Did you know that every "nice" map from a ball to itself maps at least one point to itself? Can you imagine proving facts about polynomials using projection of a sphere onto a plane? Yo' gramma sure didn't know any of this stuff! In this class, we'll talk about how mathematicians study sufficiently "nice" surfaces and use them to derive beautiful results in a wide range of fields with little more than calculus.

What are the fundamental building blocks of the universe? In what sorts of weird, strange ways can particles interact with each other? What unanswered questions remain regarding the most basic laws of physics? The answer to these questions and more will be given in this (mostly) nontechnical class about the Standard Model. Basic concepts of quantum mechanics and quantum field theory will be developed along the way to intuitively explain why our description of the universe so far is put together in the way it is. We'll also touch on open questions that are likely to be addressed at the LHC or are theoretically addressed by string theory and other models.

Learn how to endear yourself to friends and family with this special course on improving your skill in acting like an annoying, nitpicky snob. We cover techniques in picking apart grammatical errors, mocking minor flaws in logic, giving off an air of smug sarcasm, and other techniques for criticizing the inconsequential imperfections in the language of those around you.

That capitalism is the best possible economic system is something that most people in Western countries simply take for granted. Many modern thinkers, however, would readily challenge this statement. Particularly scathing lines of criticism come from postmodern movements, whose primary aim is to challenge fundamental assumptions about the world that we take for granted. This discussion-based class will address some of the stranger, more esoteric justifications from the philosophical community about why capitalism is unjust and undesirable.

In this marathon class, we start from the fundamental postulates of quantum mechanics and build up the rest of the theory from there. We take a very mathematical approach that relies heavily on linear algebra and vector calculus, so prospective students are advised to take the prerequisites seriously. The precise extent of the class will be determined by how fast the class feels comfortable moving, but at the minimum, I hope to be able to offer a complete description of all the theory necessary for understanding two-state systems and their time evolution, including well-known examples such as neutrino flavor oscillation. Possible topics beyond this include a description of the hydrogen atom, charged particles in magnetic fields, time-independent/dependent perturbation theory, etc.

Hear some crazy logical puzzles, weird physical truths, and other mind-blowing nuggets of reality that will completely change your life, make you rich and famous, and rocket you towards nirvana.

This course covers a wide variety of topics in physics beyond elementary mechanics and electrodynamics with the common theme that all results are rigorously derived from first principles, and mathematical formalism is never omitted. Students are advised to take the prerequisites seriously. The precise content of the class is flexible, and can be influenced by students who take it. Planned topics include quantum mechanics, statistical physics, and astrophysics. For Spark, the first class will cover special relativity: starting from the the postulates of special relativity, we derive the Lorentz transformations, introduce four-vectors, and discuss the geometry of space-time. Many consequences are discussed: time dilation, length contraction, relativistic dynamics, etc. Space-time diagrams and paradoxes are also covered.

This course covers a wide variety of topics in physics beyond elementary mechanics and electrodynamics with the common theme that all results are rigorously derived from first principles, and mathematical formalism is emphasized. Students are advised to take the prerequisites seriously. The precise content of the class is flexible, and can be influenced by students who take it. Planned topics include quantum mechanics, statistical physics, and astrophysics. For Spark, a special double-length class about special relativity will be offered! Starting from the the postulates of special relativity, we derive the Lorentz transformations, introduce four-vectors, and discuss the geometry of space-time. Many consequences are discussed: time dilation, length contraction, relativistic dynamics, etc. Space-time diagrams and paradoxes are also covered.

This is a non-technical introduction to quantum mechanics. By qualitatively describing many strange experimental results in quantum mechanics, we highlight ...

Title is self-explanatory. Ask questions about stuff if you're in our concentration class.

Title is self-explanatory. Ask questions about stuff if you're in our concentration class.

Title is self-explanatory. Ask questions about stuff if you're in our concentration class.

Starting from the postulates of special relativity, we derive the Lorentz transformations, define the four-vector, and derive many fundamental results ...

This course will cover AP Physics C: Mechanics as well as Electricity and Magnetism. The course will go at a ...

What exactly is postmodernism? What is it a response to? Why does it seem so difficult to understand? These questions ...

Suppose we have two particles moving toward each other at 99% of the speed of light? How fast does one ...

Get some insight on this often-confusing, poorly-formulated, more-philosophical-than-scientific musing on general relativity which Einstein somehow fell in love with. The ...

Tips, tricks, and advice for the United States Physics Team screening exams: it is taught by Kenan Diab and Haofei ...