Tensor Product: Basis for Higher Order Tensors and Its Proof

[coalquay404]

I'm not asking you to prove yourself and I'm certainly not saying that you're stupid. Regardless of how old you are and regardless of your background, the fact that you're asking questions proves that you're not thick.

Seriously, if you're in high school and you've been able to understand and absorb this much physics and mathematics then you should do very well if you choose to study physics at university. I would however suggest that you look at a book such as Chern, Chen, and Lam to learn differential geometry before trying to learn too much about general relativity.

Oh, and complex analysis is an absolute must. I'm still amazed at how many undergrads I see that don't understand it at all.

what must I explain now? stokes? gauss's? change of variables? this is exactly why I would never ask questions in the past.

You'd better get used to explaining yourself. Not only is it the best way to actually learn something, if you ever end up in grad school you'll do little else.

 

[Terilien]

I'm not asking you to prove yourself and I'm certainly not saying that you're stupid. Regardless of how old you are and regardless of your background, the fact that you're asking questions proves that you're not thick.

Seriously, if you're in high school and you've been able to understand and absorb this much physics and mathematics then you should do very well if you choose to study physics at university. I would however suggest that you look at a book such as Chern, Chen, and Lam to learn differential geometry before trying to learn too much about general relativity.

Oh, and complex analysis is an absolute must. I'm still amazed at how many undergrads I see that don't understand it at all.

I've never found a resource on complex analysis, I am VERY interested in ANY introduction to rigorous mathematics.chern chem and lam? what's the book like? does it start with gaussian geometry or full blown generality?

I'd actually prefer to study mathematics outside of physics but i can't find any non physics books that treat advanced topics with a conversational tone.

"for what will it profit a man to know the formal definition of a submanifold, yet lose sight of the it's true meaning?"

Most mathematics books, start with something like, definition 1A.

"A "insert fancy term here" is a bijective mapping between two surjective Y spaces".

I know that's not anything specific, but I think you get the point. I'd love to major in physics, but trouble with things like school are getting in the way. sometimes it takes a while for me to get over my fear of studying a certain topic. I'm generally very afraid of not understanding something.

Oh well I'm getting a tad sentimental. My problem is that i generally keep my thoughts on topics to myself because I'm very sensitive to criticism.

"More articulate in person"

I'm not trying to be whiny. I'm willing to learn formal mathematics, I just like seeing WHY. intuition is the key to mathematics and science.

I'm actually extremely new to anything formal in the field of math. I'm used to thinking of a problem and finding the answer.

 

[coalquay404]

I've never found a resource on complex analysis, I am VERY interested in ANY introduction to rigorous mathematics.chern chem and lam? what's the book like? does it start with gaussian geometry or full blown generality?

"Chern, Chen, and Lam" refers to this book. (For some reason it's far more expensive in the US store than here in the UK, even taking exchange rates into account.) S. S. Chern was possibly the greatest geometer of the last century and had an uncanny knack for explaining geometry in a perfectly correct but chatty style. This book is probably the best one (in my opinion) from which to learn geometry if you don't feel like getting bogged down in Bourbaki-style rigour. He begins with multilinear algebra and continues through Riemannian geometry, Lie groups, and fibre bundles. It really is excellent.

I'd actually prefer to study mathematics outside of physics but i can't find any non physics books that treat advanced topics with a conversational tone.

This is known as the curse of Bourbaki. Probably the best way to learn mathematics in a "conversational tone" is by doing just that: talking to people. Books are great as references, but you'll probably end up learning a lot more from other people.

"A "insert fancy term here" is a bijective mapping between two surjective Y spaces".

I know that's not anything specific, but I think you get the point. I'd love to major in physics, but trouble with things like school are getting in the way. sometimes it takes a while for me to get over my fear of studying a certain topic. I'm generally very afraid of not understanding something.

Oh well I'm getting a tad sentimental. My problem is that i generally keep my thoughts on topics to myself because I'm very sensitive to criticism.

Again, if you want to learn, get used to being criticised. You can learn a lot from books but you'll learn the most from talking to people who already know the things you're interested in. Being criticised (sometimes even viciously) is a great way to sharpen your ideas. If you can spot the difference between somebody launching an ad hominem attack and somebody who's picking your ideas apart, you can spot the difference between good criticism and bad criticism. And then you'll be half way towards getting a PhD.

 

[Terilien]

I've always wanted to meet a math professor of some sort. Unfortunately I have no idea how to.

 

[coalquay404]

I've always wanted to meet a math professor of some sort. Unfortunately I have no idea how to.

It's pretty simple. If you live near to a university, email the maths department and ask if they have any outreach programs or any staff members who are willing to talk to prospective students. I can (almost) guarantee you that you'll get a good response and that you'll have a chance to talk to somebody who's doing a job that you may one day like to have. Mathematicians and physicists are really receptive to people who show an interest in the field so try to get in contact with someone.

 

[Terilien]

It's pretty simple. If you live near to a university, email the maths department and ask if they have any outreach programs or any staff members who are willing to talk to prospective students. I can (almost) guarantee you that you'll get a good response and that you'll have a chance to talk to somebody who's doing a job that you may one day like to have. Mathematicians and physicists are really receptive to people who show an interest in the field so try to get in contact with someone.

That should be very interesting. The few moments I've had with mathematicians were the highlights of 2006! For now it won't be possible, becuase the university of toronto's math department contact page is inaccesbile.
http://www.math.utoronto.ca/
check for yourself.

i have however contacted aephraim steinberg from the physics department who said that if i show up when classes start I can attend lectures. Of course I'd rather learn my math from actual math sources. I don't want to limit my math exposure to physics sources as that would limit my contributions to both fields.

 

[coalquay404]

The contact page works fine for me. Apart from fancy formatting, this is what it contains:

Mailing address:
Department of Mathematics
University of Toronto
40 St. George St.
Toronto, Ontario
Canada M5S 2E4

General Inquiries: (416) 978-3323
Fax: (416) 978-4107

Reception/Inquiries: BA 6290.

The Department of Mathematics at St. George Campus is located at the 6th floor of the Bahen Centre for Information Technology.

The St. George campus is conveniently located in downtown Toronto, and is accessible by TTC public transit. By subway, the Department is a ten minute walk from both Queen's Park Station (located at Queen's Park Circle/University Ave. and College St.) and St. George Station (located at St. George and Bloor Sts.). The Department is also served by routes 506 Carlton (exit at College and St. George Sts.) and 510 Spadina (exit at Spadina and College Sts.)

For inquiries about admissions into the undergraduate program in mathematics, please visit the myfUTure website.
Undergraduate applications to all programs at the University of Toronto are done through the Ontario Universities' Application Centre. Please do not contact the Department for undergraduate admission application forms.

For information about the graduate program, please visit the the Graduate Studies section of our website. If you have any further questions, please contact Ida Bulat ida (at) math.toronto.edu, (416) 978-7894.

Telephone numbers for full-time faculty and staff at the University of Toronto are available through the University of Toronto Phone Directory. Email addresses and home pages for faculty, staff, graduate students, and other members of the Department can be found on our homepage.

The Mathematical Sciences Library is located at BA 6141.

The Fields Institute for Research in Mathematical Sciences is located at 222 College St., steps away from the Bahen Centre. Their postal address is

Fields Institute
222 College St.
Toronto, ON
M5T 3J1 Canada.

You may also contact them by phone at (416) 348-9710 or by fax (416) 348-9385.

 

[Terilien]

do you think they would be irritated if I called them?