Non-Calculus Alternatives for 2007-2008:

The course will focus on the mathematical aspects of public-key cryptography, the modern science of creating secret ciphers (codes), which is largely based on number theory. Additional topics will be taken from cryptanalysis (the science of breaking secret ciphers) and from contributions that mathematics can make to data security and privacy.

This course investigates the idea of higher dimensions and some of the ways of understanding them. The classic novel, Flatland, will serve as the starting point, and through discussions, writing, projects and interactive computer graphics, we will extrapolate ideas from two and three dimensions to their analogues in four dimensions and higher.

An introduction to the beauty and use of numbers. Topics will be chosen from: divisibility tests, prime numbers, perfect numbers, unbreakable computer codes, Fermat's theorem, the golden section, calendars, magic squares, quadratic reciprocity, and others.

Ancient Greek mathematicians invented the notion of abstraction (in mathematics and other fields), absolute precision, and proof. The approach to mathematics that we take today can be traced back to these Greek mathematicians. After examining some pre-Greek mathematical traditions, we study Greek mathematics, beginning with Thales and Pythagoras. Topics include the intellectual crisis caused by the discovery that not all magnitudes are commensurable; Plato and his academy; Euclid and his Elements; the three special construction problems (trisecting an angle, squaring a circle, doubling a cube); and the greatest of the Greek mathematicians, Archimedes.

Completely self-contained introduction to the mathematical theory of conflict, including parlor games, auctions, games from the Bible and games commenting on the existence of superior beings, game-theoretic analyses in literature, philosophical questions and paradoxes arising from game theory, and game theoretic models of international conflict.

Directed graphs and Gauss-Jordan elimination. Matrices and linear programming with applications of linear algebra to the social sciences.

Differential and integral calculus with applications in the social sciences. Not open to students who have passed a college calculus course; students who wish to continue the calculus should enroll in Math 112.

A mathematical treatment (not involving calculus or statistics) of political power, social choice, and international conflict. No previous study of political science is necessary, but PS 111 or 112 would be relevant.