# Undergraduate catalog 2006 - 2007, Mathematics

Note: The class catalog is published every two years. Courses listed in the catalog may not be offered in a given term. For class offerings for each semester please click on the "Offerings" links.
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
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.
 MATH 105: Discrete Mathematics Credits: 4 − Description
 MATH 106: Intro Ideas & Methods of Math Credits: 4 − Description
 MATH 107: Intro. Probability and Statistics Credits: 4 − Description
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.
 MATH 108: Intro to Linear Algebra Credits: 4 − Description
 MATH 109: Game Theory, Graphs and Math. Models Credits: 4 − Description
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.
 MATH 111: Calculus I Credits: 4 − Description
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.
 MATH 111S: Calculus I Credits: 4 − Description
 MATH 112: Calculus II Credits: 4 − Description
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.
 MATH 112S: Freshman Seminar: Calculus II Credits: 4 − Description
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.
 MATH 112Z: Calculus II Credits: 4 − Description
Content: A brief review of topics in Math 111 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.
 MATH 115: Life Science Calculus I Credits: 4 − Description
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.
 MATH 116: Life Sciences Calculus II Credits: 4 − Description
Content: Second semester calculus with an emphasis on applications to biology. Topics covered include integration, simple differential equations, multivariable calculus, discrete probability, and statistics.
Particulars: There will be weekly quizzes or written assignments, three tests and a final exam. Students intending to take Math 211 or Math 212 should take Math 112 rather than Math 116.
Prerequisites: Math 115, Math 111, or placement.
 MATH 119: Calculus with Business Applications Credits: 4 − Description
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.
 MATH 130: Basic Programming & Computer Credits: 2 − Description
 MATH 190: Freshman Seminar: Games and Gambling Credits: 4 − Description
Content: In this course we will learn some mathematics from the areas of probability, game theory, and combinatorial design theory by investigating topics from the world of sports, competitive games of strategy, casino games, lotteries, and the mathematical theory of games. Depending upon the interests of students in the class, possible topics include backgammon, poker, othello (and other board games), football and basketball pools, baseball statistics, evaluation of individual player performances in team sports such as basketball and hockey, and card games such as hearts, casino and blackjack (although the complexity of the game and the use of multiple deck shoes make a mathematical analysis of blackjack beyond the scope of this seminar, we can still make intelligent empirical observations about various playing and betting strategies; i.e., we can still have a good time playing the game).
 MATH 190: Freshman Seminar: Theory of Knots Credits: 4 − Description
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
 MATH 190: Freshman Seminar: Cryptology Credits: 4 − Description
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.
Particulars: The style of this course will be halfway between a humanities and a mathematics class.
Prerequisites: 4 or 5 on the Calculus AB exam or equivalent on the Calculus BC exam.
 MATH 190: Freshman Seminar: Mathematics and Politics Credits: 4 − Description
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: There are no prerequisites, however students should have an interest in mathematics and political science.
 MATH 207: Probability & Stats w/Applictn Credits: 4 − Description
 MATH 211: Multivariable Calculus Credits: 4 − Description
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.
 MATH 211P: Multivariable Calculus Credits: 4 − Description
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.
 MATH 212: Differential Equations Credits: 4 − Description
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.
 MATH 217: Undergrad Seminar in Analysis Credits: 2 − Description
 MATH 218: Undergrad Seminar in Analysis Credits: 2 − Description
 MATH 221: Linear Algebra Credits: 4 − Description
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.
 MATH 227: Undergrad Seminar in Algebra Credits: 2 − Description
 MATH 228: Seminar in Algebra Credits: 2 − Description
 MATH 234: Intro To Computer Usage&Prog I Credits: 3 − Description
 MATH 235: Intro To Computer Usage&Prog I Credits: 3 − Description
 MATH 245: Intro To Automata Theory II Credits: 3 − Description
 MATH 250S: Foundations of Mathematics Credits: 4 − Description
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.
 MATH 315: Numerical Analysis Credits: 4 − Description
Content: Solving scientific problems using the computer. Topics include linear and nonlinear equations, approximation and interpolation, error analysis, numerical solution of differential equations.
Particulars: 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.
 MATH 318: Complex Variables Credits: 4 − Description
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.
 MATH 321: Abstract Vector Spaces Credits: 4 − Description
Content: This course will begin with the theory of vector spaces. We will examine matrices and linear transformations and then develop their relationship. All of this builds towards the study of eigenvalues, diagonalization, and Jordan canonical form. Emphasis will be placed on rigorous proof and intuition, rather than computation.
Particulars: This course is required for the B.S. degree in Mathematics. Math 221 is no longer a prerequisite for Math 321. However, since Math 321 will assume familiarity with matrices, some students might benefit from enrolling in Math 221 prior to Math 321.
Prerequisites: Math 250.
 MATH 323: Abstract Algebra I Credits: 4 − Description
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.
 MATH 324: Abstract Algebra II Credits: 4 − Description
Content: Math 324 is a continuation of Math 323, and is primarily concerned with Ring Theory and Field Theory. Rings and fields were invented to solve problems in the theory of numbers, but now have broad applications in all parts of mathematics. Topics in Math 324 include: Rings (definition and examples), quotient rings and homomorphisms, Euclidean rings, polynomial rings, fields (definition), roots of polynomials, and elements of Galois Theory.
Particulars: There will be two exams during the semester and a final examination in addition to regular homework assignments.
Prerequisites: Math 323.
 MATH 330: Intro. to Combinatorics Credits: 4 − Description
Content: Graph theory and ordered sets; counting, recursion and generating functions; block designs, coding theory and finite geometry.
Prerequisites: Math 221 and Math 250.
 MATH 340: The Number System Credits: 4 − Description
 MATH 340E: Number System: Early Childhood Credits: 4 − Description
 MATH 341: Informal Geometry Credits: 4 − Description
 MATH 341E: Informal Geometry: Early Childh Credits: 4 − Description
 MATH 344: Differential Geometry Credits: 4 − Description
 MATH 344S: Differential Geometry Credits: 4 − Description
 MATH 345: Mathematical Modeling Credits: 4 − Description
 MATH 346: Intro. to Optimization Theory Credits: 4 − Description
Content: The course will deal with the theory of optimization and its applications. Topics include: optimization in many dimensions, optimization of functionals and variational principle, theory of constrained optimization, and applications.
Particulars: Students will learn to use Mathematica (a system for doing mathematics by computer) as an aid in problem solving.
Prerequisites: Math 221 and CS 150/170 or consent of instructor.
 MATH 348: Intro to Found of Geometry Credits: 4 − Description
 MATH 351: Partial Differential Equations Credits: 4 − Description
Content: PDE's and their origin, classification of PDE's, analytical methods for the solutions of PDE's, qualitative properties of the solutions, eigenvalue problems and introduction to numerical methods. At the end of the course students should know to use PDE's for simple models, classify PDE's and solve some simple PDE's.
Prerequisites: Math 211, Math 221.
 MATH 361: Probability & Statistics I Credits: 4 − Description
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.
 MATH 362: Probability & Statistics II Credits: 4 − Description
Content: The theory and practice of statistics. Heavy use will be made of the theory of probability developed in Mathematics 361.
Prerequisites: Math 361.
 MATH 411: Real Analysis Credits: 4 − Description
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.
 MATH 412: Real Analysis II Credits: 4 − Description
Content: This is a sequel to Math 411: Real Analysis I. Topics in differentiation and integration of functions on Euclidean n-space will be studied.
Particulars: Emphasis will be placed on proof and intuition rather than computation. This course is required for the BS degree in Mathematics.
Prerequisites: Math 411.
 MATH 425S: Mathematical Economics Credits: 4 − Description
Content: The course focuses on various models from microeconomics and on the mathematical tools used to analyze these models. The scope includes consumer behavior, theory of the firm, risk analysis, and game theory. The underlying mathematical tools come generally from constrained optimization of functions of several variables. The material studied is from the class notes and from the current literature.
Particulars: This course is required for the joint major in economics and mathematics.
Prerequisites: Econ 201, Econ 212, and Math 211 or permission of the instructors.
 MATH 430: Coding Theory Credits: 4 − Description
 MATH 445: Mathematical Economics Credits: 4 − Description
 MATH 487: Graph Theory Credits: 4 − Description
 MATH 489: Topics in Analysis Credits: 4 − Description
 MATH 495WR: Honors Credits: 4 − Description
 MATH 497R: Directed Study Credits: 4 − Description