# 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.
000MSC: W306MWF 3:00pm - 3:50pmHa 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.
000MSC: W301MWF 9:35am - 10:25amColton Magnant
001MSC: W304MWF 11:45am - 12:35pmAnnika Poerschke
002MSC: W201TuTh 1:00pm - 2:15pmTomasz Luczak
003MSC: W301MWF 2:00pm - 2:50pmFred 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.
000MSC: W304TuTh 2:30pm - 3:45pmEsmeralda 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 max-min problems and related rate problems; antiderivatives and the definite integral.
000MSC: W303MWF 8:30am - 9:20amSilke Gehrke
001MSC: W303MWF 9:35am - 10:25amPiotr Wendykier
002MSC: W302MWF 9:35am - 10:25amTobias Graf
003MSC: W201MWF 10:40am - 11:30amRay Lamb
004MSC: W306MWF 10:40am - 11:30amBenjamin Shemmer
005MSC: W302MWF 11:45am - 12:35pmChang Mo Bang
006MSC: W201MWF 12:50pm - 1:40pmRay Lamb
007MSC: W303MWF 12:50pm - 1:40pmDaniel Martin
008MSC: W302MWF 12:50pm - 1:40pmChang Mo Bang
009MSC: W201MWF 2:00pm - 2:50pmRay Lamb
010MSC: W306MWF 2:00pm - 2:50pmKinnari 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.
000MSC: W301MWF 10:40am - 11:30amJulianne 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.
000MSC: E408MWF 10:40am - 11:30amWilliam 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.
000MSC: W306MWF 12:50pm - 1:40pmSkip Garibaldi
001MSC: W301TuTh 10:00am - 11:15amVojtech Rodl
002MSC: W301TuTh 11:30am - 12:45pmShanshuang Yang
003MSC: W302TuTh 2:30pm - 3:45pmAaron 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 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 - 10:25amEdward Goetze
001MSC: W302MWF 2:00pm - 2:50pmEdward 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: W303TuTh 10:00am - 11:15amKen Keating
001MSC: W201TuTh 11:30am - 12:45pmVictoria Powers
002MSC: W303TuTh 1:00pm - 2:15pmChristian Avart
003MSC: W303TuTh 2:30pm - 3:45pmAudrey 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, yes-no 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.
001MSC: W201TuTh 1:00pm - 2:15pmVictoria 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 mis-read 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 law-abiding 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.
000MSC: W301MWF 3:00pm - 3:50pmSkip Garibaldi
 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: W201TuTh 2:30pm - 3:45pmGideon 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 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: W303MWF 11:45am - 12:35pmDavid Borthwick
 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: W303TuTh 11:30am - 12:45pmVladimir Oliker
001MSC: W301MWF 11:45am - 12:35pmEdward 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 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 10:00am - 11:15amRobert Roth
001MSC: W303MWF 10:40am - 11:30amEmily 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.
000MSC: W306TuTh 11:30am - 12:45pmAaron Abrams
001MSC: E406TuTh 2:30pm - 3:45pmSteve 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.
000MSC: W306TuTh 10:00am - 11:15amJames 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.
000MSC: W304TuTh 11:30am - 12:45pmSteve 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 in-class 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.
000MSC: W306TuTh 2:30pm - 3:45pmEric 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.
000MSC: W302TuTh 1:00pm - 2:15pmRobert 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.
000MSC: W302MWF 10:40am - 11:30amDavid Borthwick
 MATH 411: Real Analysis Credits: 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: E406MWF 11:45am - 12:35pmEmily Hamilton
 MATH 495WR: Honors Credits: 4 − Description − Sections
 MATH 497R: Directed Study Credits: 4 − Description − Sections