NEWER MATH
12:090:291:01:28938
Stephen Greenfield, Department of Mathematics
Counts in Interdisciplinary Math/Sciences
MTh 2 SEC 203 (BC)

Prerequisite: All students wishing to enroll must have a good knowledge of precalculus. Further knowledge of mathematics, computer science, and other sciences will help and is recommended.

The title is a joke: "New Math" was the name of a style of instruction a generation ago which would quickly make math deficiencies vanish. It didn't and they didn't. This seminar will cover concepts and ideas in mathematics that have been invented (or discovered!) in the last 50 years. Since mathematics can be relentlessly cumulative, and in recent years estimates are that 250,000 to 300,000 new "theorems" have been published annually (!), this may seem daunting, but we will try! Generally, the seminar will include mathematics that is essentially NEW: substantially invented/discovered within the last 50 years, mathematics that can be explained with few prerequisites (but see note above, please), mathematics that is important in areas collateral to mathematics and perhaps even to much of society, and mathematics that can be discussed effectively. Possible topics include:

• Public key cryptography (how two people far away from each other can communicate securely without prearrangement)
• The difficulty of computation (what is hard about arithmetic? - some methods of measuring the difficulty of mathematical problems)
• Probability (how to gamble: foundational for the topics following).
• Networks and reliability (really, percolation and change of state from, say, solid to liquid, and how the same mathematics is used to analyze complex systems).
• Randomness and order (what is random and why all sufficiently large systems must have at least small scale order)
• Random and not-so-random networks (including the theory and practice of the Internet's structure, scientific collaboration, chemical interactions in cells, etc.)
• Coding and compression (how information is stored and transmitted efficiently).

Most of the pedagogy will be traditional in mathematics (instructor standing, students sleeping). I'll try to actively involve students in working out examples and extensions of the material. Computers will be used for some of this and appropriate instruction will be given.

Professor STEPHEN GREENFIELD is a member of the Rutgers Department of Mathematics. Like everyone else in the business, he mostly teaches calculus. However, he recently created and several times taught a course on cryptography and public policy. He also has jointly instructed a course with a physicist. He believes that learning and teaching mathematics is interesting. See http://www.math.rutgers.edu/~greenfie/ for further information, including pictures.

Maintained by greenfie@math.rutgers.edu and last modified 12/29/2003.