Final Exam Research Presentations

If I have seen further it is only by standing on ye shoulders of giants.
[Isaac Newton in a Letter to Robert Hooke, dated 5 February 1675]

Goals and Objectives: To complete the theme of what mathematics is, you will choose a topic and see how mathematics relates to it. We have spent time in the statistics segment showing diverse perspectives as well as critically analyzing information. In this light it might seem difficult to make progress in understanding a topic or issue. However, to flip this perspective, we will conclude the semester by examining some of the amazing mathematical breakthoughs that have already occurred and how they have helped humanity. You may work with at most one other person.

You will create an attractive and professional two-page or three-page typed product (plus an annotated bibliography) that explores the interesting and important mathematical connections. Be sure that you research and include:

  1. information with clear mathematical connections
  2. information that is in your own words
  3. mathematical breakthroughs and their timeframes (can use ~ or a range of dates if a specific year is not known)
  4. real-life applications and modern significance
  5. important contributions from diverse scientists or mathematicians and diverse cultures
  6. interesting mathematical pictures that relate
  7. related equations
  8. bring in connections from at least 2 of our 3 segments (geometry of the earth and universe, personal finance and beyond, consumer statistics and probability) on geometry, algebra, statistics, probability
  9. attractive and professional two-page or three-page typed product and an annotated bibliography
  10. depth, clarity, and creativity
  11. Many different types of sources, including scholarly references and library sources. Submit an annotated bibliography of all of the sources, with annotations explaining the mathematical connections in the source, where the pictures are originally from, whether the source is a scholarly reference. Use as many pages as you need for the annotated bibliography.

Here are two sample research products
Mathematics and Film by Kaitlyn Colucci (I especially liked the visual presentation and the deep connections to geometry. The connections to statistics and probability could have been even more in depth and replaced some of the timeframe elements that are not as mathematical)
Mathematics and Cancer by Maggie Hooks and Syd Shadrick (I especially liked how much research they brought in and how they organized it, including identifying which segments it connected to. The 2009 research should have also said it connected to statistics)
These were created in Microsoft Word and Google Slides, respectively.

You will communicate your expertise in a research presentation session on the "final exam" day. Your 2-page or 3-page product and your annotated bibliography will be taped up to the wall. We will divide up the class into two research sessions. During your session, you must stand by your product and annotated bibliography (which will be taped to the wall) to to present your project to classmates and answer their questions (and your answers must demonstrate expertise of your topic). The presentation component typically involves a group of 1 or 2 students at a time listening to and looking at your project so they can take notes for peer review. During the other session, you will talk to others about their research and fill out peer review. If you work with someone else, you will each be in different research sessions.

I am happy to help in office hours and you can also make an appointment through the library Research Advisory Program (RAP)

Your grade will be based upon the criteria above as well as the depth, clarity, and creativity of the product, annotations, explanations, mathematics, peer review and self-evaluations. Here is a grading rubric. As per the syllabus, participation in the research presentations is mandatory to pass the class.

References and Topic Suggestions

Your research may take the form of topics in the book that we did not cover, further examination of something we did, or something else related to mathematics. I encourage you to be creative and find a topic that relates to mathematics that you are interested in. I am happy to give you some suggestions of topics related to your personal interests.

Books: Catalog searches on a topic or the history of a field, or books from the library or my office can provide a wealth of information.
Also take a look at:

  • Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Dordrecht; Boston : Kluwer Academic, 1997.
  • Encyclopedia of mathematics and society / Sarah J. Greenwald , Jill E. Thomley, [editors] Ipswich, Mass. : Salem Press, 2012.
    Search the library catalog for online access and this is also on the main stacks in the library too. The link worked from home once I entered my banner id, but otherwise search in the library catalog and go in from there...
  • Library Databases: The library database CQ Researcher presents a chronology for select topics and questions. Library databases such as Jstor or Academic Search Premier can also be helpful for mathematical searches.

    Websites: Websites such as the MacTutor History of Mathematics archive (O'Connor and Robertson, 2005) provide an extensive collection of articles on particular people and topics. The Earliest Known Uses of Some of the Words of Mathematics (Miller, J, 2008) can provide history on the development as well as the first published appearance of terms. Wikipedia's history pages and Google scholar can also be useful.

    This project connects in a variety of ways to the four general education goals for all students at ASU:
  • Thinking Critically & Creatively [research and creative product]
  • Communicating Effectively [writing, speaking and reflecting]
  • Making Local to Global Connections [how mathematics applies in many other settings, multiple perspectives]
  • Understanding Responsibilities of Community Membership [citations, peer review, actively listening to each others perspectives and presentations...]
    You could focus your project on a mathematical concept, a real-life concept with mathematical connections, a person, place, or more. There are many possibilities and I am happy to help you find a topic that you are interested in and also has connections to mathematicians and mathematics. Here are a variety of topics to give you an idea of some diverse possibilities.
  • technical applications: cancer, film, roller coasters, sports, your future career, real-world problems being solved by mathematicians...
  • mathematical/scientific object: black holes, pi, golden mean
  • person: David Blackwell's mathematical career and collaborations
  • place: Egypt, the universe
  • time period: World War II Mathematics
  • controversy in mathematics
  • many more possibilities---hopefully you will choose something interesting/useful/important to you as you select a topic that has enough scientific/mathematical connections and mathematicians. I can help you broaden, narrow, or refocus a topic.