Math Forum Discussions

Jonathan Groves

Posts: 2,068
From: Kaplan University, Argosy University, Florida Institute of Technology
Registered: 8/18/05

Free Online Book About Mathematical Reasoning and Proofs
Posted: Aug 2, 2009 9:34 AM

Plain Text

Dear Fellow Mathematicians,

One of my best friends is working on her Master's in
Mathematics Education to try to become a high school teacher.
However, some of the professors in her advanced undergraduate
math courses seemed to have little patience with her and
made her feel dumb, so she doesn't feel very comfortable
with mathematics proofs right now. In fact, she has never
taken a math course on mathematical reasoning and proofs,
so I think that's another big reason she doesn't feel
comfortable with proofs right now. I recently offered to
help her understand proofs better, but I don't know when
we will start. I hope we will start soon, but it's hard
to say since her summer coursework has taken her a lot of
time this summer. When she finishes soon, she will probably
not want to do this before the fall semester (if so, I
wouldn't blame her).

I had worked with her before on some proofs, and I can tell
from those experiences that I really believe she is capable
of learning this. I really believe she has more talent
than she realizes.

I tried looking for a free online math book on mathematical
reasoning and proofs so that she wouldn't feel forced to
buy a book. The only such book I found was number 72 on this list
of free online books (the list is not exhaustive):

http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html.

Here is a direct link to the webpage where the book can be downloaded:

http://people.uleth.ca/~dave.morris/books/proofs+concepts.html

The book is called "Proofs and Concepts: The Fundamentals of
Abstract Mathematics" by Dave Morris and Joy Morris. It seems to
me to be a pretty good book, but I would like a second opinion.
If someone knows a better free online book for such a study
of proofs, please let me know. I can't find any others right now.
The closest I can find is number 48 on that same list, but
it's not directly about the methods of mathematical proofs.

I plan to borrow some material from the books "Proof, Logic, and
Conjecture: The Mathematician's Toolbox" by Robert S. Wolf
and "How to Prove It: A Structured Approach" by Daniel Velleman
that I have. I believe these are very good books on the subject.
Daniel Solow's book "How to Read and Do Proofs" is also very good,
but I do not have a copy (I had the chance a few years ago to look
at it).

I had originally posted this on sci.math (except for differences
in the last two sentences of the first paragraph) back in early June
before she started her coursework this summer, but no one had replied.
So I will try here since this list is primarily about post-calculus
mathematics education (and this is a post-calculus course).

Thank you for your responses.

Sincerely yours,
Jonathan Groves