Getting better at mathematical problem solving

[JasonJo]

I am doing very well in school, but I know if I want to get into the top tier graduate schools, i need to get a lot better.

I recently purchased the Red Book and the Green Book of Mathematical Problems (it's pretty much 200 Putnam type problems/mathematical olympiad type problems). And I did horrendously...like, really badly.

Whatever, the point is, I want to get a lot better at this type of problem solving and problem solving in general. Can anyone reccomend a book (i've read some of Polya's book, but I'm looking for something that involves more material than theory and conceptual problem solving) to help me get better with my problem solving?

I don't understand why there is such a huge disparity between my grades and how I did on these problems. For maybe 3 or 4 i got half way to the solution, but the rest I either had no clue where to even begin and even after looking at the hints i had no idea. A lot of the problems involved identities I've never seen before, or a lot of complex summations, which astounded me.

any help is appreciated

 

[Aaron Barnard]

One of the best books for developing problem-solving skills for mathematics competitions is "Problem-Solving Strategies" by Arthur Engel. This book covers topics ranging from basic problem solving techniques to more advanced ones, such as mathematics induction and counting techniques. It also provides many examples and problems to help you practice your skills. Additionally, it is a great resource for coaching others in problem-solving. Other great books include "Mathematical Olympiad Challenges" by Titu Andreescu and "The Art and Craft of Problem Solving" by Paul Zeitz. These books provide more specific information on topics such as inequalities, combinatorics, and number theory.

 

[tacman]

First of all, it's great that you recognize the importance of improving your problem solving skills and are actively seeking resources to help you do so. It's also important to remember that problem solving is a skill that takes time and practice to develop, so don't be discouraged by your initial performance on these difficult problems.

One suggestion I have is to focus on building a strong foundation in the fundamentals of mathematics. This can include practicing basic algebra, geometry, and calculus problems, as well as familiarizing yourself with important theorems and concepts. Once you have a solid understanding of these fundamentals, you will be better equipped to tackle more challenging problems.

In addition to practicing on your own, it can also be helpful to work with a study group or tutor who can provide guidance and feedback on your problem solving techniques. They may also be able to recommend specific resources or materials that have been helpful to them in improving their own problem solving skills.

Another suggestion is to try approaching problems from different angles and perspectives. This can help you develop a more creative and flexible approach to problem solving. You can also try breaking problems down into smaller, more manageable parts and tackling them one at a time.

Finally, don't be afraid to ask for help or seek out additional resources. There are many online forums and communities where you can connect with other math enthusiasts and share tips and strategies for problem solving. Additionally, there are many books and resources specifically designed to help students improve their problem solving skills, so don't hesitate to do some research and find one that resonates with you.

Keep practicing, stay determined, and don't be discouraged by setbacks. With dedication and hard work, you can definitely improve your problem solving abilities and achieve your goals. Best of luck!