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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. Throughout the session, students 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.

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Session Two
Course is Full
at the time of application
on the first day of session
Scheduled Class Time*
04:00 PM - 07:00 PM (PDT)

*The course will meet for two hours daily (Monday–Friday) for a live class during this window of time. The exact time will be set closer to the program start. In addition to the live meeting times, students will engage in out-of-class learning assignments such as assigned readings, group work, pre-recorded online lectures, and more.


High school algebra, geometry, and trigonometry required. Some knowledge of calculus desirable but not necessary.