#1,170 in Science & math books
Reddit mentions of Proof Patterns
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Reddit mentions: 2
We found 2 Reddit mentions of Proof Patterns. Here are the top ones.
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Height | 9.25 Inches |
Length | 6.1 Inches |
Number of items | 1 |
Release date | March 2015 |
Weight | 6.98424446016 Pounds |
Width | 0.46 Inches |
Usual hierarchy of what comes after what is simply artificial. They like to teach Linear Algebra before Abstract Algebra, but it doesn't mean that it is all there's to Linear Algebra especially because Linear Algebra is a part of Abstract Algebra.
Example,
Linear Algebra for freshmen: some books that talk about manipulating matrices at length.
Linear Algebra for 2nd/3rd year undergrads: Linear Algebra Done Right by Axler
Linear Algebra for grad students(aka overkill): Advanced Linear Algebra by Roman
Basically, math is all interconnected and it doesn't matter where exactly you enter it.
Coming in cold might be a bit of a shocker, so studying up on foundational stuff before plunging into modern math is probably great.
Books you might like:
Discrete Mathematics with Applications by Susanna Epp
Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers
Building Proofs: A Practical Guide by Oliveira/Stewart
Book Of Proof by Hammack
Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al
How to Prove It: A Structured Approach by Velleman
The Nuts and Bolts of Proofs by Antonella Cupillary
How To Think About Analysis by Alcock
Principles and Techniques in Combinatorics by Khee-Meng Koh , Chuan Chong Chen
The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!) by Carol Ash
Problems and Proofs in Numbers and Algebra by Millman et al
Theorems, Corollaries, Lemmas, and Methods of Proof by Rossi
Mathematical Concepts by Jost - can't wait to start reading this
Proof Patterns by Joshi
...and about a billion other books like that I can't remember right now.
Good Luck.
These two are great in that they kind of take a CS approach to proofs by using the idea of a pattern:
Proof Patterns https://www.amazon.com/dp/3319162497/ref=cm_sw_r_cp_apa_i_0Y44BbDC5HWYB
How to Prove It: A Structured Approach, 2nd Edition https://www.amazon.com/dp/0521675995/ref=cm_sw_r_cp_apa_i_C244Bb8QY01F2
This is great for understanding limitations and the history of the development of proof techniques:
Reverse Mathematics: Proofs from the Inside Out https://www.amazon.com/dp/0691177171/ref=cm_sw_r_cp_apa_i_M044BbM0BMAE3
As has been suggested, you should look into mathematical logic, modern symbolic logic, which includes propositional and quantificational logic, relational logic, and perhaps even modal logic. Copi is great for a classical treatment of modern and Aristotelian logic. Gensler is great for learning translations, and Smullyan is great for mathematical logic.
You might also look into set theory and hott or type theory, but only after you've approached some of the other stuff. I can't emphasize logic enough if you want to really understand proof theory. Perhaps even check out computability and complexity theory. A lot of these topics in theoretical computer science run into the limitations and possibilities of these and other ideas. You'll then realize as others have suggested, that yes there are some fundamentals taken for granted, but real math is difficult because of the intuition needed in approaching a proof, and the possibility that you could be working on a problem that is unanswerable.