Recent content by gauss^2

Calculus of Variations (20 lectures) and Integral Equations (20 lectures) http://nptel.iitm.ac.in/courses/111104025/

LOL, you're right. I know standard hydrogen occurs as a diatomic molecule but for some reason didn't connect the dots on tritium gas being diatomic too. Thanks!

Homework Statement This is question 1-9 from French's Special Relativity Homework Equations The equations are shown in my attempt at a solution belowThe Attempt at a Solution ------------------------------------------------- The answer in the back of the book states it should cost about...

Nevermind... I just found out it could easily be done by putting the command \def\thesection{\arabic{section}} in the preamble.

Is it possible to only show section numbers without chapter numbers in a LaTeX document of class "book"? For instance, Munkres' Topology text breaks things down into chapters but the sections are numbered independent of the chapter. For instance, Sections 1-11 are in Chapter 1, 12-22 in Chapter...

You discuss subtle things like compactness, construction of the reals, the Cantor set, and rearrangements in a first college math class? Wow, I would have gotten killed learning those concepts fresh out of high school, especially at a fast pace. I do agree that stuff like equivalence relations...

Prove that (g^{-1} x g)^m = e cannot happen for a positive integer m < n. Use the fact mentioned earlier that (g^{-1} x g)^m = g^{-1} x^m g for any integer m to derive a contradiction based on the assumption that 1 \leq m < n and (g^{-1} x g)^m = e both hold.

f \colon A \to B means a function with name f from the domain A into the codomain B. For instance, consider the function f\colon \mathbb{R} \to \mathbb{R}\times \mathbb{R} defined by the rule f(x) = (x,x). In this example the domain (e.g., the set x is in) is the real line \mathbb{R} and the...

Let's set A = \{(a1,a2) \in \mathbb{R}^2: 0 \leq a1 \leq 2, 0 \leq a2 \leq 4\} and consider the case that x > 2 and y > 4 holds so that (x,y) is in the complement of A. Then take r to be the minimum of a1 - 2 and y-4. Then the ball of radius r centered at (x,y) doesn't intersect A since a1 - r...

A good first step is noticing that ... -5 = 2*(-3) + 1 -3 = 2*(-2) + 1 -1 = 2*(-1) + 1 1 = 2*0 + 1 3 = 2*1 + 1 5 = 2*2 + 1 ...

Draw a picture, pick a point in the complement, and from that see how small your open ball centered at that point should be to ensure the open ball stays in the complement. Once you have that, then you have showed every point in the complement is an interior point of the complement, so the...

The question as written seems to be asking about a specific x and not making a universally quantified statement, though I have no doubts the problem is meant to illustrate that inverses are two-sided in groups.

It has to be in a monoid, which is a set G with an associative law of "multiplication" and an identity element e \in G such that e x = x e = x for all x \in G. However, a monoid need not have a two-sided inverse for all elements like a group would. The proof should be a = e a = (bx)a = b(xa) =...

I would recommend having a multivariable calc class before doing analysis at the level of Baby Rudin. Single-variable calc you can get by on the formulas, but you tone up your geometric skills in multivariable with tangent planes, normals, volume elements and so on. Having strong geometric...

Yeah, I have viewed that entire class, and it's phenomenal. It's too bad Baby Rudin will never have the great diagrams Prof Su illustrates the material with in those videos (everybody wanted to write like Bourbaki back then it seems). Baby Rudin is really hard to understand if you can't come up...