Franklin & Marshall College

Mathematics

A list of regularly offered courses follows. The indication of when a course will be offered is based on the best projection of the department and can be subject to change.

Please note the key for the following abbreviations: (A) Arts; (H) Humanities; (S) Social Sciences; (N) Natural Sciences with Laboratory; (LS) Language Studies requirement; (NSP) Natural Science in Perspective; (NW) Non-Western Cultures requirement.

105. Preparation for College Mathematics. Every Fall

Introductory logic and algebra, elementary functions: polynomial, rational, trigonometric, exponential, logarithmic. Prerequisite: Permission of the department. Not for credit toward the mathematics major or minor. Buehrle

109. Calculus I. Every Semester

Introduction to the basic concepts of calculus and their applications. Functions, derivatives and limits; exponential, logarithmic and trigonometric functions; the definite integral and the Fundamental Theorem of Calculus. Prerequisite: Twelfth-grade mathematics or MAT 105. Staff

110. Calculus II. Every Semester

Techniques of integration, applications of integration, separable first-order differential equations, convergence tests for infinite series, Taylor polynomials and Taylor series. Prerequisite: MAT 109 or permission of the department. Staff

111. Calculus III. Every Semester

Vectors and parametric equations; functions of two variables; partial and directional derivatives; multiple integrals; line integrals. Prerequisite: MAT 110 or permission of the department. Staff

116. Introductory Statistics with Applications. Every Spring

Probability, random variables, data analysis, estimation techniques, hypothesis tests, correlation and regression, analysis of variance, contingency tables, exploratory techniques. Not for credit after MAT 216. Prerequisite: MAT 109. Not for credit toward the mathematics major or minor. Staff

130. Mathematics of Art. 2013 – 2015

This course uses mathematical perspective to analyze works of visual art (perspective drawing and perspective geometry). The first topics of this course will use one-, two- and three-point perspective 130 both to create realistic pictures and to study optical illusions. From there we will explore other dimensions: what does a four-dimensional cube look like? What does a 1.638-dimensional object look like? The course will finish with fractals and chaos theory, which we will use to draw textures of natural objects such as ferns and clouds. Crannell

211. Introduction to Higher Mathematics. Every Semester

A course designed as a transition from calculus to advanced mathematics courses. Emphasis on developing conjectures, experimentation, writing proofs and generalization. Topics will be chosen from number theory, combinatorics and graph theory, polynomials, sequences and series and dynamical systems, among others. Prerequisite: MAT 111. Staff

216. Probability and Statistics I. Every Semester

Introduction to single variable probability and statistics. Random variables. Binomial, geometric, Poisson, exponential and gamma distributions, among others. Counting techniques. Estimation and hypothesis tests on a single parameter. Prerequisite: MAT 110. Draguljić

229. Linear Algebra and Differential Equations. Every Semester

Systems of linear equations and matrices, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, nth order linear differential equations, systems of first order differential equations. Prerequisite: MAT 111. Staff

237. Discrete Mathematics. Every Fall

Basic set theory, basic proof techniques, combinatorics (the theory of counting), and graph theory with related algorithms. Prerequisite: MAT 109. Same as CPS 237. 270 – 279. Selected Topics. Intermediate level courses.

291. Directed Reading.

Reading directed by the Mathematics staff. Permission of chairperson.

316. Probability and Statistics II. Feldman Every Spring

Continuation of MAT216. Multivariate distributions. Estimation and hypothesis tests for multiple parameters. Regression and correlation. Analysis of variance. Prerequisites: MAT 111, MAT 216. Staff

323. Stochastic Processes. Spring 2013

Properties of stochastic processes, Markov chains, Poisson processes, Markov processes, queueing theory. Applications of stochastic modeling to other disciplines. Prerequisites: MAT 111, MAT 216. Staff

325. Number Theory. Fall 2012

Properties of the natural numbers and integers: divisibility, primes, number theoretic functions, Diophantine equations, congruences, quadratic reciprocity, additive number theory, unsolved problems. Prerequisite: MAT 211. Ressler

329. Fourier Series. Spring 2014

Fourier series, orthogonal series, boundary value problems, applications. Prerequisite: MAT 229. Staff

330. Abstract Algebra. Every Spring

Algebraic systems and their morphisms including sets, functions, groups, homomorphisms, factor groups, rings and fields. Prerequisite: MAT 211. Staff

331. Introduction to Analysis. Every Fall

An introduction to the ideas and proof techniques specific to mathematical analysis. Real numbers, sequences, limits, derivatives, integrals, infinite series, cardinality; other topics as chosen by instructor. Prerequisite: MAT 211. Crannell, Gethner

337. Mathematics for Optimization. Spring 2014

Discrete, deterministic models of interest to the social sciences. Linear programming, duality, simplex method, sensitivity analysis, convex sets. Selections from: assignment, transportation, network flow, nonlinear programming problems. Prerequisite: MAT 229. Staff

338. Computational Mathematics. Fall 2013

Numerical analysis as implemented on computers. Polynomial and rational approximations, numerical differentiation and integration, systems of linear equations, matrix inversion, eigenvalues, first and second order differential equations. Prerequisites: CPS 111, MAT 229. Same as CPS 338. Staff

339. Mathematical Models. Fall 2012

An introduction to the art of creating and analyzing deterministic mathematical models. Models of physical, biological and social phenomena. Topics vary with instructor; examples are predator-prey interactions, spread of epidemics, arms races and changes in global temperature. Mathematical techniques include phase-plane analysis of systems of differential equations and function iteration. Prerequisite: MAT 229. A. Levine

370 – 379. Selected Topics.

Advanced Algebra, Advanced Multivariable Calculus, Measure Theory, Algebraic Topology, History and Development of Calculus.

375. Topics in Algebra. Spring 2014

Courses of an algebraic nature such as Ring Theory, Advanced Linear Algebra and Algebraic Number Theory, that can be taken in place of, or in addition to, MAT 330 to satisfy the major requirements. May be repeated with permission of department. Prerequisite: MAT 211.

390. Independent Study.

Independent study directed by the Mathematics staff. Permission of chairperson.

391. Directed Reading.

Reading directed by the Mathematics staff. Permission of chairperson.

442. Complex Analysis. Spring 2013

Functions of one complex variable: analytic functions; mappings; integrals; power series; residues; conformal mappings. Prerequisite: MAT 331. Staff

445. Geometry. Fall 2014

Selections from: advanced synthetic geometry; groups of transformations; affine geometry; metric geometry; projective geometry; inversive geometry. Prerequisite: MAT 330. Staff

446. Topology. Fall 2013

An introduction to topological spaces and continuous functions. Prerequisite: MAT 330. Corequisite: MAT 331.

470 – 479. Selected Topics.

Study of advanced specialized areas of mathematics.

490. Independent Study.

Independent study directed by the Mathematics staff. Permission of chairperson.

491. Directed Reading.

Reading directed by the Mathematics staff. Permission of chairperson. Topics Courses Expected To Be Offered In 2012–2013 Advanced Linear Algebra.