Tensor Product: Basis for Higher Order Tensors and Its Proof

In summary, the tensor product of two tensors of lower rank forms the basis for ANY tensor of higher order. This can be proven by looking at the transformation properties of tensors and using the kronecker delta. There are 16 components in total for a tensor of rank (0,2) because there are 4 choices for the basis vector in each slot, giving a total of 4x4=16 components. However, understanding this concept and the kronecker delta may be difficult for high schoolers studying tensor analysis.
  • #36
coalquay404 said:
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.
 
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  • #37
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.
 
  • #38
do you think they would be irritated if I called them?
 

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