Franklin & Marshall College Franklin & Marshall College

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Courses Offered
Mathematics

A list of regularly offered courses follows. 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.

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. Staff

109. Calculus I.

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.

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.

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. 

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. Offered every Spring. Staff

211. Introduction to Higher Mathematics.

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.

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.

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.

Basic set theory, basic proof techniques, combinatorics (the theory of counting), and graph theory with related algorithms. Prerequisite: MAT 109. Offered every Fall. Same as CPS 237. Hu

270279. Selected Topics.

Intermediate level courses.

291. Directed Reading.

Reading directed by the Mathematics staff. Permission of chairperson.

316. Probability and Statistics II.

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.

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.

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.

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

330. Abstract Algebra.

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

331. Introduction to Analysis.

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. Gethner

337. Mathematics for Optimization.

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.

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. C. Weaver

339. Mathematical Models.

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. C. Weaver

370379. Selected Topics.

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

375. Topics in Algebra.

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.

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

445. Geometry.

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

446. Topology.

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

470479. 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 faculyy. Permission of chairperson.

Topics courses EXPECTED to be offered in 2014 – 2015 

Irresistable Integrals.

Projective Geometry Applied to Perspective Art.