Recent content by Etenim

Greetings, This might not be a question of the usual kind. However, the feelings that I perceive these days cannot be put into more mainstream a framework. I am a quite successful undergraduate (2nd term) student of Pure Mathematics. However, now that almost a year has elapsed, I feel in...

Are those proof attempts so bad that they don't deserve a comment? :( Since I am studying this on my own, some input could be very helpful.

This is certainly true. I apologize for having brought the conversation off topic. :shy:

The list is obviously only for the mathematical side of his plan to study theoretical physics, and those topics are essentially relevant. The books I have listed range from almost zero to a very sophisticated level of mathematics. All those who are interested. Even if you specialize at some...

Hey, I copied the following (dotted) list of books out of a paper on Loop Quantum Gravity (Thiemann, "Lectures on Loop Quantum Gravity"), because I couldn't write a better one. • General A fairly good encyclopedia is Y. Choquet-Bruhat, C. DeWitt-Morette, “Analysis, Manifolds and Physics”...

In most of Europe, basic linear algebra and differential/integral calculus of functions of a single real variable are part of the high-school curriculum. Gaussian elimination is the very first thing we learned, and then continued with determinants and Cramer's method. We studied the foundations...

Greetings, I am faced with a problem in Group Theory. It's not homework. I am trying to study it by myself. The statements are quite obvious, but I want to write the proofs (correctly) with more precision. Could you comment on it or suggest corrections, please? 1. Let \sigma \in Sym_n be a...

Ah. By 'naturally' defining the action of a dual basis vector on an arbitrary vector v = c^i \beta_i to be \beta^*^j ( c^1 \beta_1 + c_2 \beta_2 + \cdots + c^n \beta_n ) = c_j , we want, by the dual basis vector's linearity, \beta^*^j ( \beta_i ) = \delta_i^j , to "extract" the c_j...

Greetings, Slowly I am beginning to think that I must be some sort of retard for not getting this fundamental concept. For this post, I will adapt the bracket notation as introduced by P. Halmos' "Finite-dimensional Vector Spaces". \left[ \cdot, \cdot \right] : V \times V^* \to K . A...