Undergraduate classes, Fall 2008, 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: W301  TuTh 8:30am  9:45am  Kinnari Amin  max 30  001  MSC: W301  TuTh 10:00am  11:15am  Audrey Malagon  max 30  002  MSC: W302  TuTh 10:00am  11:15am  Michal Karonski  max 30  003  MSC: W304  TuTh 11:30am  12:45pm  Tobias Graf  max 28  004  MSC: W304  MWF 2:00pm  2:50pm  Sean Thomas  max 28  005  MSC: W306  TuTh 2:30pm  3:45pm  Silke Gehrke  max 28  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: W201  MWF 8:30am  9:20am  Catherine Crompton  max 28  001  MSC: W301  MWF 9:35am  10:25am  Chang Mo Bang  max 35  002  MSC: W304  MWF 9:35am  10:25am  Domingos Dellamonica  max 28  003  MSC: W201  MWF 10:40am  11:30am  Ray Lamb  max 35  004  MSC: W301  MWF 10:40am  11:30am  Chang Mo Bang  max 35  005  MSC: W302  MWF 11:45am  12:35pm  Zhuojun T. Magnant  max 28  006  MSC: W304  MWF 11:45am  12:35pm  Piotr Wendykier  max 28  007  MSC: W201  MWF 12:50pm  1:40pm  Ray Lamb  max 35  008  MSC: W301  MWF 12:50pm  1:40pm  Jake McMillen  max 28  009  MSC: W201  MWF 2:00pm  2:50pm  Ray Lamb  max 35  010  MSC: W302  MWF 2:00pm  2:50pm  Raya Horesh  max 28  012  MSC: W304  TuTh 2:30pm  3:45pm  Benjamin Shemmer  max 28  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. Prerequisites: Math 111, Math 115 or placement.  000  MSC: W306  MWF 8:30am  9:20am  Feng Chen  max 28  001  MSC: W304  MWF 12:50pm  1:40pm  Anastasia Svishcheva  max 28  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  TuTh 8:30am  9:45am  Vojtech Rodl  max 30  001  MSC: W303  TuTh 11:30am  12:45pm  Steve Batterson  max 30  002  MSC: W302  MWF 12:50pm  1:40pm  Skip Garibaldi  max 30  003  MSC: W303  TuTh 1:00pm  2:15pm  Shanshuang Yang  max 30  004  MSC: W302  MWF 10:40am  11:30am  Aaron Abrams  max 27  MATH 115: Life Science Calculus I  Credits: 4  − Description  − Sections 
Content: A first semester calculus class designed for life science majors.
In addition to the basics of differential and integral calculus, topics
shared with Math 111, the course includes an introduction to mathematical
modeling of competition, epidemics, and population by means of discrete
dynamics. The sequel, Math 116, includes 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: Math 115/116 is required for students obtaining a B.S. in
Biology. The calculus topics, dynamics, modeling of biological systems,
and the probability & statistics component (in Math 116) are particularly
appropriate for the life sciences. The sequence should not be taken
by students intending to major in Mathematics, Physics or Economics.  000  MSC: W201  MWF 9:35am  10:25am  Dwight Duffus  max 28  000L  MSC: W304  W 8:30am  9:20am  Veronica M. Bustamante  max 28  001  MSC: W201  MWF 9:35am  10:25am  Dwight Duffus  max 28  001L  MSC: W304  M 3:00pm  3:50pm  Veronica M. Bustamante  max 28  002  MSC: W201  MWF 11:45am  12:35pm  Lior Horesh  max 28  002L  MSC: W201  Tu 9:00am  9:50am  Marta D'Elia  max 28  003  MSC: W201  MWF 11:45am  12:35pm  Lior Horesh  max 28  003L  MSC: W304  M 5:00pm  5:50pm  Marta D'Elia  max 28  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.  000  MSC: W302  TuTh 8:30am  9:45am  Hasan Palta  max 28  001  MSC: W302  MWF 9:35am  10:25am  Paul Wrayno  max 28  002  MSC: W304  MWF 10:40am  11:30am  Jodi Black  max 28  003  MSC: W303  MWF 11:45am  12:35pm  Alexis Aposporidis  max 28  004  MSC: W303  MWF 12:50pm  1:40pm  Verena Kuhlemann  max 28  005  MSC: W306  MWF 2:00pm  2:50pm  Praphat Fernandes  max 28  MATH 190: Freshmen Seminar: The Math of Voting and Elections  Credits: 4  − Description  − Sections 
Content: In 1998, Jesse Ventura was elected governor of Minnesota even
though most of the state's population preferred either of the
other two candidates. In 2000, George W. Bush became the president
of the U.S. even though Al Gore received at least half a million
more votes than Bush. Have you ever wondered why elections
produce results that seem to be displeasing to many of the voters
involved?
In this course we will use mathematics to study voting systems,
identify paradoxical situations that
can result from the choice of a voting procedure, and examine how
using voting procedures that seem fair can result in outcomes
that differ from what the voters really wanted. We will also
use mathematics to measure power in political systems. Since this
is a presidential election year, we will use what we have learned
to study the U.S. Electoral College system. There are no prerequisites
for this course, but students should have an interest in both
mathematics and politics.  000  MSC: E408  TuTh 11:30am  12:45pm  Victoria Powers  max 16  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. Particulars: The style of this course will be halfway between a humanities and a mathematics class. There will be two written papers and one inclass mathematics exam. Prerequisites: 4 or 5 on the Calculus AB exam or equivalent on the Calculus BC exam.  001  MSC: W301  MWF 3:00pm  3:50pm  Skip Garibaldi  max 16  MATH 211: Multivariable Calculus  Credits: 4  − Description  − Sections 
Content: Vectors and 3space, functions of several variables, multiple integration, vector fields, line integrals. Prerequisites: Math 112 or Math 112s or Math 112Z.  000  MSC: W303  MWF 9:35am  10:25am  Julia Garibaldi  max 40  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  TuTh 10:00am  11:15am  Eric Brussel  max 40  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: W302  TuTh 11:30am  12:45pm  Vladimir Oliker  max 30  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  Robert Roth  max 40  001  MSC: W201  TuTh 2:30pm  3:45pm  Alessandro Veneziani  max 40  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: E408  MWF 10:40am  11:30am  Emily Hamilton  max 15  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  TuTh 2:30pm  3:45pm  Steve Batterson  max 15  MATH 270: History and Philosophy of Mathematics  Credits: 4  − Description  − Sections 
Content: (Crosslisted with Philosophy 270) Topics in the history of mathematics and their philosophical
background. Genesis and evolution of ideas in analysis, algebra,
geometry, mechanics, foundations. Historical and philosophical
aspects of concepts of infinity, mathematical rigor, probability,
etc. The emergence of mathematical schools. Particulars: In this course we will learn about the emergence of the
Calculus in the 17th and 18th centuries,
with an emphasis on early modern authors. In particular,
we will study
how the basic concepts (functions, continuity, limits,
derivatives, integrals, etc.) were developed, and what
were the motivations of the mathematicians, scientists,
and philosophers who laid the
foundations of the Calculus.
The course will be cotaught by Michele Benzi and Ursula Goldenbaum. Prerequisites: Math 112, 112Z, 112S or permission of the instructors.  000  MSC: W306  TuTh 1:00pm  2:15pm  Michele Benzi  max 25  MATH 315: Numerical Analysis  Credits: 4  − Description  − Sections 
Content: Solving scientific problems using the computer. Topics include
linear and nonlinear equations, approximation and interpolation, quadrature, 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: W304  TuTh 8:30am  9:45am  Alessandro Veneziani  max 25  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: W306  TuTh 11:30am  12:45pm  Eric Brussel  max 25  MATH 330S: Introduction to Combinatorics  Credits: 4  − Description  − Sections 
Content: Graph theory and ordered sets; counting, recursion and generating functions; block designs, coding theory and finite geometry. Particulars: The textbook will be Introductory Combinatorics by Richard A. Brualdi. Prerequisites: Math 221 and Math 250.  000  MSC: E408  TuTh 2:30pm  3:45pm  Robert Roth  max 15  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 is given spring semester. Prerequisites: Math 211 or permission of instructor.  000  MSC: W306  MWF 10:40am  11:30am  David Borthwick  max 25  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 9:35am  10:25am  Emily Hamilton  max 20  MATH 421: 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. Prerequisites: Math 221 or 321, and Math 250.  000  MSC: E406  TuTh 10:00am  11:15am  Raman Parimala  max 15  MATH 486S: Topics in Topology: Point Set Topology  Credits: 4  − Description  − Sections 
Content: This class has been canceled for Fall 2008.      William Mahavier   MATH 497R: Directed Study  Credits: 1  4  − Description  − Sections 
 000    Faculty (TBA)  
