Skip to main content

Groups Made Easy


If you’re taking quantum mechanics, QCD, quantum field theory, electricity and magnetism, or any of the other physics courses where group theory is often used, but rarely explained, then Groups and Their Graphs by Israel Grossman and Wilhelm Magnus is the book for you. It lays out the basics of group theory in simple easy to understand language. For the more esoteric minded, it even covers quaternions.

I just found this book a few weeks ago and finally picked up my own copy. It’s from a seemingly brilliant series of books called the New Mathematical Library that was started in the ‘60s. The series takes advanced or less than common mathematical concepts and explains them in a manner that is targeted at an audience with high school level math skills. Here’s a quote from the book:

"This book is one of a series written by professional mathematicians in order to make some important mathematical ideas interesting and understandable to a large audience of high school students and laymen. Most of the volumes in the New Mathematical Library cover topics not usually included in the high school curriculum; they vary in difficulty, and, even within a single book, some parts reuire a greater degree of concentration than others. Thus, while the reader needs little technical knowledge to understand most of these books, he will have to make an intellectual effort."


The book uses geometric operations such as rotations and flips on an equilateral triangle to illustrate concepts so far. While it’s easy to understand, it never talks down, or dumbs down concepts. More on this later.
Labels:

Comments

Post a Comment

Please leave your comments on this topic:

Popular posts from this blog

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain ...
10 comments
Read more

The Alcubierre Warp Drive Tophat Function and Open Science with Sage

I transferred yesterday's Mathematica file with the Alcubierre warp drive[2] line element and space curvature calculations to the  +Sage Mathematical Software System  today, (the files been  added to the public repository [3]).  If you haven't used Sage before, it's a Python based software package that's similar in functionality to Mathematica.  Oh, and it' free.  I also worked a little more on understanding the theory, but frankly, I made far more progress with the software than the theory.  What follows will be a little more of the Alcubierre theory, plus, a cool Sage interactive demo of one of the Alcubierre functions[1], as well as a bit about my first experience with using Sage. Theory The theory is fun, but it's moving slowly.  Here's the chalk board from this morning's discussion Alcubierre setup the derivation using something called the 3+1 formalism which means we consider space to be flat, (in this case), slices that are labelled ...
2 comments
Read more

How Many Files Can You Add to a GPT Project? An Interview with GPT-5 on Limits, Context Engineering Tips, and Chats

 Setting the scene: I’m tinkering with Project TouCans, knee-deep in radio logs, SQLite dumps, and Cesium code. Naturally, I’m wondering if shoving all this into one GPT Project is a recipe for brilliance… or for disaster. So I turn to Vril — you know, after Brainy from the Legion of Super-Heroes , because what else do you call your AI sidekick who always has the answers? Time to ask him straight up. [ As an aside, yes, GPT-5 has decided to sometimes call me Vail. I'm not sure why to be honest. Also, I asked Vril, er GPT-5, to write up our interview for me. Apparently, me asking it to 'Bro' up a few stories, just for fun, has convinced Vril that I use 'Like,' more than I actually might. ] Me (Vail): So Vril, how many files can I throw into a GPT Project before it just starts choking? Like, is there some magic number where the context window taps out and everything falls apart? GPT-5 (Vril): Great question. There’s no single hard file limit. What matters is ...
Post a Comment
Read more