What makes putnam-style problems 'different' from other problems?

  • Thread starter DrWillVKN
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In summary, mathematical competitions have a specific style and time limit, but they do not necessarily reflect one's ability to conduct mathematical research. While being good at competitions may require a strong understanding of theory and problem-solving skills, it is not the only measure of success in research. Similarly, being a slow thinker or not excelling in competitions does not mean one cannot excel in research.
  • #1
DrWillVKN
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I have only begun to study mathematics, and the competitions look pretty exciting. I heard the math competition style problems follow a certain style and follow specific heuristics of solving, compared to non competition problems.

So what is this 'difference'? Besides the fact that they were written using known results and are meant to be solved within 6 hours, is there really a difference?

Is it possible for someone to just do loads of putnam-style problems and do well on it? I know it is very, very useful to get into that problem solving sort of mindset when researching mathematics, but is it necessary for someone to be able to solve putnam-style problems in order to do well in mathematical research?

So if you aren't good at doing putnam problems, does that mean you aren't a good mathematician in general?
 
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  • #2
I don't know what putnam is, but most of the time these mathematical competitions have nothing to do with research.

Being good in a mathematical competition means that you know a lot of theory (like the AM-GM inequality and others), that you have solved a lot of problems and that you have a quick mind.

However, research is (in my limited experience about something else). Of course you'll need to know a lot of theory to be able to do research. However, research doesn't mean that you can solve any problem in 6 hours. In fact, some problems will take you weeks to solve. It also requires a lot of creativity. Competitions want you to be creative too, but not so much.

I have met a lot of professors who claimed that they were really "slow" thinkers. That means that they had to do a lot of effort to understand a problem in all it's complications. That means that they would be very, very bad in competitions. Nonetheless, they were really smart and good in their research.

So, I would say: no, if you aren't good at competitions, then you can still be good in research.
 
  • #3
While I agree to most of what micromass said, I don't agree to this: but most of the time these mathematical competitions have nothing to do with research. Being good in a mathematical competition means that you know a lot of theory.

This can be true, but not always. You can be a good researcher although if you are not good at competitions, but, mathematical competitions has everything to do with math research. Normally, Olympiad type questions are open-ended, just like actual research.

I won't stick to the fact that one should be good at mathematical "theory" to be good at competition, I'm one counter example.

To answer your question: No, it is neither necessary nor sufficient to be able to solve putnam-style problems to be a good math researcher. But remember, if you can be good at it, not by simply using the tactics, but by understanding thoroughly from where it came, then you can shine in areas other than math, like Theoretical Computer Science, Physics, Engineering, etc,.
 
  • #4
There are 12 Questions on the test and you have a seemingly reasonable 6 hours. If the Putnam was graded like a normal test (65% to pass in this case at least 79 points) then only 30 undergraduates in the whole country were going to pass. Almost nobody is actually "good" at these questions because the test is extremely difficult. Don't beat yourself up if you can't do them consistently.
 
  • #5


Putnam-style problems are different from other problems in several ways. Firstly, they are designed specifically for mathematical competitions, which means they often have a level of difficulty and creativity that sets them apart from other problems. Additionally, they often require a combination of different areas of mathematics and may involve more complex concepts and techniques.

Moreover, Putnam-style problems often have a unique structure and format that sets them apart from other problems. They may involve multiple parts or require a specific approach to solving them, such as using specific heuristics or techniques. This makes them challenging and requires a different way of thinking compared to traditional mathematical problems.

While practicing and solving Putnam-style problems can certainly improve one's problem-solving skills and mathematical thinking, it is not necessary to be able to solve these problems in order to be successful in mathematical research. Mathematical research involves a wide range of skills and approaches, and being able to solve Putnam-style problems is just one aspect of it.

Furthermore, being good at solving Putnam-style problems does not necessarily mean one is a good mathematician in general. These problems may require a specific set of skills and techniques, but they do not encompass all aspects of mathematics and do not determine one's overall mathematical ability.

In conclusion, Putnam-style problems are unique and challenging mathematical problems designed for competitions. While they may require a different approach and set of skills, they do not define one's mathematical ability or determine success in mathematical research.
 

1. What exactly is a Putnam-style problem?

A Putnam-style problem is a type of mathematical problem that is designed to test students' problem-solving skills and their ability to think creatively and critically. These problems are typically more challenging and complex than traditional math problems, and often require students to apply multiple concepts and techniques to arrive at a solution.

2. How are Putnam-style problems different from regular math problems?

Putnam-style problems differ from regular math problems in several ways. Firstly, they tend to be more open-ended and require a deeper understanding of mathematical concepts. They also often involve multiple steps and require students to come up with their own approach to solving the problem, rather than following a set formula or algorithm.

3. What skills do Putnam-style problems help develop?

Putnam-style problems are great for developing critical thinking, problem-solving, and analytical skills. They also help students develop their creativity, as they often require thinking outside the box to arrive at a solution. Additionally, these problems can help students improve their ability to work under pressure and manage their time effectively.

4. Can anyone solve Putnam-style problems, or do you need a specific level of mathematical knowledge?

While Putnam-style problems do require a strong foundation in mathematics, anyone can work on solving them, regardless of their level of knowledge. In fact, these problems are designed to challenge students and push them beyond their comfort zone, helping them improve their skills and expand their understanding of math concepts.

5. Are Putnam-style problems only for math majors or can anyone benefit from solving them?

Putnam-style problems are not limited to math majors and can benefit anyone who enjoys solving challenging problems. In fact, many universities and colleges have Putnam-style problem-solving groups or clubs that welcome students from all majors to participate. These problems can help students develop valuable skills and improve their problem-solving abilities, regardless of their major or career aspirations.

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