Studying Spivak's Calculus Textbook Course

[Kid_Electro]

At UofT the first year math for the math and physics program is mat157, an introductory calculus analysis course where "Calculus" by Spivak is used. How can one prepare oneself for such a course? Where can one obtain a good knowldedge of proof techniques and anything else inorder to do well in this course? The problem is in high school we never touched much on proofs, or questions in the style of Spivak's Calculus. Any advice?

 

[kdinser]

Get the book as early as possible and start at chapter 1. Do every problem and example they give an answer to so you can verify that your doing it right. Try and get about a third of the way through it before class starts. Don't move on until you understand a section completely. The people in the homework forum are fantastic at helping out if you don't understand something from the book. It takes a lot of commitment, but takes a lot of pressure off you at the beginning of a semester.

 

[mathwonk]

when i was in high school i went to the univ library a lot and looked in books on proofs. but i got my start from a book called principles of mathematics, by allendoerfer and oakley.

it starts with a good section on logic and proofs and moves on from there treating a lot of interesting toopics in an elementary way, with proofs. finally it introduces calc, but i dint get that far.

there are used copies out there of [carl] allendoerfer and [cletus] oakley.

 

[mathwonk]

heres one right here fopr 6 bucks.
Principles of Mathematics
Allendoerfer - Oakley Bookseller: Add-More Books
(Danville, VA, U.S.A.) Price: US$ 6.75
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US$ 3.75
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Book Description: McGraw-hill, Many, 1955. Cloth. Book Condition: Very Good. No Jacket. 8vo - over 7¾" - 9¾" tall. The hard cover has very light shelf wear ...The book may have minor flaws that may have gone unnoticed.. Hard Back. Bookseller Inventory # NF 06241

their fundamentals of freshman mathematics is probably a newer version of the same book, but may be watered down for the new stupid approach to teaching. i have not seen it. i recommend the old one since standards were higher in the 50's and 60's, when spivak was written also.

 

[mathwonk]

another great book, is geometry, by harold jacobs, which begins with logic and proofs. much lower level than allendoerfer, written for high school, but intelligently.

 

[mathwonk]

heres a copy

Geometry (ISBN: 0716704560)
Harold R. Jacobs Bookseller: Frugal Media Corporation
(Austin, TX, U.S.A.) Price: US$ 10.00
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US$ 3.70
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Book Description: W.H. Freeman & Company, 1974. Hardcover. Book Condition: GOOD. USED Ships within 12 hours with great customer service!. Bookseller Inventory # 1151509

 

[mathwonk]

allendoerfer and oakley is really at the level you need for spivak though.

 

[Kid_Electro]

mathwonk and kdinser thanks for the advice.
I'm going to order the allendoerfer book right now.

 

[Kid_Electro]

should I get the Spivak solution book?

 

[kdinser]

should I get the Spivak solution book?

That depends a lot on your self control. Having that book close at hand can put you in the habit of just grabbing it every time you get stuck. It can become a crutch, a crutch that you won't have on the test. It's nice to have if you get really stuck and just can't figure something out, but I've found the homework forum on this site to be much more helpful then a solution manual. Often times, just typing out and explaining the problem that I'm planning to post shows me something that I had been overlooking.

 

[mathwonk]

never get the solution book for any book. i have one for edwards penney, but i have only used it as a doorstop now for about 20 years.

better, make your own solutions book. but do not give it to anyone.

 

[Kid_Electro]

Sounds good!

 

[neurocomp2003]

"Problem solving through Problems" by Larson

 

[kdinser]

better, make your own solutions book. but do not give it to anyone.

It's funny, I've actually been doing that for the last couple semesters for calc III, diff eq, and linear algebra. I just hadn't been thinking of it as making a solution manual, but I guess that's what it amounts to. Every time I encountered a new theorem or proof, or when I was trying to create a standard approach to solving certain types of problems, I would try to write out what it means in my own words. It's how I realized why mathematicians come up with so much funky notation, without it, it takes a few lines to explain the difference between (a,b) and [a,b] .

 

[Kid_Electro]

I would like to do the Math and Physics program, but to be honest I am scared somewhat of the Spivak course etc.. :(