Math 251, Topics in Applied Mathematics

251 is a course whose topic may change from year to year. Students may elect 251 more than once.

251A Fall 2005: Cryptology and Coding Theory: The Mathematics of Secure and Reliable Communication

Cryptography, the science of developing "secret codes" or  ciphers for secure and confidential communication, is essential to  both e-commerce and military operations. Cryptology includes the study  of both cryptography and cryptanalysis, the breaking of ciphers. Coding theory consists of mathematical techniques for detecting and correcting  errors that occur during data transmission. These topics are critical  to information exchange today. Through this exploration into the technical,  social, and historical aspects of cryptology and coding theory, students  will learn and extensively use basic concepts from number theory, finite  field and ring theory, matrix algebra, and the software package MAGMA.  Highlighted topics include the RSA cryptosystem, digital signatures,  DES, linear and cyclic codes, Reed-Solomon codes, and the McEliece  cryptosystem.
Prerequisite: Math 116 or the equivalent; or CS 230 and permission of instructors
Distribution: Mathematical Modeling
This course will be taught at Wellesley College, by Prof. Gordon Pritchett (Babson) and Prof. Sarah Spence (Olin)

251B Spring 2006: Operations Research 

This course studies the algebraic and geometric foundations of optimization  and its applications to decision making in private and public sector  management. We will study linear and integer programming, i.e., maximizing  and minimizing linear functions whose variables must satisfy linear  equations or inequalities, and where we may also require that the variables  be integers. Applications will be selected from mathematical models  in such areas as production, inventory, scheduling, investment, harvesting, transportation, and distribution. Small-scale problems will be solved by hand, and larger-scale problems by computer. The theoretical level  will be similar to 206, but students will do fewer proofs and more  modeling. Math 251 counts toward the mathematics major/minor as an  elective. Majors can fulfill the major presentation requirement in  this course in 2005-06.
Prerequisite: 206 or permission of the instructor
Distribution: Mathematical Modeling

Previous topics have included Advanced Statistics, Operations Research, Statistical Quality Control, Partial Differential Equations, Mathematical Modeling, and Introduction to Numerical Analysis.