Intro to Math Research Course

As part of our MAA Tensor Women & Mathematics Grant, Elena Pavelescu and I developed a course to introduce students to mathematical research. This was a one credit hour seminar course, with a suggested prerequisite of second-semester calculus. Many of the students enrolled in our course were not mathematics or statistics majors. Below is an outline of the course content. Each week, the students submitted a reflection on their mathematical journey that week. This could be related to the content covered or to their progress on their individual research topics. We found that it was helpful to have required individual meetings with the students on their research topics early and often.

Introduction to the Class

• Syllabus

• We watched the following video in class and discussed it: https://www.youtube.com/watch?v=UitkuhpDUpc (shortest version)

• Additional resources:

  • Interview based on the original talk: https://www.quantamagazine.org/math-and-the-best-life-an-interview-with-francis-su-20170202/ (medium version)

  • Transcript and link to the original talk: https://mathyawp.wordpress.com/2017/01/08/mathematics-for-human-flourishing/ (longest version)

• Assignment:

  • We recorded eight videos with introductions to possible research topics. The students were to watch the videos and write a reflection on the videos and which topics appealed to them.

Introduction to LaTeX

• We watched and discussed a video on "What is math research?" https://www.youtube.com/watch?v=BkvunRrwiqw

• We introduced Overleaf as a tool for working with LaTeX documents and collaboration. We learned some of the commands by working through the following exercise. 

  • LaTeX Exercise tex  

  • LaTeX Exercise pdf 

• Additional resources:

  • Overleaf https://www.overleaf.com/

  • The Not So Short Introduction to LaTeX by Tobias Oetiker https://tobi.oetiker.ch/lshort/lshort.pdf

  • Detexify https://detexify.kirelabs.org/classify.html

  • The Comprehensive LaTeX Symbol List by Scott Pakin https://tug.ctan.org/info/symbols/comprehensive/symbols-a4.pdf

  • The Beamer Class by Till Tantau, Joseph Wright, and Vedran Miletic https://tug.ctan.org/macros/latex/contrib/beamer/doc/beameruserguide.pdf 

• Assignments:

  • Modify a template from Overleaf to create a Resume/CV.

  • Reflection on that week's mathematical journey with a decision on which research topic to work on.

Ethical Guidelines

• We read and discussed the AMS Ethical Guidelines in class. http://www.ams.org/about-us/governance/policy-statements/sec-ethics 

• Assignments:

  • The University of South Alabama requires students engage in research to complete Responsible Conduct of Research training through the CITI program. Completion of this training and upload of the completion certificate was required.

  • Reflection on that week's mathematical journey.

Advice on Mathematical Writing

• We selected some examples from Advice on Mathematical Writing by Keith Conrad and discussed them in class. 

  • Writing Exercise tex   

  • Writing Exercise pdf  

• Additional resources

  • "Advice on Mathematical Writing" by Keith Conrad https://kconrad.math.uconn.edu/blurbs/proofs/writingtips.pdf 

  • "Mathematical Writing Tips" by Robert Foote http://persweb.wabash.edu/facstaff/footer/Courses/Expectations/WritingTips.pdf 

  • "Some Guidelines for Good Mathematical Writing" by Francis Edward Su http://digitaleditions.walsworthprintgroup.com/publication/?m=7656&i=268254&p=20&ver=html5 

  • Mathematical Writing by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts https://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematical_writing.pdf 

• Assignment

  • Reflection on that week's mathematical journey.

Giving a Presentation

• We watched and discussed selected videos from "Technically Speaking." http://techspeaking.denison.edu/Technically_Speaking/Home.html 

• Additional resource:

  • "Tips on giving talks" by Jordan Ellenberg https://quomodocumque.files.wordpress.com/2010/09/talktipsheet.pdf 

• Assignments:

  • Prepare a presentation for the next week on their research topic and any initial progress.

  • Reflection on that week's mathematical journey.

Student Presentations

• Students gave their prepared presentations during class.

• Assignment:

  • Reflection on that week's mathematical journey.

Introduction to Computing Tools

• We focused on Python notebooks. We started with a basic loop template and adjusted it to make more complicated examples.

  • A summary of arithmetic operators in Python. https://www.w3computing.com/python/arithmetic-operators/

  • Loop template

  • Class examples 2022 

  • Class examples 2023 

• Additional resources:

  • https://www.wolframalpha.com/ 

  • https://jupyter.org/try

  • https://www.online-python.com/

  • https://colab.research.google.com/ 

• Assignment:

  • Reflection on that week's mathematical journey.

Undergraduate Research Programs

• We discussed research opportunities at our institution and other summer programs.

• Additional resources:

  • List of REUs in math 

  • Lists of REUs in other subjects 

  • REUs in medicine 

  • https://colab.research.google.com/ 

• Assignment:

  • Write a mock proposal for summer research.

  • Reflection on that week's mathematical journey.

Other Activities

• Especially toward the end of the semester, we had other activities, as they fit into the schedule.

  • Colloquium speakers giving guest lectures on their mathematical journey

  • Field trip to the Undergraduate Research Symposium on campus

  • Panel discussion with graduate students

• Assignments:

  • Reflection on that week's mathematical journey. If a colloquium speaker gave a guest lecture that week, the students should also attend the colloquium and include a discussion of it in their reflection. Alternative videos were provided for students who could not attend the colloquium.

  • The final assignment was a paper and a presentation given during the final exam period.