MATH 383 - Topics in Mathematics

Credits: 3 in fall and winter, 4 in spring

Spring 2022, MATH 383A-01: The Mathematics of Information (3). Prerequisite: MATH 201 and MATH 222. The modern world runs on information. Huge numbers of bits (0s and 1s) are passing invisibly through the wires and air around you right now. These bits encode various types of data including text, pictures, audio/video signals etc. In 1948, a pioneering paper by Claude Shannon founded a new research area: information theory. Among other things, this investigates the process of converting streams of symbols from one form to another and various associated questions that are still the focus of much modern research. For example, what is the most efficient way to go about encoding a stream of data so that it can be transmitted as quickly as possible over some channel or stored using a minimal amount of space? How can one build in redundancy so that errors due to noise (scratches on a CD/DVD, electromagnetic interference etc.) can be detected and corrected? What should you do if privacy/secrecy is important? In this course, we will see how some of these questions can be formalized and addressed mathematically. Bush.

Spring 2022, MATH 383B-01: Configuration Spaces (3). Prerequisite: MATH 201 or MATH 221 or MATH 222. A configuration space is a mathematical object that encodes all the possible states of a system that has multiple moving parts. Examples of such systems include mechanical linkages as well as physical brain-teasers like the Rubik’s cube. The mathematical study of configuration spaces is applied widely in a number of practical fields, such as robotics. In this course we will study the configuration spaces associated to various types of mechanisms, puzzles, and gadgets. We will learn how to analyze the complexity of mechanical linkages and the difficulty of logic-based puzzles such as Sudoku. Students will have the opportunity to design and build their own examples. Abrams.