Stanford University Mathematics Camp - Program 1: Abstract Algebra & Number Theory (Session 2 Afternoon Class)

SUMaC welcomes an elite group of talented current 10th- and 11th-grade students from around the world for three weeks of intensive online study in advanced mathematics. Program I topics are introduced through five motivating problems such as limitations of straight-edge and compass constructions, classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of symmetry in structures. The mathematics central to solving these problems comes from the areas of abstract algebra and number theory. Abstract algebra originated in the early part of the 19th century through the study of polynomial equations. This branch of mathematics lies at the core of many areas of modern mathematical research. Number theory concerns properties of the integers, and has its origins in ancient mathematics. Number theory remains a very active field of study with interesting open problems and important applications in computer science.