The Art and Craft of Problem Solving
by Paul Zeitz · first published 1999
80% recommend20% neutral
Why HN recommends it
Practical guide to mathematical problem solving that teaches strategies through challenging, approachable problems. Suited to anyone learning Olympiad-style math or building a problem solver's mindset.
Summarised by Claude from recommending comments
This text blends interesting problems with strategies, tools, and techniques to develop the mathematical skill and intuition necessary for problem solving.
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…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?
on “Problem Solving Techniques” ↗…facing: 1. You most likely wouldn't have had a problem solver's education. So the first thing to do would be do start understanding how problem solvers approach Mathematics. I suggest two books: - The Art and Craft of Problem Solving by Paul Zeitz - How to Solve It by George Polya There are also others, e.g., http://www.amazon.com/Math-Olympiad-Resources/lm/1SWDJ5NA047... Keep in mind that most proofs you see are highly polished…
on “Ask HN: How Do I Get Math?” ↗…take this opportunity to give a small suggestion :-) I was wondering if you guys could make Mathematics more problem solving centric (see www.artofproblemsolving.com for an example approach. Also "The Art and Craft of Problem Solving" by Paul Zeitz and George Polya's "How to solve it") Most of the Mathematics in school curriculum is just plug n' chug work at a slightly higher level. Students do not get any insights into how really…
on “How a Tech Non-Profit Became the Hottest Ticket in Silicon Valley” ↗…Mathematics by Knuth, which contains a lot of Mathematical tools and techniques useful in areas of Computer Science, I'd recommend the following to learn how good problem solvers approach Mathematics: 1. The Art and Craft of Problem Solving by Paul Zeitz. 2. How to Solve It by George Polya. I'd also recommend learning any of the competition Mathematics topics like number theory, combinatorics or geometry as base material to improve your…
on “Ask HN: Learn Math the Hard Way” ↗…That homepage isn't very informative, but you can search for any topic and find explanations and problems that can be solved from that. For example: radical axis [2] If you're looking for a book, The Art and Craft of Problem Solving by Paul Zeitz is the most recommended. [1] http://www.artofproblemsolving.com/wiki/index.php/Main_Page [2] http://www.artofproblemsolving.com/wiki/index.php/Radical_ax...
on “Tricki, a repository of mathematical know-how” ↗…analysis,testing and debugging w/trace routines, I/O algorithms) but of course in much more detail with much harder problems. To understand the first few hundred pages on mathematical preliminaries, the books "The Art and Craft of Problem Solving" by Zeitz and "Concepts of Modern Mathematics" by Stewart, were essential, both of which were recommended here in other book list posts. I also had already read the CS:APP book which covers x86-64 assembly…
on “The most mentioned books on Stack Overflow” ↗What you need is a book on how to solve problems using a strategy, like the first few chapters of 'The Art and Craft of Problem Solving' by Zeitz and 'How to Solve it' by Polya. The Zeitz book specifically refers to the issues in abstract word problems and strategies for understanding them. 'Introduction to Mathematical Reasoning' by…
on “University of Tokyo Graduate School Entrance Exam – Mathematics (2016) [pdf]” ↗I really recommend "The Art and Craft of Problem Solving" by Paul Zeitz, who coached the winning USA team in the International Math Olympiad: https://www.goodreads.com/book/show/593458.The_Art_and_Craft... One of the things he focuses on is repeatedly challenging…
on “Ask HN: How do you guys develop mental toughness?” ↗I'm a big fan of Art and Craft of Problem Solving by Zeitz. The main downside is that there isn't an official solution manual, so checking your work takes a little more work. But one of the main upsides is that there isn't an official solution manual,…
on “Classic Mathematics Books for Lifelong Learners” ↗I'd recommend "The Art and Craft of Problem Solving" by Paul Zeitz, who coached the U.S. International Mathematical Olympiad team. https://www.amazon.com/exec/obidos/ASIN/0471789011/artofprob...
on “Ask HN: Which books teach mental models?” ↗…contains some nice problems, with solutions by (I repeat myself) one of the finest minds in the business. It's also quite cheap. If you're interested in this, you should also look at Paul Zeitz's "The art and craft of problem-solving"; it has more pages and more substance to it, but it's twice the price and wasn't written by a Fields medalist. ---- Pedantic note: Tim Gowers, not Tom.
on “The Mind of a Mathematician” ↗I'm re-reading these classics: 1. SICP(The Structure and Interpretation of Computer Programs) 2. The Art and Craft of Problem Solving by Paul Zeitz 3. Tribe of Hackers: Cybersecurity Advice from the Best Hackers in the World --- [1]https://github.com/allenleein/knowledge-base/blob/gh-pages/C... [2]https://github.com/allenleein/knowledge-base/blob/gh-pages/C...…
on “What's your favorite technical book to read during this time of home quarantine?” ↗…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.
on “Masterclass on mathematical thinking” ↗…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.
on “Ask HN: How to learn mathematical proofs from scratch?” ↗…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
on “Ask HN: Free online courses for gifted maths students” ↗