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Reddit mentions of Problem-Solving Strategies (Problem Books in Mathematics)

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Reddit mentions: 6

We found 6 Reddit mentions of Problem-Solving Strategies (Problem Books in Mathematics). Here are the top ones.

Problem-Solving Strategies (Problem Books in Mathematics)
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Found 6 comments on Problem-Solving Strategies (Problem Books in Mathematics):

u/rfurman · 12 pointsr/math

First, consistently solving A1 and B1 is a great start! Puts you well above the typical. Be sure to pay attention to how you write it up: Putnam graders are very strict and solutions most often get 0, 1, 9, or 10 points. Be also aware of what your goals are and don’t get anxious, you’re not looking to solve everything, so it's good to fully solve one problem before moving on. Putnam problems in particular often have short clean solutions that are really satisfying to find.

You also can't beat just working through problems. Putnam 1985-2000 by Vakil, Kedlaya, Poonen is fantastic as it gives many ways of solving or approaching each of the problems. It also gives just the right level of hints. This way you can learn both by working through the problem and by seeing the different perspectives. For example, with a single problem there may be a long brute-force solution, a quick but hard to discover solution, and a quick solution based on advanced math (you can use most things that come up in an undergrad math curriculum, even elliptic curves).

The Art and Craft of Problem Solving is a great read for general strategies and practice, and will remain relevant throughout any later work.

Mathematical Olympiad Challenges by Andreescu and Gelca shows off a few major problem solving styles and has a great selection of problems. I studied it in high school and it ended up being very important for me getting Putnam Fellow.

Earlier I had also studied Problem-Solving Strategies but that may be too big and not as focused on Putnam type of problems

u/JimJimmins · 6 pointsr/math

It's difficult to make recommendations without being certain of what you actually know and what you imagine mathematics to be like. A lot of university-level mathematics is technical and requires familiarity of high-level concepts. This is in contrast to softer popular mathematics, which is more related to solving problems and contest questions. One of the things I've noted about pre-university students passionate about mathematics is that they assume that the subject is only about problem-solving and fail to take into mind the level of technical knowledge that must be learnt and memorized to be a mathematician.

If you're simply looking for problems to solve, try The Art and Craft of Problem Solving by Zeitz or Problem Solving Strategies by Engel. Generally any book geared to the Olympiad or regional competitions will be alright. Here, you're not looking for a specific body of knowledge, but rather an approach to thinking and persevering when handling tough problems.

But if you're looking to learn more about 'technical' mathematics, you'll need to know the basics of numbers and sets. Numbers & Proofs by Allenby is a good introduction, using an approach that gets you to actively solve problems. Once you get past that, then you can try your hand on analysis or group theory or linear algebra or even basic graph theory. But keep in mind that with 'technical' mathematics, all knowledge is built on understanding of previous fields, so don't rush through it or you'll get discouraged by any difficulty or unfamiliarity you'll encounter.

u/nikoma · 4 pointsr/math

Hi, here I will post some great books, some free (by Santos), some not (others).

Junior problem seminar: Santos

Number Theory for Mathematical contests: Santos

The Art and Craft of Problem solving: Zeitz

Problem-Solving Strategies: Engel

Mathematical Olympiad Treasures: Andreescu, Enescu

Mathematical Olympiad challenges: Andreescu, Gelca

Problems from the book: Andreescu

Those are more or less the "general" books, they always contain the main topics of mathematical olympiads, they usually aren't focused on just one topic, for one-topic books see here: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=319&t=405377

u/[deleted] · 2 pointsr/math

My favorite is Problem Solving Strategies. Has a great mix of instruction with loads of problems for you to practice with and covers most problem solving areas.

If you are training for competition math, picking up books of old problems also helps -- but while any problem solving book is going to be geared at a student training for competitions, problem solving strategies is good regardless of your purpose.

u/TheBB · 2 pointsr/math

I can heartily recommend Engel's book (even for people who don't want to go to a competition, there's a lot of fun problems in there).

u/NoCondom · 1 pointr/askdrugs

Study chess opening books, learnthe fridrich method and read this book from cover to cover.

Then, go around claiming to be a genius.