Creating Your Own Problems: Tips and Guidelines

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In summary, creating one's own problems is considered the best way to develop and train problem solving skills. A suggestion for becoming an "active" problem solver is to get a job or read books such as "Mathematics and Plausible Reasoning" and "How to Solve It" by G. Polya. Some examples of problems that can stimulate problem solving abilities are pigeonhole principle problems, strategy problems, and number theory problems. It is also helpful to think in groups and books such as "Math Olympiad Challenges" and "Number Theory" can be found at local bookstores.
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symplectic_manifold
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They say the best way to develop and train problem solving skills is by creating one's own problems.

I'm still a "passive" problem solver but I'd like to learn solving problems in an "active" way.

Could you give me some advice, name some guidelines on how to create new, own problems?

Thanks in advance. :smile:
 
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  • #2
Try getting a job.
 
  • #3
Try looking at these books:

1) Mathematics and Plausible Reasoning by G. Polya
2) How to Solve It by G. Polya
 
  • #4
Some types of problems that i create and jog my brain are
1) pigeonhole principle problems
2) strategy problems
3) number theory problems (remainders, in-my-head multiplication)
*algebra problems don't seem to stimulate (move this number to the other side isn't really thinking)
I find that thinking in groups really helps my problem solving abilities
If you go to your local bookstore
you'd probably be able to find...
1) Math Olympiad Challenges
2) Number Theory (part of the Dover Collection)
 

1. What is the purpose of creating your own problems?

The purpose of creating your own problems is to challenge yourself and improve your problem-solving skills. By creating your own problems, you are able to identify areas where you may struggle and work on finding solutions. It also allows you to think critically and creatively, which are important skills in any scientific field.

2. How can I come up with original and challenging problems?

One way to come up with original and challenging problems is to think about real-world issues or current research topics in your field. You can also try brainstorming with a group or discussing potential problems with your peers or mentors. Don't be afraid to think outside the box and explore multiple solutions to a problem.

3. What are some tips for creating effective problem statements?

Effective problem statements should be clear, concise, and specific. They should also include the relevant background information and clearly define the problem to be solved. It's also helpful to break down larger problems into smaller, manageable parts and to make sure the problem is feasible and can be solved using available resources.

4. How can I ensure that my created problems are relevant and meaningful?

To ensure that your created problems are relevant and meaningful, it's important to consider the impact they could have on your field or society as a whole. You can also seek feedback from colleagues or experts in the field to ensure that the problem is addressing a current issue or gap in knowledge. Additionally, conducting thorough research and staying up-to-date on current developments in your field can help you create more relevant problems.

5. How can creating my own problems benefit my scientific career?

Creating your own problems can benefit your scientific career in several ways. It can help you develop critical thinking and problem-solving skills, which are essential in any scientific field. It can also showcase your creativity and ability to think outside the box, which can be attractive to potential employers or collaborators. Additionally, solving your own problems can lead to new discoveries and contributions to your field, which can enhance your reputation and career prospects.

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