A logical approach to discrete math

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1. agentultraJan 2023
   How To Solve It by G. Polya https://press.princeton.edu/books/paperback/9780691164076/ho...

   A Logical Approach to Discrete Math by David Greis and Fred Schneider, https://link.springer.com/book/10.1007/978-1-4757-3837-7

   I'm self-taught so for me it was learning how to write proofs that gave me a big boost in being able to branch out into different area of interest and not give up. :)

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2. agentultraJan 2023
   It’s still ugly! There’s nothing wrong with that. Everyone will have different opinions on these things. Bike shedding will probably never go away.

   The semantics are what matter (at least in most programming languages)!

   To me, syntax wise, I just can’t stand inline type definitions. CrabML becomes close to what I can grok syntax-wise. I spent many years with C++ and I can read TyoeScript… but to me they’re examples of bad syntax, not role models.

   However if you read A Logical Approach to Discrete Math or Programming in the 1990s you’ll know just how syntax matters… most programming languages can’t even reach this level of which is why I think semantics are more important.

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3. agentultraOct 2019
   The Art of Computer Programming

   Structure and Interpretation of Computer Programs

   Purely Functional Data Structures

   Programming in the 1990s

   A Logical Approach to Discrete Math

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4. hodgesrmFeb 2019
   Somewhat dated but...I really like "A Logical Approach to Discrete Math" by Gries and Schneider. It uses an algebraic approach to introduce logic then works its way into number theory, graphs, and sets. There are a lot of good exercises and the topics are highly relevant for CS.

   The content is so valuable that it deserves a year in high school in my opinion, though that is a minority view where I live.

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5. agentultraApr 2017
   I would expect no less even in an introductory text. Mathematics is meant to be precise and formal mathematics even more so. Prosaic pedagogy might suit a liberal arts introduction but it won't help the reader to convince themselves that the statements and theorems proposed are true and valid.

   The syntactic approach is really useful as a programmer. A Logical Approach to Discrete Math[0] teaches programmers how to develop proofs in this style using logic and syntactic substitution. Once shown how easy it is to achieve rigour it is hoped that work-a-day programmers can formulate their own proofs and develop stronger specifications using mathematical tools.

   I'm not a formally trained mathematician and am completely self-taught as a programmer but with some background in set and graph theory I found it approachable. It's certainly a good companion text to learning more practical systems like TLA+ or Lean.

   [0] https://www.amazon.ca/Logical-Approach-Discrete-Math/dp/0387...

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6. tkosanJul 2016
   The book “A Logical Approach to Discrete Math” by David Gries is excellent for learning math on a theoretical level, and for understanding proofs.

   I have found that writing software that automatically solves elementary algebra equations using the techniques humans use is also a very good method for understand how math works at a deep level. Here is a demo of a step-by-step equation solver that I am currently writing:

   https://youtu.be/cy6bwNBkAK0

   Contact me by email if you are interested in learning more about either of these options (my email address is in my profile).

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