Stanford Pre-Collegiate Summer Institutes - The Mathematics of Symmetry

Symmetry plays an important role throughout mathematics and the sciences, and this course will lead students on an exploration of symmetry as it takes on different meanings in a range of contexts. The familiar concept of geometric symmetry can be used to understand properties of geometric objects, and it plays an important role in art and architecture as well as science and engineering. Symmetry can also be explored mathematically in the context of number systems, algebraic structures, and mathematical puzzles. In addition to an investigation of geometric symmetry, this course will explore a class of popular mechanical puzzles, as well as algebraic properties of numbers. While studying symmetry, students will learn how artists like MC Escher created his intriguing designs and planar tessellations. Students will see how symmetry operations have properties shared by numeric operations and also by puzzles such as Rubik's Cube. The course will introduce students to the abstract mathematical objects known as a group, which is used to capture the essence of these various kinds of symmetry. Group Theory is a branch of mathematics that grew out of geometry, algebra, and number theory and has a wide range of applications other branches of mathematics, as well as many scientific and engineering fields. This course will develop the basic terminology and tools of group theory and apply them to symmetry, puzzles, number systems, and other mathematical problems. The course will help students develop problem solving skills through challenging and engaging problems on a range of topics. Application process includes: preliminary application, online application, written responses, work samples (if applicable), teacher recommendations, standardized test scores, transcript, $50 application fee. Need-based financial aid is available with the completion of an additional financial aid application.