Math Research

To do math research as an undergraduate, find a faculty member whose research interests align with yours, actively engage with their work by reading relevant papers, identify a specific research question within their field, and work closely with them to develop and investigate the problem, utilizing existing mathematical tools and techniques while learning new ones as needed; consider seeking opportunities like Research Experiences for Undergraduates (REUs) to gain further exposure and experience in mathematical research. 

Key steps:

• Explore your interests:

  Browse through different areas of mathematics to find a topic that excites you, such as number theory, topology, analysis, or applied mathematics. 

• Find a mentor:

  Reach out to math professors at your university and inquire about research opportunities, highlighting your interest in their research area. 

• Read relevant literature:

  Familiarize yourself with existing research in your chosen area by reading published papers, focusing on understanding key concepts and open questions. 

• Identify a research question:

  Discuss potential research questions with your mentor, aiming for a focused problem that is manageable yet impactful within the scope of an undergraduate project. 

• Develop a plan:

  Work with your advisor to outline a research plan, including specific goals, methods, and timelines. 

• Learn necessary tools:

  Acquire the mathematical skills needed to tackle your research question, which may involve taking relevant upper-level courses or learning new software packages. 

• Conduct research:

  • Explore examples and counterexamples: Analyze concrete cases to gain insights into the problem. 
  • Apply existing techniques: Utilize established mathematical methods to investigate your research question. 
  • Develop new approaches: If necessary, explore innovative techniques or modifications to existing methods to address your specific problem. 

• Communicate your findings:

  • Present your work: Prepare presentations to share your research progress at departmental seminars or conferences. 
  • Write a research paper: Draft a clear and concise paper detailing your research process, results, and conclusions, with your advisor's guidance. 

Important considerations:

• Start early:

  Begin exploring research opportunities as early as your sophomore year to gain sufficient exposure and build a strong foundation. 

• Be patient:

  Mathematical research can be challenging and may require time to make significant progress. 

• Seek help:

  Don't hesitate to ask your advisor questions and seek guidance throughout the research process. 

• Consider REU programs:

  Look for Research Experiences for Undergraduates (REUs) in mathematics to gain valuable research experience at another institution.

In this video I talk about undergraduate research in mathematics. How much does it matter? What do you all think? -  Aug 9, 2020 - The Math Sorcerer  

A quick look at the process of writing and publishing a math research article from start to finish. This paper was typical in some ways, atypical in other ways. Aug 25, 2023 - Chris Staecker

People usually think math is a dry uncreative subject. It's really not at all though. Doing math research was surprisingly emotional. There's a joy to doing it that's hard to explain. Mar 13, 2021 - Mithuna Yoganathan