Mathematics behind Theoretical Physics (Study Group Invitation)

Hope everyone is having a good summer!

Since the topic of Math is inextricably tied to that of Physics and nearly everyone has trouble understanding the Physics without the language of mathematics, I thought I'd pass along this notice from the Math/Physics Google Group based in Los Angeles. For those who really want to know more about physics and how it really works, this is a GREAT place to begin mathematically. It may all sound a lot more difficult and complicated than it really is because of the strange names and jargon, but it should be entirely surmountable by those with a background in high school algebra (and specifically doesn't include any trigonometry or calculus as a prerequisite!) Feel free to request to join the Google group to post questions there or see what is currently going on.




In preparation for Dr. Michael Miller’s UCLA Extension Fall '09 course in Group Theory with the follow-on course in Galois Theory for the Winter, several of us had discussed earlier in the year of mounting a Summer attack on Abstract Algebra in general so that we could get more out of the Fall/Winter offerings.

It’s my opinion that anyone with a high school background in math should be able to keep up with the subject as calculus, linear algebra, etc. are NOT necessary at all for these subjects which underpin many areas of Theoretical Physics, Quantum Mechanics, Coding Theory, Digital Communications, and other areas of science. Plus, there are many of us who will be there to help you out as we all progress.)

Toward that end, it has been suggested we spend a week or two working through Robert Ash’s Primer of Abstract Mathematics, which should get everyone (without any prior experience or even the best of us who can always use a reminder) up to speed on some of the abstract mathematical preliminaries needed/assumed for most group theory and abstract algebra texts. (Subjects like methods of proof, basic set theory, well-orderings, Zorn’s Lemma/Axiom of Choice, and basic definitions like injective, surjective, bijective, and other relatively simple constructs which can consume some time early in one’s studies.)

Following that it’s been suggested that we begin to work through Ash’s Basic Abstract Algebra which is an inexpensive Dover Text, and relatively likely to be the text for the class. These text recommendations have been made primarily for their clarity, simplicity, and relatively inexpensive price.

The goal of the group is generally to plow through as much preliminary work as possible between now and the beginning of the class such that we can obtain more out of the lectures as well as potentially utilize/work through Serge Lang’s towering Algebra text in the Fall.

If you’d like to join us, please confirm the text recommendations and/or suggest others and let us know which recurring day of the week would work best for you for in-person meetings. Please also indicate which side of town and what day(s)/ time(s) would be most convenient for you drive-wise for in person meetings. In the past, we’ve been meeting in the area near the 405 and Rosecrans from 6:30 pm – 8:30 pm in the evenings once a week. The goal is to attempt to accommodate (time and location to) as many people as possible. It’s certainly possible and feasible for you to work though this without joining us in person, but will require some additional effort and utilization of email and online tools.

We’d like to lock in the texts in the next few days to give everyone time to obtain them. Then we’ll lock in a meeting time early next week so that we can begin delving into them as soon as possible.

We all look forward to hearing your thoughts.



Suggested Texts:

A Primer of Abstract Mathematics

Basic Abstract Algebra


The most commonly used University texts include:
Thomas Hungerford’s Abstract Algebra: An Introduction (I suggest the 2nd edition to save significantly on the price over the 3rd edition which wasn’t changed much)
J.J. Rotman’s First Course in Abstract Algebra
Dummit and Foote Abstract Algebra
John Fraleigh First Course in Abstract Algebra

Keep in mind that these are SIGNIFICANTLY more expensive than the ones recommended above, but may be well worth the investment as supplements.