Stat 001. Statistical Thinking.
description: Statistics provides methods for collecting and analyzing data and generalizing from their results. Statistics is used in a wide variety of fields, and this course provides an understanding of the role of statistics in these fields and in everyday life. It is intended for students who want an appreciation of statistics, including the ability to critically interpret and evaluate statistical claims but who do not imagine they will ever need to carry out statistical analyses themselves. (Those who may need to carry out statistical analyses should take STAT 011.) This course cannot be counted toward a major in mathematics, is not a prerequisite for any other course, and cannot be taken for credit after or simultaneously with any other statistics course, including AP Statistics and ECON 031.
prerequisite: Four years of traditional high school mathematics (precalculus).
1 credit.
Each semester.
Fall 2006. Everson. Spring 2007. Everson.

Math 003. Introduction to Mathematical Thinking.
description: Students will explore the world of mathematical ideas by sampling logic, number theory, geometry, infinity, topology, probability, and fractals, while we emphasize the thinking and problem-solving skills these ideas stimulate. Class meetings will involve presentation of new material; group work on problems and puzzles; and lively, passionate discussions about mathematics. This course is intended for students with little background in mathematics or those who may have struggled with math in the past. Students planning to go on to calculus should consult with the instructor. This course does not count toward a major in mathematics.
Writing course.
1 credit.
Spring semester.
Spring 2007. Bergstrand.

Math 007. Elementary Topics In Mathematics In Applied Contexts.
description: This course is offered occaisionally and is interdisiplinary in nature. It provides an intoduction to some area of mathematics in the context of its use in another discipline. A recent version of this course was taught in the Linguistics Program. This course does not count towards a major in mathematics.
prerequisite: Four years of traditional high school mathematics (precalculus).
1 credit.
Not offered every year.
Not offered 2006-2007.

Stat 011. Statistical Methods.
(Cross-listed as SOAN 010E)
description: STAT 011 prepares students to carry out basic statistical analyses with the aid of computer software. Topics include basic summary statistics and graphics, design of surveys and experiments, one and two-sample t-tests and tests of proportions, chi-square tests, and an introduction to linear regression and analysis of variance. The course is intended for students who want a practical introduction to statistical methods and who intend to do, or think they may eventually do, statistical analysis, especially in the biological and social sciences. Students who receive credit on entrance for the Statistics AP Exam should not take this course; they have placed out of it and will lose their AP credit if they take it. Students who have earned credit for the former STAT 002 or STAT 002C will not receive credit for STAT 011. Note that STAT 011 overlaps considerably with ECON 031; both courses cover similar topics, although ECON 031 focuses more on economic applications while STAT 011 draws examples from a variety of disciplines.
prerequisite: Four years of traditional high school mathematics (precalculus).
1 credit.
Each semester.
Fall 2006. Wang. Spring 2007. Everson.

Math 015. Elementary Single-Variable Calculus.
description: A first-semester calculus course with emphasis on an intuitive understanding of the concepts, methods, and applications. Graphical and symbolic methods will be used. The course will mostly cover differential calculus, with an introduction to integral calculus at the end. Applications to biological science and social science will receive special attention.
prerequisite: Four years of traditional high school mathematics (precalculus) and placement into this course through Swarthmore’s Calculus Readiness Examination or Calculus Placement Examination.
1 credit.
Fall semester.
Fall 2006. Grinstead.

Math 023. Brief Survey of Calculus Through Second Year.
description: This survey covers key topics in single- and several-variable calculus for students who do not plan to take any more calculus. In single-variable calculus, topics may include antiderivatives, the fundamental theorem, probability, geometric series, and modeling with differential equations. Topics in several variables may include contour plots, partial derivatives, and Lagrange multipliers. Emphasis on applications in biological and social sciences. Cannot be substituted for either MATH 025 or 033 as courses required for the major.
prerequisite: MATH 015 or placement by examination.
1 credit.
Each semester.
Fall 2006. Maurer. Spring 2007. Klotz.

Math 025. Further Topics in Single-Variable Calculus.
description: The continuation of MATH 015 for students who wish to major in mathematics, physics, chemistry, or engineering, or who want the option of continuing to several-variable calculus. The course covers the fundamental theorem, integration, geometric series, Taylor polynomials and series, and an introduction to differential equations.
prerequisite: MATH 015 or placement by examination.
1 credit.
Each semester.
Fall 2006. Talvacchia. Spring 2007. Bergstrand.

Math 025S. Single-Variable Calculus Seminar.
description: MATH 025S covers the same material as the lecture-based MATH 025 but uses a seminar format (maximum 12 students) with additional meetings and lots of hands-on activities (e.g., writing, oral presentations, group work, and computer work). Intended for students who think they could benefit from the collaborative seminar format and who wish to be challenged to excel in calculus so that they gain more confidence to continue with mathematics and science.
prerequisite: Placement by examination.
First-year seminar.
1 credit.
Fall semester.
Fall 2006. Bergstrand.

Math 026. Advanced Topics in Single-Variable Calculus.
description: This course is for students who place out of the first half of MATH 025. The material goes into more depth on sequences, series, and differential equations than does MATH 025 and includes power series and convergence tests. This course, or MATH 025, is required of all students majoring in mathematics, physics, chemistry, or engineering.
prerequisite: Placement by examination.
1 credit.
Fall semester.
Fall 2006. Hunter.

Math 027. Linear Algebra.
description:This course covers systems of linear equations, matrices, vector spaces, linear transformations, determinants and eigenvalues. Many applications to other disciplines are presented. Students may take only one of MATH 027, MATH 028, and MATH 028S for credit.
prerequisite: A grade of B or better in some math course numbered 025 or higher or placement by examination.
1 credit.
Each semester.
Fall 2006. Klotz, Shapiro. Spring 2007. Rusin.

Math 028. Linear Algebra Honors Course.
description: More theoretical, abstract, and rigorous than MATH 027. The subject matter will be equally as valuable in applied situations, but applications will be emphasized less and students will do many proofs.MATH 028 is intended for students with exceptionally strong mathematical skills, especially if they are thinking of a mathematics major. Students may take only one of MATH 027, MATH 028, and MATH 028S for credit.
prerequisite: A grade of B or better in some math course numbered 025 or higher or placement by examination.
1 credit.
Each semester.
Fall 2006. Grood, Shimamoto. Spring 2007. Maurer.

Math 028S. Linear Algebra Honors Seminar.
description: MATH 028S covers the same material as the lecture-based MATH 028 but uses a seminar format (maximum 12 students) with additional meetings. Hands-on student participation takes the place of most lectures. Students may take only one of MATH 027, MATH 028, and MATH 028S for credit.
prerequisite: Placement by examination.
1 credit.
Fall semester.
Fall 2006. Johnson.

Math 029. Discrete Mathematics.
description: An introduction to noncontinuous mathematics. The key theme is how induction, iteration, and recursion can help one discover, compute, and prove solutions to various problems_often problems of interest in computer science, social science, or management. Topics include algorithms, graph theory, counting, difference equations, and finite probability, with special emphasis on how to write mathematics.
prerequisite: Placement by examination. Familiarity with some computer language is helpful but not necessary.
Writing course.
1 credit.
Each semester.
Fall 2006. Grood. Spring 2007. Shimamoto.

Stat 031. Data Analysis and Visualization.
description: This course will study methods for exploring and modeling relationships in data. We introduce modern techniques for visualizing trends and formulating hypotheses. We will also discuss methods for modeling structure and patterns in data, particularly using multiple regression and related methods. The format of the course emphasizes writing assignments and interactive problem solving using real datasets.
prerequisite: Credit for AP Statistics, STAT 011, STAT 061, or ECON 031; or STAT 001 and permission of the instructor.
Writing course.
1 credit.
Spring semester.
Spring 2007. Wang.

Math 033. Basic Several-Variable Calculus.
description: This course considers differentiation and integration of functions of several variables with special emphasis on two and three dimensions. Topics include partial differentiation, extreme value problems, Lagrange multipliers, multiple integrals, line and surface integrals, Green's, Stokes', and Gauss' theorems. The department strongly recommends that students take MATH 034 instead, which provides a richer understanding of this material by requiring linear algebra (MATH 027 or 028) as a prerequisite. Students may only take one of MATH 033, MATH 034, and MATH 035 for credit.
prerequisite: MATH 025, 025S, or 026 or placement by examination.
1 credit.
Each semester.
Fall 2006. Grood. Spring 2007. Grood.

Math 034. Several-Variable Calculus.
description: The same topics as MATH 033 are covered except in more depth using the concepts of linear algebra. The department strongly recommends that students take linear algebra first so that they are eligible for this course. Students may only take one of MATH 033, MATH 034, and MATH 035 for credit.
prerequisite: MATH 025, 025S, or 026; and MATH 027, 028, or 028S.
1 credit.
Each semester.
Fall 2006. Shapiro. Spring 2007. Shapiro.

Math 035. Several-Variable Calculus Honors Course.
description: This version of MATH 034 will be more theoretical, abstract, and rigorous than its standard counterpart. The subject matter will be equally as valuable in applied situations, but applications will be emphasized less and students will do many proofs. It is intended for students with exceptionally strong mathematical skills and primarily for those who have completed MATH 028 or 028S successfully. Students may take only one of MATH 033, MATH 034, and MATH 035 for credit.
prerequisite: A grade of C or better in MATH 028 or 028S or permission of instructor.
1 credit.
Spring semester.
Spring 2007. Grinstead, Talvacchia.

Stat 041. Topics in Statistics.
description: The choice of topics will depend somewhat on the interest and mathematical background of the students, but may include a study of issues in multivariate analysis and statistical inference (Bayesian statistics in particular).
prerequisite: One course in Statistics.
1 credit.
Not offered every year.
Not offered 2006-2007.

Math 043. Basic Differential Equations.
description: This course emphasizes the standard techniques used to solve differential equations.  It will cover the basic theory of the field with an eye towards practical applications. Standard topics include first-order equations, linear differential equations, series solutions, first-order systems of equations, Laplace transforms, approximation methods, and some partial differential equations. Compare with MATH044. Students may not take both MATH 043 and 044 for credit. The department prefers majors to take MATH 044.
prerequisite: Several-variable calculus or permission of the instructor.
1 credit.
Spring semester.
Spring 2007. Shapiro.

Math 044. Differential Equations.
description: An introduction to differential equations that has a more theoretical flavor than MATH 043 and is intended for the student who enjoys delving into the mathematics behind the techniques. Problems are considered from analytical, qualitative, and numerical points of view, with an emphasis on the formulation of differential equations and the interpretations of their solutions.  This course does not place as strong an emphasis on solution techniques as MATH 043 and thus may not be as useful to the more applied student. Students may not take both MATH 043 and 044 for credit. The department prefers majors to take MATH 044.
prerequisite: Linear algebra and several-variable calculus or permission of the instructor.
1 credit.
Spring semester.
Spring 2007. Stromquist.

Math 046. Theory of Computation.
(Cross-listed as CPSC 046)
description: See computer science for description.

Math 053. Topics in Analysis.
description: Course content varies from year to year depending on student and faculty interest. Recent topics have included financial mathematics, dynamical systems,and Fourier analysis.
prerequisite: Linear algebra and several-variable calculus. In 2007 STAT 067 is also required, or permission of the instructor.
1 credit.
Spring semester alternate years.
Spring 2007. Stromquist.

Math 054. Partial Differential Equations.
description: The first part of the course consists of an introduction to linear partial differential equations of elliptic, parabolic, and hyperbolic type via the Laplace equation, the heat equation, and the wave equation. The second part of the course is an introduction to the calculus of variations. Additional topics depend on the interests of the students and instructor.
prerequisite: Linear algebra, several-variable calculus, and either MATH 043, MATH 044, PHYS 050, or permission of the instructor.
1 credit.
Spring semester alternate years.
Not offered 2006-2007.

Math 055. Topics in Geometry.
description: Course content varies from year to year. See the current catalog entry. Also see Math 075.
prerequisite: Linear algebra and several-variable calculus or permission of the instructor.
1 credit.
Fall semester alternate years.
Fall 2006. Talvacchia.

Math 056. Modeling.
description: An introduction to the methods and attitudes of mathematical modeling. Because modeling in physical science and engineering is already taught in courses in those disciplines, applications in this course will be primarily to social and biological sciences. Various standard methods used in modeling will be introduced: differential equations, Markov chains, game theory, graph theory, and computer simulation. The emphasis, however, will be on how to apply these subjects to specific modeling problems, not on their systematic theory. The format of the course will include projects as well as lectures and problem sets.
prerequisite: Linear algebra and several-variable calculus or permission of the instructor.
1 credit.
Alternate years.
Not offered 2006-2007.

Math 057. Topics in Algebra.
description: Course content varies from year to year depending on student and faculty interest. Recent offerings have included coding theory, groups and representations, and finite reflection groups. See also MATH 077.
prerequisite: Linear algebra.
1 credit.
Spring semester alternate years.
Not offered 2006-2007.

Math 058. Number Theory.
description: The theory of primes, divisibility concepts, and multiplicative number theory will be developed with students doing many proofs.
prerequisite: Linear algebra and several-variable calculus or permission of the instructor.
1 credit.
Alternate years.
Fall 2006. Stromquist.

Math 059. Topics in Discrete Mathematics.
description: Topics vary from year to year. Past topics have included combinatorial matrix theory, linear programming, game theory, graph theory combinatorial algorithms, number theoretic algorithms, and complexity theory. See also MATH 079.
prerequisite: MATH 029 and at least one higher numbered mathematics course.
1 credit.
Fall semester alternate years.
Not offered 2006-2007.

Stat 061. Probability and Mathematical Statistics I.
description: This course introduces the mathematical theory of probability, including density functions and distribution functions, joint and marginal distributions, conditional probability, and expected value and variance. It then develops the theory of statistics, including parameter estimation and hypothesis testing. The emphasis is on proving results in mathematical statistics rather than on applying statistical methods. Students needing to learn applied statistics and data analysis should consider STAT 011 or 031 in addition or instead of this course.
prerequisite: One of MATH 023, 033, or 034, or permission of the instructor.
1 credit.
Fall semester.
Fall 2006. Everson.

Math 063. Introduction to Real Analysis.
description: This course concentrates on the careful study of the principles underlying the calculus of real valued functions of real variables. Topics will include continuity, compactness, connectedness, uniform convergence, differentiation, and integration.
prerequisite: Linear algebra and several-variable calculus or permission of the instructor.
Writing course.
1 credit.
Usually offered fall semester only.
Fall 2006. Johnson. Spring 2007. Grood.

Math 067. Introduction to Modern Algebra.
description: This course is an introduction to abstract algebra and will survey basic algebraic systems: groups, rings, and fields. Although these concepts will be illustrated by concrete examples, the emphasis will be on abstract theorems, proofs, and rigorous mathematical reasoning.
prerequisite: Linear algebra or permission of the instructor.
Writing course.
1 credit.
Fall semester.
Fall 2006. Shimamoto.

Math 069. Combinatorics.
description:This course continues the study of noncontinuous mathematics begun in MATH 029. The topics covered include three broad areas: counting theory, graph theory, and design theory. The first area includes a study of generating functions and Polya counting. The second area is concerned with relations between certain graphical invariants. Topics such as extremal graph theory and Ramsey theory may be introduced. The third area introduces combinatorial structures such as matroids, codes, and Latin squares.
prerequisite: MATH 029 and at least one other course in mathematics
1 credit.
Alternate years.
Fall 2006. Bergstrand.

Math 073. Advanced Topics in Analysis.
description: An advanced version of MATH 053, sometimes given instead, and requiring the core course in analysis (MATH 063).
prerequisite: Linear algebra and MATH 063.
1 credit.
Alternate years.
Not offered 2006-2007.

Math 075. Advanced Topics in Geometry.
description: An advanced version of MATH 055, sometimes given instead, and typically requiring MATH 063, 067, or both.
prerequisite: See the instructor.
1 credit.
Fall semester alternate years.
Not offered 2006-2007.

Math 077. Advanced Topics in Algebra.
description: An advanced version of MATH 057, sometimes given instead, and requiring the core course in algebra (MATH 067).
prerequisite: Linear algebra and MATH 067.
1 credit.
Spring semester alternate years.
Not offered 2006-2007.

Math 079. Topics in Discrete Mathematics.
description: An advanced version of MATH 059, sometimes offered instead of MATH 059.
prerequisite: MATH 029 and MATH 069.
1 credit.
Fall semester alternate years.
Not offered 2006-2007.

Math/Stat 093. Directed Reading.

Math/Stat 096. Thesis.

Math 097. Senior Conference.
description: This course is required of all senior mathematics majors in the course program. It provides an opportunity to delve more deeply into a particular topic agreed on by the student and the instructor. This focus is accomplished through a written paper and an oral presentation.
0.5 credit.
Fall semester.
Fall 2006. Stromquist.

Math 101. Real Analysis II Seminar.
description: This seminar is a continuation of Introduction to Real Analysis (Math 063). Topics may include the inverse and implicit function theorems, differential forms, calculus on manifolds, and Lebesgue integration.
prerequisite: MATH 063.
1 credit.
Spring semester.
Spring 2007. Maurer.

Math 102. Modern Algebra II Seminar.
description:This seminar is a continuation of Introduction to Modern Algebra (MATH 067). Topics covered usually include field theory, Galois theory (including the insolvability of the quintic), the structure theorem for modules over principal ideal domains, and a theoretical development of linear algebra. Other topics may be studied depending on the interests of students and instructor.
prerequisite: MATH 067.
1 credit.
Each semester.
Fall 2006. Shapiro. Spring 2007. Shimamoto.

Math 103. Complex Analysis Seminar.
description: A brief study of the geometry of complex numbers is followed by a detailed treatment of the Cauchy theory of analytic functions of a complex variable: integration and Cauchy's Theorem, power series, residue calculus, conformal mapping, and harmonic functions. Various applications are given and other topics, such as elliptic functions, analytic continuation and the theory of Weierstrass, may be discussed.
prerequisite: MATH 063.
1 credit.
Alternate years.
Not offered 2006-2007.

Math 104. Topology Seminar.
description: An introduction to point-set, combinatorial, and algebraic topology: topological spaces, classification of surfaces, the fundamental group, covering spaces, simplicial complexes and homology (including related algebra).
.prerequisite: MATH 063 and O67.
2 credits.
Alternate years.
Not offered 2006-2007.

Math 105. Probability Seminar.
description: An introduction to measure-theoretic probability theory. Topics may include branching processes, renewal theory, random walks, stochastic processes, laws of large numbers, characteristic functions, the Central Limit Theorem, Markov chains, the Poisson process, and percolation.
prerequisite:STAT 061.
1 credit.
Alternate years.
Spring 2007. Grinstead.

Math 106. Advanced Topics in Geometry Seminar.
description: The course content varies from year to year among differential geometry, differential topology, and algebraic geometry.
prerequisite: MATH 045 and 063, or permission of the instructor.
1 credit.
Alternate years.
Spring 2007. Talvacchia.

Stat 111. Mathematical Statistics II Seminar.
description:This seminar is a continuation of STAT 061. It deals mainly with statistical models for the relationships between variables. The general linear model, which includes regression, variance, and covariance analysis, is examined in detail. Topics may also include nonparametric statistics, sampling theory, and Bayesian statistical inference.
prerequisite: Linear algebra and a grade of C+ or better in Stat 061.
1 credit.
Alternate years.
Not offered 2006-2007.