The Art and Craft of Problem Solving

What Hacker News says

1. blackbear_Mar 2025
   Not sure which other topics you mean, but "1000 exercises in probability" should keep you busy for a while (one can find the PDF online). For other math oriented riddles, check out "The colossal book of short puzzles and problems" and "The art and craft of problem solving"
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2. jgordJan 2024
   Not free, but in addition to AoPS.com books and website, I highly recommend :

   - Algebra book by Gelfand [ amazon print n demand I guess ]

   - A Decade of the Berkeley Math Circle by Zvezdelina Stankova and Tom Rike

   - The Art and Craft of Problem Solving by Paul Zeitz

   Also have a look at https://mathcircles.org and any math competitions available locally

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3. ForHackernewsJan 2023
   The Art and Craft of Problem Solving https://archive.org/details/the-art-and-craft-of-problem-sol...

   This is only math book I've ever read that teaches the mindset needed to work mathematics problems, rather than mathematical concepts or techniques.

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4. dragon96Jun 2022
   Regardless of which text you choose, I recommend writing proofs (full sentences and all) for the solutions that were harder to come by, or you feel difficulty expressing clearly. And if you can, get some feedback on the proofs. (Happy to take a look at a few if you DM me)

   The process of writing will hopefully help you:

     - build awareness of when your arguments are not airtight or when you make false assumptions
     - modularize your thinking 
     - become more fluent with logical "vocabulary"
   

   As for books, my personal favorites were Problem Solving Strategies (Engel) and Art and Craft of Problem Solving (Zeitz). They're both really approachable, have plenty of examples, and will give you a different perspective on what math can be about.
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5. EmphereJan 2022
   I would like to second this recommendation. For a long time I thought their content was low quality edutainment because of the generally 90s website design and the generic stock photos used for courses(admittedly, that's...a pretty shallow line of reasoning). The courses are usually taught by university professors, have a well thought out lesson plan and have helpful accompanying guidebooks (you can also request course transcripts, I believe). For example, the course linked above is taught by Paul Zeitz based on his book, "The Art and Craft of Problem Solving", which is a classic for learning Olympiad-level problem solving techniques. I've also learned a lot from their history courses.
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6. georgewsingerNov 2020
   People often talk about the importance of problem solving skills, but there's shockingly few resources that analyze the problem solving process from a general point of view (outside of some problem solving domain). Does anyone have any non-orthodox suggestions for books/essays on problem solving?

   Polya's "How to Solve It" and Paul Zeitz's "Art and Craft of Problem Solving" are both great. Are there other resources on this topic that are worth reading?

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