Joan D. Lukas
Professor Emerita of Mathematics
Science 3-172 617 287-6454
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 .
Second paper discussing recent developments in some area of mathematics, due December 13.
Presentation & participation: 10%
Victor J. Katz “A History of Mathematics: Brief Version”. Addison-Wesley, 2004.
Additional books, journals, and materials for enrichment and individual projects will be obtained as needed from a variety of sources.
MacTutor History of Mathematics
The Math Forum
Canadian Society for the History and Philosophy of Mathematics
This syllabus is available at
http://www.cs.umb.edu/~joan/ma370 (html document)
Week 1: (September 6, 8) Early Development of Mathematics –Egypt and Mesopotamia
Additional References: Arnold Chace et al, Eds. “The Rhind Mathematical Papyrus”. Reston, VA: National Council of Teachers of Mathematics, 1967.
Asger Aaboe, “Episodes from the Early History of Mathematics”. Washington: Mathematical Association of America, 1998. Chapter 1: Babylonian Mathematics.
Week 2: (September 13, 15 ) Early Greek Mathematics – The Pythagoreans
Additional References: Dudley Underwood, “Numerology or, what Pythagoras Wrought”, Mathematical Association of America, 1997.
HW1- due 9/15
Week 3: (September 20, 22) The Mathematics of Euclid
Additional References: Thomas Heath: “The Thirteen Books of Euclid”. Cambridge: Cambridge University Press, 1926.
HW2 - due 9/22
Week 4: (September 27, 29) Archimedes and Later Hellenistic Mathematics
Katz, Chapters 3, 4.
Additional References: Archimedes “Measurement of a Circle”.
Video from Walters Art Gallery in Baltimore, MD. “The Archimedes Palimpsest”.
HW3 - due 9/29
Week 5: ( October 4, 6) Indian and Chinese Mathematical Contributions
Katz, Chapters 5,6
Additional References: Florian Cajori, “A History of Mathematical Notations”, New York: Dover, 1993. (First ed., 1929-30).
Lam Lay-Yong “The Chinese Connection Between the Pascal Triangle and the Solution of Numerical Equations of Any Degree”, Historia Mathematica, 17, 4, 1980.
Week 6: (October 11, 13) Islam and Arabic Mathematics
Katz, Chapter 7
Additional References: J.L. Berggren, “Episodes in the Mathematics of Medieval Islam” Springer-Verlag, 1986
Midterm Assigned – October 13.
Week 7: (October 18, 20) Medieval and Renaissance Mathematics
Katz Chapter 8,9
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
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.