Problem-solving strategies
by Arthur Engel · first published 1998
100% recommend
Why HN recommends it
An Olympiad-style problem collection that teaches competition problem-solving techniques through worked problems. It is fun and serves as a good step up for those preparing for math competitions or discrete math.
Summarised by Claude from recommending comments
Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem-solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," "pro
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Bunch of problems like this are in the book "Problem-Solving Strategies" by Arthur Engel [1], I believe even including this particular one. Fun book. [1]https://www.google.com/books/edition/Problem_Solving_Strateg...
on “My Favorite Math Problem” ↗If you are looking for a physical book, try Problem Solving Strategies (http://www.amazon.com/Problem-Solving-Strategies-Problem-Boo...) or Problem Solving Through Problems (http://www.amazon.com/Problem-Solving-Through-Problems-Larso...).
on “Ask YC: Math problems” ↗…best way to prepare imo is to just do proofs between now and the start of the course. Try to find practice proof problems online and see if you can do them or find an entry-level book on discrete math. Problem-Solving Strategies by Engel is a good but slightly more advanced book for a beginner.
on “Ask HN: Resources to learn real analysis?” ↗Problem-Solving Strategies by Arthur Engel. It's more than a textbook and not easily absorbed. The book + the internet is a powerful combination for not just learning cool math skills but building mental models/ problem framing…
on “Ask HN: Recommend a maths book for a teenager?” ↗After reading all the comments I am sharing my choices 1. The foundations of mathematics by Stewart and Tall 2. Problem Solving Strategies by Arthur Engels 3. Journey into Mathematics by Rotman 4. Concrete Mathematics by Knuth et al.
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗…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.
on “Ask HN: How to learn mathematical proofs from scratch?” ↗…There are a lot of free high-quality resources on the wiki, and they sell courses and books. A couple classic books: https://www.amazon.com/Art-Craft-Problem-Solving-3E/dp/11194... https://www.amazon.com/Problem-Solving-Strategies-Problem-Bo... And obviously, competition problems! For example, this is the AMC: https://amc-reg.maa.org/default.aspx; competition websites usually have an archive of past editions freely available.…
on “A public school in Florida built America’s greatest math team” ↗…much on increasing intelligence, but on let's call it "educating" intelligence - thinking skills. In this category I would recommend (without any scientific evidence behind): - Learning yourself about Problem Solving Strategies - Reading (fiction and non-fiction) - Writing and summarizing - Reading about Skepticism, Critical Thinking, The Scientific Method or in general Epistemology and trying to use them in your tasks You…
on “Ask HN: Ways to increase mental sharpness or intelligence?” ↗…books devoted to Olympiad preparation, there are websites completely devoted to Olympiads, there are freely available problems sets (with complete solutions). To name the few: Hungarian Problem Books, Problem-Solving Strategies, Challenging Problems in Algebra, books by Titu Andreescu - a former US IMO coach, who published a lot of books on math and IMO prep, http://www.cut-the-knot.org/
on “Calculus For The People” ↗