"Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection." — Hermann Weyl
Symmetry has captivated thinkers from ancient Greek philosophers to modern physicists, playing a crucial role in scientific and artistic endeavors. From Pythagoras' mathematically ordered universe and Renaissance masterpieces like Leonardo da Vinci's "Vitruvian Man," to the Enlightenment's scientific advancements by Isaac Newton and Christiaan Huygens, symmetry has shaped our understanding of natural laws.
In the 19th century, crystallography and group theory furthered this knowledge, culminating in Emmy Noether's theorem linking symmetries to conservation laws. Today, symmetry is integral to modern physics, technology, mathematics, and the arts, underpinning particle classification, quantum computing, and structural design. Understanding symmetry bridges students to advanced studies, providing a foundation for college-level physics and beyond. "Seeking Symmetry" immerses students in this rich concept, combining historical and modern perspectives through interactive sessions and practical projects.
This course requires the knowledge of a few mathematical concepts covered at the ICGSE level:
We strongly suggest that you refresh yourself by consulting appropriate resources (e.g ZNotes) or simply ask us questions regarding these during the course.
The course will run from July 1 to August 16th over a span of 6 weeks and will be conducted online. Each week will comprise three sessions. On Mondays and Wednesdays, theory sessions will be held. Here, we aim to introduce and discuss new concepts. Each of these sessions will consist of two Pomodoro segments (25 minutes of work followed by a 5-minute break) amounting to 1 hour. On Fridays, we will focus on applying the concepts through problem-solving and programming exercises which will consist of three Pomodoro sessions totaling 1.5 hours.
Furthermore, we also offer simple group projects as an optional component which shall serve as extensions of the tutorials. This will be followed by short presentations of the same.
Weekly schedule. Each clock figure indicates a Pomodoro segment.
Here we provide an overview of the content we will cover on a weekly basis. A detailed version alongside a weekly updating set of notes will be made available to the registered participants. This is of course, by no means a substitute for one's own notes but rather a supplement.
We begin with a commentary on the origins of the study of symmetries dating from antiquity and delve into mirrors and our historical fascination with them. This will be followed by a discussion on some peculiar mathematical fantasy worlds to investigate symmetries.