Book recommendations for problem solving
+ a mysterious degree 4 equation
The standard undergrad math curriculum has loads of material to cover: analysis, topology, algebra, differential geometry, PDEs, … the list goes on and on.
But we never specifically practice problem solving!
In this issue, I’ll share my favorite books to practice problem solving specifically.
My two favorite problem books
The Art and Craft of Problem Solving by Paul Zeitz. This is honestly one of my favorite books of all time. It goes through many different strategies to develop mathematical skill and intuition necessary for problem solving. The strategies in the book are highly non-trivial. There are lots of examples and practice problems to get your hands dirty!
Problem Solving Strategies by Arthur Engel. This book has a similar flavor as the first book. It has a lot of strategies to get better at problem solving. The problems in this book are a bit more approachable than the first one.
Online Lists of Problems
The internet has many repositories with interesting problems, freely available (with solutions). Here are a few:
The Center for Education in Math and Computing (CEMC) at Waterloo University has a Problem of the Week for middle-school and high-school students. The CEMC has been running the Problem the Week since I was in middle school (I’m talking 2011) and I have many fond childhood memories of working on these problems.
The CEMC Math Competitions. These are various high-school math contests, ordered by grade-level, with solutions.
The Art of Problem Solving website has problems and solutions from many past math contests.
The Putnam Math Competition past problems. The Putnam is a notoriously difficult math contest for undergrad students. The median score is typically zero. (The point is, these problems are hard, so beware!)
Problem of the Week
In the spirit of problem solving, here’s this week’s problem:
Solve the equation
Got a solution to the challenge problem? Submit it here.
Solution from last week
See here for the solution to last week’s problem. (Special thanks to Peter (Toronto), Matt Lunix (Loveland, OH), and Ibrahim (California) for submitting solutions to this challenge problem.)
Thanks for reading and happy learning! Until next time,
Adithya