What are some open problems that would make a good honors thesis.

In summary, an undergraduate interested in topology/differential geometry is looking to complete an independent study in the subject. They are seeking open problems for original research that have not been explored by other mathematicians yet. However, this may be a challenging task that requires a significant amount of time, energy, and supervision. The conversation also mentions two books that may be helpful in finding potential problems. Finally, there is a question about the progress of solving problems from one of the books.
  • #1
Silvers931
12
0
I'm interested in topology/differential geometry and before I eventually graduate I am looking to complete an independent study in the subject.

What are some open problems that would be a good fit for an undergrad like me?
 
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  • #2
You mean in the sense of doing a survey about the problem?
 
  • #3
Well, original research, like a topic other mathematicians haven't got around to yet.
 
  • #4
This will take a lot of time, energy and supervision unless (and even if) you have an exceptional background. It is not just a matter of intelligence; graduate-level Mathematics is exceptionally -technical and it is very difficult even to even get definitions you can understand. I don't mean to dissuade you, but just to let you know what to expect.
 

1. What are some examples of open problems that would make a good honors thesis?

Examples of open problems that would make a good honors thesis vary depending on the field of study, but some common examples include exploring the potential effects of climate change on a specific species or ecosystem, investigating the effectiveness of a new medical treatment or technology, or analyzing the impact of a social or political issue on a community.

2. How do I choose an open problem for my honors thesis?

Choosing an open problem for your honors thesis involves identifying a gap in current knowledge or understanding in your field of study. This can be done by reviewing recent research and identifying areas that have not been extensively studied, or by discussing potential topics with your advisor or professors.

3. How can I ensure that my chosen open problem is significant enough for an honors thesis?

To ensure that your chosen open problem is significant enough for an honors thesis, it is important to consider the potential impact or contribution of your research. This can include the potential to advance knowledge or understanding in your field, or the potential to have real-world applications or implications.

4. Can I work on an open problem that has already been researched?

Yes, you can work on an open problem that has already been researched. However, it is important to ensure that your approach or methodology is unique and adds to the existing body of knowledge on the topic. Your thesis should also clearly state how your research differs from previous studies and why it is still relevant.

5. How can I effectively structure my honors thesis around an open problem?

To effectively structure your honors thesis around an open problem, it is important to clearly define your research question and objectives. You should also carefully plan and organize your methodology, data collection and analysis, and discussion of results to effectively address the open problem and make a strong argument for your findings.

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