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Student Reports: A Rewarding Undertaking - Undergraduate Assignment Formats

Frank J. Swetz

The following pages are examples of assignments from a college course in the history of mathematics (from Professor R. M. Davitt, University of Louisville):


Assignment:  Topics for Classroom Presentations


Note: Your instructor will provide the student who chooses a specific topic for her/his classroom presentation with at least one solid resource for that subject.

Note: The topics are listed in the order in which they will be covered. The earlier ones will definitely be presented by students. However, depending upon the final, stabilized population of the course, it is quite possible that the last few topics will not be the subjects of classroom presentations.

Pithy Descriptions of the Topics

1.         The Pythagorean Theorem and Pythagorean triples

2.         The three classical Greek construction problems

3.         The Golden Section

4.         The history and properties of π

5.         The history and properties of 0

6.         The history and properties of e

7.         The history and properties of i

8.         Theories of the infinite

9.         Hilbert’s Tenth Problem

10.       The Four Color Theorem

11.       The Continuum Hypothesis

12.       Kepler’s Conjecture

13.       Fermat’s Last Theorem

14.       The Riemann Hypothesis

15.       The Prime Number Theorem

16.       The Goldbach Conjecture

17.       The Poincaré Conjecture

18.       Just six numbers - The deep forces that shape the universe

19.       The question of NP-completeness

20.       The Fundamental Theorem of Algebra


The instructor always reserves the right to direct students to “more appropriate” topics based upon his perceptions of their mathematical backgrounds and mathematical maturity. In other words, he doesn’t want anyone getting in over her/his head. The level of sophistication needed to understand and discourse intelligently upon some of the latter topics is quite high.


Frank J. Swetz, "Student Reports: A Rewarding Undertaking - Undergraduate Assignment Formats," Convergence (July 2007)