 10:00am - 11:15amEric Brussel
MATH 212: Differential EquationsCredits: 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: W304MWF 2:00pm - 2:50pmGideon Maschler
MATH 221: Linear AlgebraCredits: 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: W201TuTh 11:30am - 12:45pmAlessandro Veneziani
001MSC: W304TuTh 1:00pm - 2:15pmMichele Benzi
MATH 250: Foundations of MathematicsCredits: 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.
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: W306MWF 11:45am - 12:35pmEmily Hamilton
MATH 250S: Foundations of MathematicsCredits: 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: E408MWF 9:35am - 10:25amWilliam Mahavier
001MSC: E406TuTh 11:30am - 12:45pmRobert Roth
MATH 315: Numerical AnalysisCredits: 4− Description− Sections
Content: Solving scientific problems using the computer. Topics include linear and nonlinear equations, approximation and interpolation, error analysis, numerical solution of differential equations.
Particulars: Math 221, and CS 150 or CS 170, or equivalent programming experience. A number of (mathematical) problem assignments and (computer) programming assignments will be assigned. All programming assignments will be done using MATLAB. No previous MATLAB experience is required. A number of (mathematical) problem assignments and (computer) programming assignments will be assigned.
Prerequisites: Math 221, and CS 150 or CS 170, or equivalent programming experience.
000MSC: W303TuTh 1:00pm - 2:15pmJames Nagy
MATH 318: Complex VariablesCredits: 4− Description− Sections
Content: An introduction to complex numbers and functions of a complex variable. Emphasis will be placed on both the similarities and differences between real and complex functions and their development. The course will develop the calculus of complex functions including continuity, differentiation, integration, and power series. Other topics will include residues and applications.
Prerequisites: Math 211 and 250 or consent of instructor.
000MSC: W302MWF 11:45am - 12:35pmShanshuang Yang
MATH 361: Probability & Statistics ICredits: 4− Description− Sections
Content: After an overview of finite probability theory, the course will deal primarily with continuous probability theory. Topics include distribution models (binomial, geometric, uniform, normal, Poisson, and exponential), the Chebyshev inequality, expectation, moment generating functions, the central limit theorem plus applications.
Particulars: There will be a final exam and two hour exams. The sequel to this course is Math 362 which is devoted primarily to statistical problems such as estimation, sampling and hypothesis testing procedures. Math 362 usually is given spring semester.
Prerequisites: Math 211 or permission of instructor.
000MSC: W306TuTh 10:00am - 11:15amAndrzej Rucinski
MATH 411: Real AnalysisCredits: 4− Description− Sections
Content: Analysis of sets and functions in n-space. The course will begin with the study of basic topological properties and then proceed through continuity and differentiation. Classical results from real analysis such as the extreme value theorem, chain rule, equality of mixed partials, and inverse function theorem will be presented. Emphasis will be placed on rigorous proof and intuition rather than computation.
Prerequisites: Math 211, Math 221 and Math 250.
000MSC: W306MWF 10:40am - 11:30amDavid Borthwick
MATH 488S: Topics in Algebra: Number TheoryCredits: 4− Description− Sections
Content: Gauss called number theory the "queen of Mathematics". We will cover classical topics in that royal discipline such as congruences, the Chinese Remainder Theorem, prime numbers, and nonlinear Diophantine equations, as well as very modern topics like applications to cryptography.
Prerequisites: Math 221 and Math 250.
000MSC: W201TuTh 2:30pm - 3:45pmRobert Roth
MATH 497R: Directed StudyCredits: 1 - 4− Description− Sections