Undergraduate classes, Fall 2006, Mathematics
Note: All courses taken towards the major or minor must be taken on a letter grade basis, not pass/fail.
MATH 101: Trigonometry and Algebra  Credits: 4  − Description  − Sections 
Content: This course is intended for students planning to take Math 111 (calculus) who did not take trigonometry in high school or who need remedial work in precalculus topics. Topics include factoring, the cartesian plane, functions and their graphs, the trigonometric functions, the logarithm and exponential functions, and elementary ideas in analytic geometry. Particulars: Usually three tests and a final examination are given during the semester. Some instructors collect homework or give impromptu quizzes.  000  MSC: W306  MWF 3:00pm  3:50pm  Ha Nguyen   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: W301  MWF 9:35am  10:25am  Colton Magnant   001  MSC: W304  MWF 11:45am  12:35pm  Annika Poerschke   002  MSC: W201  TuTh 1:00pm  2:15pm  Tomasz Luczak   003  MSC: W301  MWF 2:00pm  2:50pm  Fred Helenius   MATH 109: Game Theory, Graphs and Math. Models  Credits: 4  − Description  − Sections 
Content: We will study game theory, graph theory, and other mathematical topics. Game theory computes optimal strategies in simple situations where there is conflict. Graphs are points connected by lines that could be models for practical situations. We aim to gain experience in confronting, studying and solving problems. Particulars: Usually there will be three exams and a final.  000  MSC: W304  TuTh 2:30pm  3:45pm  Esmeralda Nastase   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: W303  MWF 8:30am  9:20am  Silke Gehrke   001  MSC: W303  MWF 9:35am  10:25am  Piotr Wendykier   002  MSC: W302  MWF 9:35am  10:25am  Tobias Graf   003  MSC: W201  MWF 10:40am  11:30am  Ray Lamb   004  MSC: W306  MWF 10:40am  11:30am  Benjamin Shemmer   005  MSC: W302  MWF 11:45am  12:35pm  Chang Mo Bang   006  MSC: W201  MWF 12:50pm  1:40pm  Ray Lamb   007  MSC: W303  MWF 12:50pm  1:40pm  Daniel Martin   008  MSC: W302  MWF 12:50pm  1:40pm  Chang Mo Bang   009  MSC: W201  MWF 2:00pm  2:50pm  Ray Lamb   010  MSC: W306  MWF 2:00pm  2:50pm  Kinnari Amin   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 10:40am  11:30am  Julianne Chung   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: W306  MWF 12:50pm  1:40pm  Skip Garibaldi   001  MSC: W301  TuTh 10:00am  11:15am  Vojtech Rodl   002  MSC: W301  TuTh 11:30am  12:45pm  Shanshuang Yang   003  MSC: W302  TuTh 2:30pm  3:45pm  Aaron Abrams   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  Edward Goetze   001  MSC: W302  MWF 2:00pm  2:50pm  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: W303  TuTh 10:00am  11:15am  Ken Keating   001  MSC: W201  TuTh 11:30am  12:45pm  Victoria Powers   002  MSC: W303  TuTh 1:00pm  2:15pm  Christian Avart   003  MSC: W303  TuTh 2:30pm  3:45pm  Audrey Malagon   MATH 190: Freshman Seminar: Mathematics and Politics  Credits: 4  − Description  − Sections 
Content: Can a game explain the irrationality of the arms race of the 1980's? Is democracy, in the sense of reflecting the will of the people, impossible? In this course we will use mathematics to explore questions like these. The "politics" in the course will cover five topics such as international conflict, yesno voting systems, political power, and social choice. The "mathematics" will be conceptual rather than computational and will include symbolic representation and manipulation, game theory, mathematical modeling, and logical deduction. Particulars: Text: Mathematics and Politics: Strategy, Voting, Power, and Proof, by Alan. D. Taylor Prerequisites: Freshmen only class. There are no prerequisites, however students should have an interest in mathematics and political science.  001  MSC: W201  TuTh 1:00pm  2:15pm  Victoria Powers   MATH 190: Freshman Seminar: Cryptology  Credits: 4  − Description  − Sections 
Content: When you buy something on the web, you broadcast your credit card number to untold numbers of other computers. How is your number kept secret? When you swipe your credit card at the grocery store checkout, sometimes the machine knows that it misread your card without calling Visa. How does it know? These questions and others will be answered. Also, we will discuss the role of secret codes and codebreaking in wartime, criminal activity, and the lives of lawabiding citizens.
The style of this course will be halfway between a humanities and a mathematics class. Particulars: The style of this course will be halfway between a humanities and a mathematics class. Prerequisites: Freshmen only class. 4 or 5 on the Calculus AB exam or equivalent on the Calculus BC exam.  000  MSC: W301  MWF 3:00pm  3:50pm  Skip Garibaldi   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: W201  TuTh 2:30pm  3:45pm  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: W303  MWF 11:45am  12:35pm  David Borthwick   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: W303  TuTh 11:30am  12:45pm  Vladimir Oliker   001  MSC: W301  MWF 11:45am  12:35pm  Edward Goetze   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 10:00am  11:15am  Robert Roth   001  MSC: W303  MWF 10:40am  11:30am  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: W306  TuTh 11:30am  12:45pm  Aaron Abrams   001  MSC: E406  TuTh 2:30pm  3:45pm  Steve Batterson   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: W306  TuTh 10:00am  11:15am  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: W304  TuTh 11:30am  12:45pm  Steve Batterson   MATH 323: Abstract Algebra I  Credits: 4  − Description  − Sections 
Content: Groups (definition and examples), cosets, Lagrange's Theorem, symmetric and alternating groups, Cayley's Theorem, isomorphisms, Cauchy's Theorem, quotient groups and homomorphisms, and the action of a group on a set. Additional topics may include the Sylow Theorems, and the theory of rotation groups. Particulars: Two inclass exams during the semester and a final examination. There will be regular homework assignments. Classroom participation is expected for all students. Prerequisites: Math 221 or 321, and Math 250.  000  MSC: W306  TuTh 2:30pm  3:45pm  Eric Brussel   MATH 330: Intro. to Combinatorics  Credits: 4  − Description  − Sections 
Content: Graph theory and ordered sets; counting, recursion and generating functions; block designs, coding theory and finite geometry. Prerequisites: Math 221 and Math 250.  000  MSC: W302  TuTh 1:00pm  2:15pm  Robert Roth   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: W302  MWF 10:40am  11:30am  David Borthwick   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: E406  MWF 11:45am  12:35pm  Emily Hamilton   MATH 495WR: Honors  Credits: 4  − Description  − Sections 
 MATH 497R: Directed Study  Credits: 4  − Description  − Sections 

