Membrane Theory And Quantum Mechanics

[Hassan]

[quote name='philothea' post='1877479' date='May 28 2009, 07:55 PM'][url="http://www.amazon.com/gp/product/0306447908?ie=UTF8&tag=amberdine-20&link_code=as3&camp=211189&creative=373489&creativeASIN=0306447908"]Principles of Quantum Mechanics[/url]

accompanied by

[url="http://www.amazon.com/gp/product/0306450364?ie=UTF8&tag=amberdine-20&link_code=as3&camp=211189&creative=373489&creativeASIN=0306450364"]Basic Training in Mathematics[/url]

both by R. Shankar. They're both college textbooks, but were written to be usable by someone teaching themselves. They use the much nicer "Bra/Ket" notation, too.

If anyone wants a light and fun but still accurate introduction, I highly recommend [url="http://www.amazon.com/gp/product/0964350416?ie=UTF8&tag=amberdine-20&link_code=as3&camp=211189&creative=373489&creativeASIN=0964350416"]What is Quantum Mechanics?: A Physics Adventure[/url] by the Transnational College of Lex. They're a Japanese language study group, and it's got, ah, cartoons in it, but it's really good. (Some math: matrices, fourier transforms, but you can skim it if you need.) [/quote]

I wish I had more time. Right now most of my spare time goes to staying ahead in terms of political science books, articles etc. I'm going to refresh my knowledge of logic and set theory this summer but I just don't have enough time to read such books and truely digest the knowledge. I think I would like to get those to though (at a cheeper price) and perhapse read them slowly. Honestly I'm seriously considering the PeaceCorps after college and would love to really devote those two years, when I'm not doing my official duties, to just immerse myself in the higher maths and logic (physics too, but logic is my true love).

Do you know any good books for Calculus? Like higher as well as lower (so I could catch up/brush up with that, although I know the math book had a brief review, how comprehensive is it in your oppinion?)/

[Innocent]

[quote name='Hassan' post='1878244' date='May 30 2009, 10:01 AM']Do you know any good books for Calculus? Like higher as well as lower (so I could catch up/brush up with that, although I know the math book had a brief review, how comprehensive is it in your oppinion?)/[/quote]

I'm not an expert to the level of Philothea, and moreover, my academic area is not pure science, and so you should probably not give my recommendation as much weightage as hers. Having said that, the best introductory book to Calculus I've read was:

[url="http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480"]Calculus Made Easy - Silvanus P. Thompson.[/url]

Also, I need to brush up my Analytical Geometry. Can you suggest a good book?

[Hassan]

[quote name='Innocent' post='1878340' date='May 30 2009, 01:22 AM']I'm not an expert to the level of Philothea, and moreover, my academic area is not pure science, and so you should probably not give my recommendation as much weightage as hers. Having said that, the best introductory book to Calculus I've read was:

[url="http://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480"]Calculus Made Easy - Silvanus P. Thompson.[/url]

Also, I need to brush up my Analytical Geometry. Can you suggest a good book?[/quote]


[i]Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences[/i]

It's a bit dated

[Innocent]

[quote name='Hassan' post='1878342' date='May 30 2009, 12:03 PM'][i]Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences[/i]

It's a bit dated [/quote]

Oh, the Descartes book. It's already on my reading list. It's been on my reading list ever since I read G. Polya's [i]How To Solve It.[/i] Have you read that?

Edited May 30, 2009 by Innocent

[Hassan]

[quote name='Innocent' post='1878343' date='May 30 2009, 01:38 AM']Oh, the Descartes book. It's already on my reading list. It's been on my reading list ever since I read G. Polya's [i]How To Solve It.[/i] Have you read that?[/quote]


Just skimmed some parts. I bought Hawkings "God Created the Intigers" a few years back and have skimmed it.

[Innocent]

What about Penrose's [i]The Road To Reality[/i]? I used to read bits of it. (it was in the reference section of my college library.) but I never completed it.

Also since you appear to have studied logic, what would be in your opinion, a good introductory book?


Have you gone through the OUP "A Very Short Introduction" series book on Logic? (Obviously, the books of this series are not meant to be used for a thorough study, just as an appetiser. )

Edited May 30, 2009 by Innocent

[Hassan]

[quote name='Innocent' post='1878349' date='May 30 2009, 02:00 AM']What about Penrose's [i]The Road To Reality[/i]? I used to read bits of it. (it was in the reference section of my college library.) but I never completed it.

Also since you appear to have studied logic, what would be in your opinion, a good introductory book?[/quote]

Penrose book always looked neat, I bought a copy for my Grandfather but never read it myself.

Symbolic Logic by Irving M. Copi is nice.


[quote]Have you gone through the OUP "A Very Short Introduction" series book on Logic? (Obviously, the books of this series are not meant to be used for a thorough study, just as an appetiser. )[/quote]

A little bit

[philothea]

[quote name='Hassan' post='1878244' date='May 29 2009, 11:31 PM']I wish I had more time. Right now most of my spare time goes to staying ahead in terms of political science books, articles etc. I'm going to refresh my knowledge of logic and set theory this summer but I just don't have enough time to read such books and truely digest the knowledge. I think I would like to get those to though (at a cheeper price) and perhapse read them slowly. Honestly I'm seriously considering the PeaceCorps after college and would love to really devote those two years, when I'm not doing my official duties, to just immerse myself in the higher maths and logic (physics too, but logic is my true love).

Do you know any good books for Calculus? Like higher as well as lower (so I could catch up/brush up with that, although I know the math book had a brief review, how comprehensive is it in your oppinion?)/[/quote]
Yep, that's what I did a while back, just took a couple years to study. It was nice.

As for calculus books... that's hard. Innocent's suggestion is good, but every calculus book I've tried (including [i]Calculus Made Easy[/i]) at some point makes an unexplained leap between what they just taught and what they expect you to get from it. Also, calculus is a huge subject, and for physics I need only certain, not-very-rigorous bits of it.

[url="http://www.amazon.com/gp/product/0521017076?ie=UTF8&tag=amberdine-20&link_code=as3&camp=211189&creative=373489&creativeASIN=0521017076"]Maths: A Student's Survival Guide: A Self-Help Workbook for Science and Engineering Students[/url] has a very good section on calculus (along with algebra, trig, geometry, and vectors). The "Basic Training" book by Shankar I linked to earlier is mostly calculus. Those two cover everything I need for physics at the level I'm interested in.

To supplement those, I collect a lot of cheap/electronic calculus texts, so every time I get stuck (which is a lot ) I can try someone else's explanation. Dover has good paperback textbooks in the $10 range, a lot of professors publish their own online for free, and of course there are loads of used ones around.

Edited May 30, 2009 by philothea

[Innocent]

[quote name='Hassan' post='1878390' date='May 30 2009, 09:04 PM']Symbolic Logic by Irving M. Copi is nice.[/quote]
Thanks for the recommendation. I noticed on Amazon that the same author has a book titled [url="http://www.amazon.com/Introduction-Logic-Irving-M-Copi/dp/0131898345/ref=pd_sim_b_2"]"Introduction To Logic."[/url] Is the book you recommend an improvement on this one?

I'll try to get the book you recommended and read it when I have time.

Philothea,

I've heard many good things about this maths book:

[url="http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=pd_cp_b_2?pf_rd_p=413864201&pf_rd_s=center-41&pf_rd_t=201&pf_rd_i=0691025096&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=0PRRS5R2F75PXR2ZMBKG"]What is Mathematics? - Richard Courant.[/url]

Have you read it? Would you recommend it?

[philothea]

[quote name='Innocent' post='1878493' date='May 30 2009, 01:47 PM']Philothea,

I've heard many good things about this maths book:

[url="http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=pd_cp_b_2?pf_rd_p=413864201&pf_rd_s=center-41&pf_rd_t=201&pf_rd_i=0691025096&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=0PRRS5R2F75PXR2ZMBKG"]What is Mathematics? - Richard Courant.[/url]

Have you read it? Would you recommend it?[/quote]
I'm familiar with Courant's book, and it's certainly well done, but I like [url="http://www.amazon.com/gp/product/039304002X?ie=UTF8&tag=amberdine-20&link_code=as3&camp=211189&creative=373489&creativeASIN=039304002X"]Mathematics: From the Birth of Numbers[/url] by Jan Gullberg better, myself. It's 50+ years newer, and so includes modern concepts like fractals, and it also has problems to work on, with answers. I never understand anything until I can work on it. Of course, it's also more expensive.

There are previews of both books at Amazon. They both seem to cover the same basic material, in the same general way. Courant was a renowned mathematician, though, and Gullberg is just a science writer. Courant's book is probably more technically rigorous. Might be a matter of taste. I kinda like pictures.

[Innocent]

Thanks for the recommendation, Philothea!