1. Examine in detail the notion of continuity from an historical perspective from the time of Newton through the time of Weierstrass. What fundamental changes have occurred in the last 150 years - if any - on continuity?
2. Give a history of analytic geometry texts used in the United States from 1850-1975. (This should contain a comparative analysis of content, rigor, style, uses of graphs, and text design. At least 12 examples should be cited.)
3. Give a history of reform calculus movement in the United States. (This study should be comprehensive.) taken by Heidi Sass
4. Give a study of the paradoxes of infinity, including Zeno's four and others. taken by Paul Goains.
5. From as near a mathematical perspective as possible, what were the medieval notions of infinity?
6. Discuss recent trends in the history of Indian mathematics.
7. Select "thread of mathematic" and trace it from its beginning to current times. OR select a "thread of mathematics," trace it from its beginning to its end, and analyze why it ended.
8. Describe the notion congruence by dissection. How far has it evolved? Give its history.
9. Describe human cognitive ability at "number sense" from the work of Piaget to Dehaene. taken by Blanca Binstock
10. Trace the occurrence of paradoxes in mathematics from the Greeks to the twentieth century. Discuss several in detail with their resulting resolution vis-a-vis the development of mathematics or their non-resolution.
11. Give a complete accounting of the translations (from Greek to Arabic to Greek/Latin/local vernacular, etc) of Euclid’s The Elements, including, but not limited to, why these translations were made at that particular time.
12. What contributions toward rigor did Weierstrass bring to mathematics?
13. Trace the development of iterative processes from antiquity to the great French mathematician Picard.
14. Discuss the use of permutation groups in the development of abstract algebra.
15. Give an historical account of existence and uniqueness of solutions to partial differential equations during the first half of the 20th century.
16. Outline the history of the calculus of variations. What particular role did Euler play. What happened to the field by the early twentieth century.
17. Trace the history of attempts to solve by radicals polynomial equations of order greater than 4, beginning with Cardano and concluding with Abel. taken by Dakota Blair.
18. Give a critique of the axioms and postulates of Euclid’s geometry and more modern treatments which clarify the unwritten assumptions of Euclid. Discuss Hilbert’s postulational system. Also, play close attention to the parallel lines postulate, and what has happened in consequence (non-euclidean geometries). taken by Sam Terfa.
19. Describe the history of modern transform theory, including the Fourier transform, the Laplace transform, and general integral kernel transform. What were the original motivations to develop them?
20. Study Issac Barrow’s geometrical calculus.
21. Trace the origin and development of the three fundamental partial differential equations: the parabolic, the elliptic, and the hyperbolic. What new mathematics was developed to solve them?
22. Trace the notion of convergence from the ancient primitive concepts through the integral calculus as developed by Riemann. (Actually, this requires an examination of the notion of rigor in finding limits.)
23. Give an account of mathematics in the service of the military. Begin with Archimedes, proceed through Galileo, and up to modern times.
24. Give an history of the mathematics developed during the Second World War in the service of war. taken by Bobby Hill.
25. Trace the development of the theory of mathematical fluid dynamics.
26. The 20th century has seen a reemergence of constructive mathematics. Give an accounting of this development. What were the issues? Why was the current development of mathematics unsatisfactory to the new constructivists?
27. Trace Oresme's theory of indivisibles and infinitesimals. Include findings on his impact upon the development of calculus in the 17th century.
28. Who is Bourbaki? What is Bourbaki's impact on modern mathematics. taken by Bethany Jones.
29. Give an historical account of Hilbert's 23 problems. How many have been solved? What are the prognoses for the others? taken by Sarah Woods.
30. What was Descartes' philosophy? How did it change forever the way man was to think about the universe? taken by Cindy Bervig.
31. Explain in detail how Cantor developed his theory of sets. What problems did he begin with? What gains did he make? Was Cantor really insane?
32. Trace the historical thread of solvability for groups.
33. Give an account of the post-modernist philosophy as applied to mathematics instruction in K-12 in the United States from 1980-2000. taken by Kathy Quint.
34. Trace the development of probability from its origins to modern day. taken by Molly Mason
35. The history of mathematics in finance and economics.
36. Trace the historical thread of error correcting codes.
37. The development of the formal notion of an hypothesis test, social statistics, and their effect on judicial systems.
38. Trace in detail the development of the logarithm. taken by Jennifer Travis