Office hours: Tu Th 2:45 – 3:45 PM and by appointment
This course traces the development of mathematics from ancient times up to and including the 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problem solving . Attention will also be paid to the relevance of history to mathematics teaching.
Prerequisites & Requirements
The course prerequisite is the successful completion of at least one semester of calculus. Students will be expected to attend every class session and participate in discussions, to solve problems, research particular areas of mathematical history, and present the results of their research to the class. Students who are interested in the uses of historical material in the mathematics classroom will have an opportunity to explore this area as part of their course work.
Problem assignments: 20%
Problem-solving in a historical context, problems assigned from
text throughout semester.
Take-home mid-semester exam:30%
Will be assigned October 13 and due October 25.
First paper tracing mathematical developments in some culture, due November 15 .
Additional References: L.E. Sigler, “Fibonacci’s Liber Abacci”, Springer 2003.
William Dunham “Journey through Genius”, Wiley,1990, Chapter 6.
Week 8: (October 25, 27) Analytic Geometry and PreCalculus
Katz, Chapter 8
Additional References: René Descartes, “The Geometry”.
Midterm Due – October 27. Week 9: (November 1, 3) Development of the calculus
Katz, Chapter 11, 12.
Additional References: Carl Boyer, The History of the Calculus and its Conceptual Development, Dover, 1959
Week 10: (November 8, 10) ) The development of probability Katz, Chapter 11.
Additional References: Ian Hacking: “The Emergence of Probability”, Cambridge University Press, 1975 and Peter Bernstein: “Against the Gods- The Remarkable Story of Risk”, John Wiley & Sons, 1996.
Week 11: (November 15, 17) Algebra and Number Theory
Katz, Section 11.3, Section 16.5
Additional References: I. Bashmakova & G. Smirnova “The Beginnings & Evolution of Algebra, Mathematical Association of America, 2000.
1st paper due – November 15 Week 12: (November 22) Geometry
Katz, Chapter 15, 19.
Week 13: (November 29, December 1) Modern extensions and refinements of the idea of number
Katz, Chapter 17, 20.
Additional References: William Dunham “Journey through Genius”, Wiley,1990,
Chapters 11 and 12.
Week 14: (December 6, 8) Student Presentations on Term Papers Week 15: (December 13) Summary and Review
2nd paper due Accommodations:
Section 504 of the Americans with Disabilities Act of 1990 offers guidelines for curriculum modifications and adaptations for students with documented disabilities. If applicable, students may obtain adaptation recommendations from the Ross Center for Disability Services, CC-2010 (617-287-7430). The student must present these recommendations and discuss them with each professor within a reasonable period, preferably by September 10, the end of the Add/Drop period.
Students are required to adhere to the University Policy on Academic Standards and Cheating, to the University Statement on Plagiarism and the Documentation of Written Work, and to the Code of Student Conduct as delineated in the Catalog of Undergraduate Programs and online at http://www.umb.edu/student_affairs/programs/judicial/csc.html.