**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**
**Joan.Lukas@umb.edu**
**Course Description**
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.
__Papers:__ 40%
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%
**Course Text**
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.
**Web Resources:**
__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)
__http://www.cs.umb.edu/~joan/ma370/Syllabus.doc__(Word document)
**Syllabus**
**Week 1: (September 6, 8) Early Development of Mathematics –Egypt and Mesopotamia**
Katz, 1.
__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 **
Katz, 2.2
__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.
**1**^{st} paper due – November 15
**Week 12: (November 22) Geometry**
Katz, Chapter 15, 19.
__Additional References:__.
**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.
**Student Conduct: **
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__.
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