Math Undergrad Thesis Topic Advice

In summary, the conversation discusses the topic of choosing a topic for an undergraduate thesis in the field of applied mathematics. The speaker is a junior in an Applied Math program who is interested in pursuing a Ph.D after completing their undergrad. They mention the Math Subject GRE and their lack of formal introduction to topics like abstract algebra and topology. After talking with their adviser, they are considering a thesis topic that involves topology in preparation for the exam. They are seeking advice on areas of applied topology that would be suitable for an undergraduate thesis, such as differential geometry, soliton, non-linear partial differential equations, and numerical methods. The speaker is also advised to look in the applied math section of the library and consult with professors in the field.
  • #1
gungywamp
11
0
Hello everyone, I was wondering if anyone with more experience than I could give some advice about choosing a topic for my undergrad thesis.

I'm currently a Junior in an Applied Math program, and I am interested in going to graduate school for a Ph.D after I complete my undergrad. I am aware that I should be taking the Math Subject GRE, and that there are a few topics on the exam that I have not been formally introduced to, specifically abstract algebra and topology. I plan to take the exam near the end of the 2011 fall semester, and I will be able to take a course in abstract algebra during the fall. After some talks with my adviser, I have come to the conclusion that it would be worth considering a thesis topic that involves topology, so that I will be forced to do some independent study with direction before the exam.

This is where my question comes in. As a student of applied mathematics, I am most interested in applications, and being relatively uninformed about topology, I was wondering if there are any areas of the field that would appeal to an applied math major. I am still open to just buying some books and studying on my own so that I can free myself up to do a thesis on something I know I am interested in (e.g., pde's, modeling, mathematical physics), but I am still weighing my options. Any advice?

TLDR: What kinds of topics are there in applied topology that would be good for an undergraduate thesis?
 
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  • #3
we share the same problem..until now i can hardly find a thesis topic in applied math...i don't know...i still don't know to which field i should focus..heeelp..
 
  • #4
Google it! I googled this: research topics in mathematical physics and found this link
http://www.ma.hw.ac.uk/maths/Research/resdet.html

there are tonnes of other stuff, just google it.
 
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  • #5
http://en.wikipedia.org/wiki/Soliton" seem to be an active area of applied math research. Also non-linear partial differential equations and numerical methods. On the more physics side there are things like Hamiltonian dynamics, fluid dynamics etc.

You may want to look in the applied math section in the library and chat to some professors in the field

EDIT: you said with applied topology. Sorry these have nothing to do with topology. Although a little bit of geometry and topology come into Hamiltonian dynamics and symplectic geometry.
 
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What are some tips for choosing a math thesis topic?

There are a few things to keep in mind when choosing a math thesis topic. First, think about your interests and strengths within the field of math. It's important to choose a topic that you are passionate about and have some background knowledge in. Second, consider the current research and trends in math and choose a topic that is relevant and has the potential for further exploration. Finally, talk to your advisor or other professors for their input and suggestions.

How do I narrow down my research idea for a math thesis?

To narrow down your research idea, start by doing some preliminary research on potential topics. This can help you identify any gaps in the existing literature and narrow down your focus. You can also brainstorm with your advisor or other math faculty for their input. Additionally, consider the resources and time available for your thesis and choose a topic that is feasible within those constraints.

What are some common mistakes to avoid when choosing a math thesis topic?

One common mistake is choosing a topic that is too broad or too narrow. A broad topic can be overwhelming and difficult to cover thoroughly in a thesis, while a narrow topic may not have enough material for a comprehensive study. Another mistake is choosing a topic that is too similar to an existing study, as this may not contribute significantly to the current research. Lastly, make sure to choose a topic that you are genuinely interested in and motivated to work on.

How can I ensure that my math thesis topic is original and innovative?

To ensure that your thesis topic is original and innovative, it's important to do thorough research on existing literature in your chosen area of math. This will help you identify any gaps or areas that have not been extensively studied. Additionally, brainstorm with your advisor or other faculty members for potential new angles or perspectives on a topic. Finally, make sure to incorporate your own ideas and insights into your research to make it unique.

What resources are available to help me with my math thesis topic?

There are many resources available to help you with your math thesis topic. Your advisor and other faculty members are great sources of guidance and support. Additionally, your university library and online databases can provide access to a wide range of research materials. You can also attend conferences and workshops to learn about the latest developments in math research and network with other researchers in your field.

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