Recent content by nucl34rgg

If you look at the definition of subspace topology, and what the open sets are specifically of K, it will be immediate why the statement holds.

The entire point of note taking is that it is to help the person remember. What we call a "good note taker" is simply someone with good handwriting or typing skills. It's probably the people that never take any notes but still do well that have the best comprehension since it means they don't...

I'd recommend checking out the GR lecture series from MIT OCW rather than that one. Susskind aimed his at a general audience. The ones from MIT are an actual course.

That's why you ban talking during the test. Any form of communication should be perceived as an attempt to cheat unless proven otherwise.

The only time dependence in the basis vectors will arise as a phase so it is simplest to consider the basis the same as in the initial time and then just multiply by the time dependent phase.

Keep in mind what dS represents. It should have a magnitude equal to the differential surface area and a direction pointing normal to the surface. That direction vector ought to be normalized.

I strongly recommend ditching physics and studying engineering/CS. To study physics these days is almost certainly a vow of poverty. Ditto for math. Better options include electrical or chemical engineering, mechanical/aeronautical engineering, computer engineering, computer science, or...

One property you need to know is that i^2=-1 so you can use this to simplify the power expression. You also need to know about complex conjugation.

You're transporting the tangent vectors from the tangent space at one point on the curve to a different tangent space at a different point so that the vectors remain parallel as you travel an infinitesimal amount along a curve from the first point to the second point. Does that make sense?

I have watched many OCW lectures. Barton Zwiebach has excellent lectures on quantum mechanics. Walter Lewin's lectures are unrivaled for elementary physics. I think MIT OCW is an excellent resource. They usually hve solutions and problems on the site.

To learn the basics of quantum mechanics, you should learn the following topics first at an undergrad level: calculus (stewart) linear algeba (axler) general chemistry (not sure what the best book is) ordinary differential equations (devaney) partial differential equations (haberman) classical...

I'm not in string theory, but pure math is similar in terms of employment prospects. My humble opinion is that it is a vow of poverty. Get out while you can! Our graduate education chews people up and spits them out. Many aspire to become professors, but very few can be. It's kind of like the...

The denominator was squared and then square rooted. He is expressing the magnitude.

I've never actually needed it. Even in analysis, the most complicated expressions just required a bit of careful thought. I've never dealt with anything complex enough to require that I translate it into symbolic logic. As long as you know contrapositives and how to negative quantifiers, I think...

Loomis and Sternberg's calculus book is a good example of an old school rigorous math book with a lot of physics insights as well.