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.
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: W302  MWF 8:30am  9:20am  Silke Gehrke   001  MSC: W304  MWF 9:35am  10:25am  Fred Helenius   002  MSC: W303  TuTh 11:30am  12:45pm  Praphat Fernandes   003  MSC: W306  TuTh 1:00pm  2:15pm  Jodi Black   004  MSC: W306  TuTh 2:30pm  3:45pm  Andrzej Dudek   005  MSC: W302  MWF 3:00pm  3:50pm  Kinnari Amin   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 maxmin problems and related rate problems; antiderivatives and the definite integral.  000  MSC: W301  MWF 9:35am  10:25am  Tobias Graf   001  MSC: W302  MWF 9:35am  10:25am  Chang Mo Bang   002  MSC: W301  MWF 10:40am  11:30am  Ray Lamb   003  MSC: W302  MWF 10:40am  11:30am  Chang Mo Bang   004  MSC: W201  MWF 11:45am  12:35pm  Ha Nguyen   005  MSC: W301  MWF 12:50pm  1:40pm  Ray Lamb   006  MSC: W306  MWF 12:50pm  1:40pm  Sean Thomas   007  MSC: W201  MWF 2:00pm  2:50pm  Ray Lamb   009  MSC: W304  MWF 3:00pm  3:50pm  Benjamin Shemmer   010  MSC: W301  MWF 8:30am  9:20am  Feng Chen   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: W303  MWF 2:00pm  2:50pm  Ying Wai (Daniel) Fan   001  MSC: W201  MWF 3:00pm  3:50pm  Jake McMillen   MATH 112S: Freshman Seminar: Calculus II  Credits: 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.  000  MSC: E408  MWF 10:40am  11:30am  William Mahavier   MATH 112Z: Calculus II  Credits: 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.  000  MSC: W303  MWF 9:35am  10:25am  Edward Goetze   001  MSC: W302  TuTh 10:00am  11:15am  Aaron Abrams   002  MSC: W304  MWF 10:40am  11:30am  Shanshuang Yang   004  MSC: W304  MWF 11:45am  12:35pm  Steve Batterson   005  MSC: W304  MWF 12:50pm  1:40pm  Steve Batterson   MATH 115: Life Science Calculus I  Credits: 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 115116 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.  000  MSC: W201  MWF 9:35am  10:25am  Dwight Duffus   000L  MSC: W303  W 8:30am  9:20am  Lior Horesh   001  MSC: W201  MWF 9:35am  10:25am  Dwight Duffus   001L  MSC: W303  W 3:00pm  3:50pm  Lior Horesh   004  MSC: W201  MWF 10:40am  11:30am  Edward Goetze   004L  MSC: W303  M 3:00pm  3:50pm  Jeremiah Pack   005  MSC: W201  MWF 10:40am  11:30am  Edward Goetze   005L  MSC: W303  W 5:00pm  5:50pm  Jeremiah Pack   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: E208  TuTh 10:00am  11:15am  Victoria Powers   000L  MSC: W306  M 8:30am  9:20am  Alexis Aposporidis   001  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   001L  MSC: W306  W 8:30am  9:20am  Alexis Aposporidis   002  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   002L  MSC: W306  F 8:30am  9:20am  Alexis Aposporidis   003  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   003L  MSC: W306  M 2:00pm  2:50pm  Anastasia Svishcheva   004  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   004L  MSC: W306  W 2:00pm  2:50pm  Anastasia Svishcheva   005  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   005L  MSC: W306  F 2:00pm  2:50pm  Anastasia Svishcheva   006  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   006L  MSC: W306  M 3:00pm  3:50pm  Verena Kuhlemann   007  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   007L  MSC: W306  W 3:00pm  3:50pm  Verena Kuhlemann   008  MSC: E208  TuTh 10:00am  11:15am  Victoria Powers   008L  MSC: W306  F 3:00pm  3:50pm  Verena Kuhlemann   MATH 190: Freshman Seminar: Sports, Games and Gambling  Credits: 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 ongoing 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  001  MSC: W302  MWF 12:50pm  1:40pm  Ron Gould   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  002  MSC: W302  TuTh 1:00pm  2:15pm  Aaron Abrams   MATH 211: Multivariable Calculus  Credits: 4  − Description  − Sections 
Content: Vectors and 3space, 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  MWF 10:40am  11:30am  Gideon Maschler   MATH 211P: Multivariable Calculus  Credits: 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 3space, 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.  000  MSC: W201  TuTh 10:00am  11:15am  Eric Brussel   MATH 212: Differential Equations  Credits: 4  − Description  − Sections 
Content: First and secondorder 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  MWF 2:00pm  2:50pm  Gideon Maschler   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 matheconomics. 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: W201  TuTh 11:30am  12:45pm  Alessandro Veneziani   001  MSC: W304  TuTh 1:00pm  2:15pm  Michele Benzi   MATH 250: 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. 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: W306  MWF 11:45am  12:35pm  Emily Hamilton   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: E408  MWF 9:35am  10:25am  William Mahavier   001  MSC: E406  TuTh 11:30am  12:45pm  Robert Roth   MATH 315: Numerical Analysis  Credits: 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.  000  MSC: W303  TuTh 1:00pm  2:15pm  James Nagy   MATH 318: Complex Variables  Credits: 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.  000  MSC: W302  MWF 11:45am  12:35pm  Shanshuang Yang   MATH 361: Probability & Statistics I  Credits: 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.  000  MSC: W306  TuTh 10:00am  11:15am  Andrzej Rucinski   MATH 411: Real Analysis  Credits: 4  − Description  − Sections 
Content: Analysis of sets and functions in nspace. 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.  000  MSC: W306  MWF 10:40am  11:30am  David Borthwick   MATH 488S: Topics in Algebra: Number Theory  Credits: 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.  000  MSC: W201  TuTh 2:30pm  3:45pm  Robert Roth   MATH 497R: Directed Study  Credits: 1  4  − Description  − Sections 

