/sci/ - Science & Math

>>10390312
To "get good" at any sort of mathematics you need to actually DO mathematics, not just read them passively. I know you don't literally mean to just read the book, but this is an important thing to note, nonetheless. The following quote from Paul Halmos encapsulates my point well:

>The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method, the method in which the teacher plays the role of an omniscient but largely uncommunicative referee between the learner and the facts. (...)

>The right way to read mathematics is first to read the definitions of the concepts and the statements of the theorems, and then, putting the book aside, to try to discover the appropriate proofs. If the theorems are not trivial, the attempt might fail, but it is likely to be instructive just the same. To the passive reader a routine computation and a miracle of ingenuity come with equal ease, and later, when he must depend on himself, he will find that they went just as easily as they came. The active reader, who has found out what does not work, is in a much better position to understand the reason for the success of the author's method, and, later, to find answers that are not in books.

As for the "notation" you speak of, it's just a pretty standard way to write, as generically as possible, a number as the product of its prime factors. for instance, instead of [math]a = t_1^{g_1} t_2^{g_2} \ldots t_v^{g_v}[/math] we could've written [math]24=2^3\cdot3[/math], but this is merely one particular case: here, [math]a=24[/math] and [math]v=2[/math]. A good book if you want to study this, in particular, is David Burton's Elementary Number Theory.