Writing Proofs
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Many of the exercises this semester will be proofs, rather than calculations. Often the emphasis is on "What's true, and why?" rather than "What's the numerical answer?".
If you just aren't used to that, I'd suggest starting with True-False practice. You can find these at the end of every chapter of your text (Leon's Linear Algebra), and more on the author's website. My web pages listed below offer this practice too.
After you get used to this kind of thinking, you can study sample proofs from the text, and my lectures, and try the exercises yourself. If you get stuck, some other books may help. I'd suggest Velleman's inexpensive and fairly easy paperback "How to prove it" - I bought one at a local bookstore for about 15 dollars. You can also find the basics of logic in any Discrete Math book, in the library, for example. There is also a very thorough book by Morash on reserve in the FIU library.
Perhaps if you get stuck, you can tell me what kind of help you need. For now, why don't you try these drills:
Proofwriting, Part I, "and"
and "or" exs
Proofwriting, Part II, "if-then"
exs (see thm 3.3.2 below, for a harder example)
Proofwriting, Part III, quantifier exs
Examples of proofs, mostly from Ch.1.
Determinants and Induction (the detailed
reasoning behind Thm 2.1.2)
Proof of Theorem 3.3.2B in great detail,
with a short drill.
The following were written for my Summer 2000 class. They are not interactive but go beyond Parts I-III above and do have a few exercises. Any page numbers refer to the 5th Edition of our text.
Summer 2000, Parts 1-3
Summer 2000 Parts 4-5
Summer 2000 version Parts 6-8 (includes
induction)