• 2009-2010 Courses:
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Fall 2009

• MATH 100: Mathematics and Democracy

  Mathematics has a substantive role to play in the implementation of democracy. How do we ensure equitable representation? How do we fairly divide finite resources (and share responsibilities and burdens)? How do we ensure that the results of our elections reflect the popular will? Social scientists and mathematicians have turned some powerful mathematical tools onto the investigation of such questions in recent years. We will study some of that work with the dual goals of gaining appreciation for the power and elegance of the mathematical approach to problem-solving and understanding at a deeper level how to construct a just society. 6; S/CR/NC; Mathematics and Natural Sciences; offered Fall 2009 -- S. Kennedy

• MATH 101: Calculus with Problem Solving

  An introduction to the central ideas of calculus with review and practice of those skills needed for the continued study of calculus. Problem solving strategies will be emphasized. (Meets Monday through Friday). Not open to students who have received credit for Math 111. 6; Mathematics and Natural Sciences; offered Fall 2009 -- E. Egge

• MATH 111: Introduction to Calculus

  An introduction to the differential and integral calculus. Derivatives, antiderivatives, the definite integral, applications, and the fundamental theorem of calculus. Requires placement via the Calculus Placement Exam 1, see Mathematics web page. Not open to students who have received credit for Mathematics 101. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 115: Statistics: Concepts and Applications

  Introduction to statistical concepts with emphasis on understanding and interpretation of statistical information, especially in the context of media reports and scholarly articles. Examples taken from a wide-range of areas such as public policy, health and medicine, and the social and natural sciences. Computationally less intensive than Math 215. Students will learn how to use statistical software. Topics include: Uncertainty and variability, statistical graphs, types of studies, correlation and linear regression, two-way tables, and inference. Not open to students who have already received credit for Math 211, Math 215 or Psychology 200/201. 6; Mathematics and Natural Sciences; offered Fall 2009, Spring 2010 -- L. Chihara, K. St. Clair

• MATH 121: Calculus II

  Integration techniques, improper integrals, the calculus of the logarithmic, exponential and inverse trigonometric functions, applications, Taylor polynomials and infinite series. Prerequisite: Mathematics 101, 111 or placement via Calculus Placement Exam #2. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 211: Introduction to Multivariable Calculus

  Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green's theorem. Prerequisite: Mathematics 121 or 131 or placement via Calculus Placement Exam #3. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 215: Introduction to Statistics

  Introduction to statistics and data analysis. Practical aspects of statistics, including extensive use of statistical software, interpretation and communication of results, will be emphasized. Topics include: exploratory data analysis, correlation and linear regression, design of experiments, basic probability, the normal distribution, sampling distributions, estimation, hypothesis testing, and two-way tables. Not open to students who have already received credit for Math 115 or Math 275. Students who have received MS credit for Psychology 200/201 cannot receive MS credit for Math 215. Students who have taken Math 211 are encouraged to consider the more advanced Math 265-275 probability-statistics sequence. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 232: Linear Algebra

  Vector spaces, linear transformations, determinants, inner products and orthogonality, eigenvectors and eigenvalues; connections with multivariable calculus. Prerequisite: Mathematics 211. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- J. Armel, J. Goldfeather, S. Patterson, H. Wong

• MATH 236: Mathematical Structures

  Basic concepts and techniques used throughout mathematics. Topics include logic, mathematical induction and other methods of proof, problem solving, sets, cardinality, equivalence relations, functions and relations, and the axiom of choice. Other topics may include: algebraic structures, graph theory, and basic combinatorics. Prerequisite: Mathematics 232 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- D. Haunsperger, E. Egge, M. Krusemeyer

  Extended departmental description for MATH 236

  This course is intended to introduce students to certain features of the mathematical enterprise including: (1) basic structures in mathematics; (2) the nature of formal arguments that establish the validity of theorems; (3) strategies for problems-solving; and (4) analogies that exist among various mathematical concepts. Amidst all of this mathematical formality, you will discover some remarkable facts. In particular, you will learn that when Buzz Lightyear said "To infinity and beyond!", he was being mathematically precise.

  Math 236 is the last course in the math sequence that is required of all math majors, and is the first course that suggests what being a math major (as opposed to a math user) is all about. If you are undecided about majoring in math, taking this course before you make the decision might prove helpful.

• MATH 244: Geometries

  Euclidean geometry from an advanced perspective; projective, hyperbolic, inversive, and/or other geometries. In addition to foundations, various topics such as transformation and convexity will be treated. Recommended for prospective secondary school teachers. Prerequisite: Mathematics 236. 6; Mathematics and Natural Sciences; offered Fall 2009 -- S. Kennedy

• MATH 265: Probability

  Introduction to probability and its applications. Topics include discrete probability, random variables, independence, joint and conditional distributions, expectation, limit laws and properties of common probability distributions. Prerequisite: Mathematics 211. 6; Mathematics and Natural Sciences; offered Fall 2009 -- L. Chihara, K. St. Clair

• MATH 321: Real Analysis I

  A systematic study of concepts basic to calculus, such as topology of the real numbers, limits, differentiation, integration, convergence of sequences, and series of functions. Prerequisite: Mathematics 236 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Fall 2009 -- G. Nelson

• MATH 332: Advanced Linear Algebra

  Selected topics beyond the material of Mathematics 232. Topics may include the Cayley-Hamilton theorem, the spectral theorem, factorizations, canonical forms, determinant functions, estimation of eigenvalues, inner product spaces, dual vector spaces, unitary and Hermitian matrices, operators, infinite-dimensional spaces, and various applications. Prerequisite: Mathematics 236 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Fall 2009 -- J. Goldfeather

• MATH 400: Integrative Exercise

  A supervised small-group research project for senior mathematics majors. Required of all senior majors. Prerequisite: Mathematics 236 and successful completion of three courses from among: Mathematics courses numbered above 236, Computer Science 252, Computer Science 254. 3; S/NC; Does not fulfill a distribution requirement; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

Winter 2010

• MATH 111: Introduction to Calculus

  An introduction to the differential and integral calculus. Derivatives, antiderivatives, the definite integral, applications, and the fundamental theorem of calculus. Requires placement via the Calculus Placement Exam 1, see Mathematics web page. Not open to students who have received credit for Mathematics 101. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 121: Calculus II

  Integration techniques, improper integrals, the calculus of the logarithmic, exponential and inverse trigonometric functions, applications, Taylor polynomials and infinite series. Prerequisite: Mathematics 101, 111 or placement via Calculus Placement Exam #2. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 206: A Tour of Mathematics

  A series of eight lectures intended for students considering a Mathematics major. The emphasis will be on presenting various striking ideas, concepts and results in modern mathematics, rather than on developing extensive knowledge or techniques in any particular subject area. 1; S/CR/NC; Mathematics and Natural Sciences; offered Winter 2010 -- Staff

• MATH 211: Introduction to Multivariable Calculus

  Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green's theorem. Prerequisite: Mathematics 121 or 131 or placement via Calculus Placement Exam #3. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 215: Introduction to Statistics

  Introduction to statistics and data analysis. Practical aspects of statistics, including extensive use of statistical software, interpretation and communication of results, will be emphasized. Topics include: exploratory data analysis, correlation and linear regression, design of experiments, basic probability, the normal distribution, sampling distributions, estimation, hypothesis testing, and two-way tables. Not open to students who have already received credit for Math 115 or Math 275. Students who have received MS credit for Psychology 200/201 cannot receive MS credit for Math 215. Students who have taken Math 211 are encouraged to consider the more advanced Math 265-275 probability-statistics sequence. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 232: Linear Algebra

  Vector spaces, linear transformations, determinants, inner products and orthogonality, eigenvectors and eigenvalues; connections with multivariable calculus. Prerequisite: Mathematics 211. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- J. Armel, J. Goldfeather, S. Patterson, H. Wong

• MATH 236: Mathematical Structures

  Basic concepts and techniques used throughout mathematics. Topics include logic, mathematical induction and other methods of proof, problem solving, sets, cardinality, equivalence relations, functions and relations, and the axiom of choice. Other topics may include: algebraic structures, graph theory, and basic combinatorics. Prerequisite: Mathematics 232 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- D. Haunsperger, E. Egge, M. Krusemeyer

  Extended departmental description for MATH 236

  This course is intended to introduce students to certain features of the mathematical enterprise including: (1) basic structures in mathematics; (2) the nature of formal arguments that establish the validity of theorems; (3) strategies for problems-solving; and (4) analogies that exist among various mathematical concepts. Amidst all of this mathematical formality, you will discover some remarkable facts. In particular, you will learn that when Buzz Lightyear said "To infinity and beyond!", he was being mathematically precise.

  Math 236 is the last course in the math sequence that is required of all math majors, and is the first course that suggests what being a math major (as opposed to a math user) is all about. If you are undecided about majoring in math, taking this course before you make the decision might prove helpful.

• MATH 241: Ordinary Differential Equations

  An introduction to ordinary differential equations, including techniques for finding solutions, conditions under which solutions exist, and some qualitative analysis. Prerequisites: Mathematics 232 or permission of the instructor. 6; Mathematics and Natural Sciences; offered Winter 2010 -- M. Krusemeyer

• MATH 245: Applied Regression Analysis

  A second course in statistics covering simple linear regression, multiple regression and ANOVA, and logistic regression. Exploratory graphical methods, model building and model checking techniques will be emphasized with extensive use of statistical software to analyze real-life data. Prerequisites: Mathematics 215 (or equivalent) or 275. 6; Mathematics and Natural Sciences; offered Winter 2010, Spring 2010 -- L. Chihara, R. Dobrow

• MATH 275: Introduction to Statistical Inference

  Introduction to mathematical statistics. The mathematics underlying fundamental statistical concepts will be covered as well as applications of these ideas to real-life data. Topics include: confidence intervals, hypothesis testing, parameter estimation, maximum likelihood, goodness of fit tests and regressions. A statistical software package will be used to analyze data sets. Prerequisite: Mathematics 265. 6; Mathematics and Natural Sciences; offered Winter 2010 -- K. St. Clair

• MATH 342: Abstract Algebra I

  Introduction to algebraic structures, including groups, rings, and fields. Homomorphisms and quotient structures, polynomials, unique factorization. Other topics may include applications such as Burnside's counting theorem, symmetry groups, polynomial equations, or geometric constructions. Prerequisite: Mathematics 236 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Winter 2010 -- E. Egge

• MATH 354: Topology

  An introduction to the topology of surfaces. We will cover basic point-set, geometric and algebraic topology. Topics include continuity, connectedness and compactness; triangulations and classification of surfaces; topological invariants (Euler characteristic); homology. Prerequisite: Mathematics 236. 6; Mathematics and Natural Sciences; offered Winter 2010 -- H. Wong

  Extended departmental description for MATH 354

  The oldest (in more sense than one!) topology joke: A topologist is a person who doesn’t know the difference between a coffee cup and a donut.  In this course, we’ll look at the mathematics underpinning the intuition.  What is a topological space and what kinds of deformation are allowable?  For instance, we might want to keep the donut-ness of a donut and not allow it to be squished into one giant doughball.   We’ll build definitions from the ground up, ending with some modern algebraic techniques for distinguishing topological spaces apart. 

   

• MATH 395: Seminar in Mathematics: Functional Analysis

  Selected topics in Functional Analysis, the study of infinite dimensional vector spaces. Possible topics include topologies and convergence, Banach and Hilbert spaces, dual spaces, linear operators, compact self-adjoint operators, and distributions. Prerequisite: Math 321. 6; Mathematics and Natural Sciences; offered Winter 2010 -- J. Armel

  Extended departmental description for MATH 395

  When studying linear algebra in finite dimensions, there is really only one reasonable topology, and all linear transformations are continuous. An infinite dimensional vector space, however, may admit many different topologies, leading to different notions of convergence and continuity. As we investigate these concepts, we will move away from the idea of a function away from a correspondence between two sets. In real analysis, you may have already seen that two functions are identified if they agree almost everywhere, so their values at a particular point are of little importance. We will continue this as we first consider how functions behave as simply points in a vector space. Toward the end of the course, we will study a further generalize functions in a way that will allow us to take the derivative of anything you could ever dream of (discontinuous functions, measures, differential operators, and more).

• MATH 400: Integrative Exercise

  A supervised small-group research project for senior mathematics majors. Required of all senior majors. Prerequisite: Mathematics 236 and successful completion of three courses from among: Mathematics courses numbered above 236, Computer Science 252, Computer Science 254. 3; S/NC; Does not fulfill a distribution requirement; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

Spring 2010

• MATH 106: Introduction to Mathematics

  This course is designed to provide an understanding of fundamental concepts, and examples of applications, of mathematics. It attempts to provide insights into the nature of mathematics and its relation to other branches of knowledge, and helps students develop skill in mathematical reasoning. No prerequisites. 6; Mathematics and Natural Sciences; offered Spring 2010 -- M. Krusemeyer

• MATH 111: Introduction to Calculus

  An introduction to the differential and integral calculus. Derivatives, antiderivatives, the definite integral, applications, and the fundamental theorem of calculus. Requires placement via the Calculus Placement Exam 1, see Mathematics web page. Not open to students who have received credit for Mathematics 101. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 115: Statistics: Concepts and Applications

  Introduction to statistical concepts with emphasis on understanding and interpretation of statistical information, especially in the context of media reports and scholarly articles. Examples taken from a wide-range of areas such as public policy, health and medicine, and the social and natural sciences. Computationally less intensive than Math 215. Students will learn how to use statistical software. Topics include: Uncertainty and variability, statistical graphs, types of studies, correlation and linear regression, two-way tables, and inference. Not open to students who have already received credit for Math 211, Math 215 or Psychology 200/201. 6; Mathematics and Natural Sciences; offered Fall 2009, Spring 2010 -- L. Chihara, K. St. Clair

• MATH 121: Calculus II

  Integration techniques, improper integrals, the calculus of the logarithmic, exponential and inverse trigonometric functions, applications, Taylor polynomials and infinite series. Prerequisite: Mathematics 101, 111 or placement via Calculus Placement Exam #2. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 211: Introduction to Multivariable Calculus

  Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green's theorem. Prerequisite: Mathematics 121 or 131 or placement via Calculus Placement Exam #3. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 215: Introduction to Statistics

  Introduction to statistics and data analysis. Practical aspects of statistics, including extensive use of statistical software, interpretation and communication of results, will be emphasized. Topics include: exploratory data analysis, correlation and linear regression, design of experiments, basic probability, the normal distribution, sampling distributions, estimation, hypothesis testing, and two-way tables. Not open to students who have already received credit for Math 115 or Math 275. Students who have received MS credit for Psychology 200/201 cannot receive MS credit for Math 215. Students who have taken Math 211 are encouraged to consider the more advanced Math 265-275 probability-statistics sequence. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- Staff

• MATH 232: Linear Algebra

  Vector spaces, linear transformations, determinants, inner products and orthogonality, eigenvectors and eigenvalues; connections with multivariable calculus. Prerequisite: Mathematics 211. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- J. Armel, J. Goldfeather, S. Patterson, H. Wong

• MATH 236: Mathematical Structures

  Basic concepts and techniques used throughout mathematics. Topics include logic, mathematical induction and other methods of proof, problem solving, sets, cardinality, equivalence relations, functions and relations, and the axiom of choice. Other topics may include: algebraic structures, graph theory, and basic combinatorics. Prerequisite: Mathematics 232 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Fall 2009, Winter 2010, Spring 2010 -- D. Haunsperger, E. Egge, M. Krusemeyer

  Extended departmental description for MATH 236

  This course is intended to introduce students to certain features of the mathematical enterprise including: (1) basic structures in mathematics; (2) the nature of formal arguments that establish the validity of theorems; (3) strategies for problems-solving; and (4) analogies that exist among various mathematical concepts. Amidst all of this mathematical formality, you will discover some remarkable facts. In particular, you will learn that when Buzz Lightyear said "To infinity and beyond!", he was being mathematically precise.

  Math 236 is the last course in the math sequence that is required of all math majors, and is the first course that suggests what being a math major (as opposed to a math user) is all about. If you are undecided about majoring in math, taking this course before you make the decision might prove helpful.

• MATH 245: Applied Regression Analysis

  A second course in statistics covering simple linear regression, multiple regression and ANOVA, and logistic regression. Exploratory graphical methods, model building and model checking techniques will be emphasized with extensive use of statistical software to analyze real-life data. Prerequisites: Mathematics 215 (or equivalent) or 275. 6; Mathematics and Natural Sciences; offered Winter 2010, Spring 2010 -- L. Chihara, R. Dobrow

• MATH 295: Seminar in Set Theory

  Introduction to set-theoretic foundations of mathematics. The axiom system of Zermelo-Fraenkel, cardinal and ordinal numbers, and the Axiom of Choice. As time permits, additional topics may include construction of the real numbers, transfinite induction, or consistency/independence proofs. Prerequisite: Mathematics 236 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Spring 2010 -- G. Nelson

• MATH 315: Topics in Probability & Statistics: Introduction to Stochastic Processes

  Random walk, Markov chains, Poisson process, Brownian motion, with applications. Prerequisite: Mathematics 265. 6; Mathematics and Natural Sciences; offered Spring 2010 -- R. Dobrow

• MATH 341: Fourier Series and Boundary Value Problems

  Fourier series and their applications to boundary value problems in partial differential equations. Topics include separation of variables, orthogonal sets of functions, representations of functions in series of orthogonal functions, Fourier transforms, and uniqueness of solutions. Prerequisite: Mathematics 241. 6; Mathematics and Natural Sciences; offered Spring 2010 -- S. Patterson

  Extended departmental description for MATH 341

  Math 341 has two major themes.  One is the development of a method of solution of certain partial differential equations.  The other is a careful examination of some of the surprising consequences of that method.

  The partial differential equations considered are the heat equation, Laplace’s equation, the wave equation and Schrödinger’s equation.  Examination of the method (called Fourier’s method) leads to expressing a given function as an infinite series (a Fourier series) of sines and cosines.  

  Topics include Fourier series and integrals, inner-product spaces, orthogonality, self-adjoint operators, and Sturm-Liouville theory. Consideration of equations in cylindrical and spherical coordinate systems will give rise to special functions such as Legendre polynomials and Bessel functions.

• MATH 351: Functions of a Complex Variable

  Algebra and geometry of complex numbers, analytic functions, complex integration, series, residues, applications. Prerequisite: Mathematics 211. 6; Mathematics and Natural Sciences; offered Spring 2010 -- S. Patterson

  Extended departmental description for MATH 351

  What happens to calculus when you replace the real variable x by the complex variable z = x + iy and the real-valued function y = f(x) by the complex-valued function w = f(z)? For starters, the statement "f is differentiable" becomes more powerful while the idea of integration becomes more flexible---you can now integrate along various paths in the complex plane. This subject is inherently elegant – arguably among the most beautiful subjects in mathematics. But, perhaps surprisingly, this subject is also one of the most practical and can be applied to "real" mathematical and physical problems in which no complex number occurs.  This course has connections with many other upper-level math courses. Those who have taken other courses should enjoy discovering some of those connections. However, Math 211 is really the only prerequisite.

• MATH 352: Abstract Algebra II

  An intensive study of one or more of the types of algebraic systems studied in Mathematics 342. Prerequisite: Mathematics 342 or consent of the instructor. 6; Mathematics and Natural Sciences; offered Spring 2010 -- M. Krusemeyer

  Extended departmental description for MATH 352

  So you liked Abstract Algebra I? Then it might well get even better, because you now have the tools to study one or more selected areas in some depth. The choice of topics is not quite fixed yet - there won't be a textbook, and your specific requests or interests might influence what gets done - but the current plan is to spend about five weeks each on the representation theory of finite groups and on Galois theory. Representation theory, which involves describing the structure of groups by using their homomorphisms to matrix groups, is used in classifying and predicting elementary particles (which we won't do) and in chemistry, as well as in mathematics. Galois theory establishes unexpected deep connections between fields and groups - more precisely, between field extensions and groups of automorphisms - and is used widely elsewhere in mathematics, especially within algebra. Both topics have quite beautiful results, but you can't state the results before you really get into the material! However, if you're not sure whether to take the course, feel free to stop by and talk; I might be able to give you some of the flavor of the material by showing an example or two.

• MATH 400: Integrative Exercise

  A supervised small-group research project for senior mathematics majors. Required of all senior majors. Prerequisite: Mathematics 236 and successful completion of three courses from among: Mathematics courses numbered above 236, Computer Science 252, Computer Science 254. 3; S/NC; Does not fulfill a distribution requirement; offered Fall 2009, Winter 2010, Spring 2010 -- Staff