PACIFIC UNION COLLEGE SYLLABUS - Winter 2003

MATH 451    HISTORY OF MATHEMATICS


COURSE DESCRIPTION: A survey of major developments in mathematics from antiquity to modern times.  The courseinvolves historically relevant problem sets, class discussions, and presentations by students and teacher.  Prerequisite:MATH 131.

OBJECTIVES: While of value to anyone interested in mathematics, this course is specially designed for mathematicsmajors who intend to teach in college or high school. It thus concentrates on the history of those topics typically covered inan undergraduate curriculum or in elementary or high school. It is hoped that the prospective teacher will gain a knowledge of how we arrived with our present mathematics, a knowledge that will provide a deeper understanding of many of theimportant concepts of mathematics.

TEXT: David M. Burton, The History of Mathematics: An Introduction, McGraw-Hill, 2003 (fifth ed.).

HISTORY OF MATH WEB SITES: You may find the following sites useful for study and projects.

Archimedes Home Page www.mcs.drexel.edu/~crorres/Archimedes/contents.html

Biographies of Women Mathematicians www.scottlan.edu/lriddle/women/women.htm

British Society for the History of Math www.dcs.warwick.ac.uk/bshm/resources.html

Math Forum Internet Resource Collection forum.swarthmore.edu/library/topics/history/

INSTRUCTOR: Lloyd Best (Lbest@puc.edu). Phone: office/6591; home/942-9680. Fax: office/965-7135.

OFFICE: CSH 238C. HOURS: Mon: 9-10, 2-3; Tues: 9-10, 2-4; Wed: 9-10; Thurs: 9-10, 2-4; Fri: 9-10.


GRADING: The final grade will be based on Homework (25%), Projects (25%), and Tests (50%).

A A- B+ B B- C+ C C- D+ D D-
92% 88% 84% 80% 75% 70% 65% 60% 57% 53% 50%

LEARNING DIFFERENCES: PUC strives to accommodate students with documented learning differences. If you havea learning disability, or think you might have one, please check with the Counseling Center. They can provide a diagnosisand will work with your professors to accommodate your situation.

ATTENDANCE: An attendance record for this class will be kept. While class attendance is not directly figured into yourgrade, some topics are presented in lectures that are not in the text. In addition, announcements made during classes have thesame force as statements in this syllabus.

HOMEWORK: Students will be asked regularly to present solutions to homework problems to the class. Assignments willbe announced in class. Assigned work is due at the beginning of class on the due date. Late work is not accepted unlessdue to illness or other emergency. A Missing Work Appeal Form must be attached to the late work. If approved, the workwill either be graded or averaged with other homework scores.

PROJECTS: Two projects will be required during the quarter. At least one of the projects should provide a biography of amathematician with explanations of some of his/her mathematical contributions.

Projects must use non-textbook sources, must give credit to these sources, and should be several pages in length.  Projectdeadlines can be found on the class schedule on the opposite side of this page.

TESTS: Tests must be taken at the scheduled time (see class schedule). Only tests which are missed due to illness oremergency circumstances may be made up. If you must miss a test, you are required to notify me in advance.

ACADEMIC INTEGRITY: You are encouraged to work with other students on assignments, but your work shouldreflect your own understanding. All test work must be completely your own. A student involved in cheating (or assistinganother student in cheating) on a test should expect to be dismissed from the course with a failing grade. See PUC's Codeof Academic Integrity (page 229 of the General Catalog) for further details.


Class Schedule

Date Homework To Turn In This Day Class Lecture/Discussion
Jan 7 None §1-1,2: Primitive Counting,

Number Recording of the Egyptians and Greeks

Jan 9 H1-1,2 §1-3: Number Recording of the Babylonians
Jan 10 H1-3 §2-1,2: The Rhind Papyrus, Egyptian Arithmetic
Jan 14 H2-1,2 §2-3,4: Three problems from the Rhind Papyrus,

Egyptian Geometry

Jan 16 H2-3,4 §2-5,6: Babylonian Mathematics, Plimpton
Jan 17 H2-5,6 §3-1,2: Geometrical Discoveries of Thales,

Pythagorean Mathematics

Jan 21 Martin Luther King Jr. Day No class
Jan 23 H3-1,2 §3-3: The Pythagorean Problem
Jan 24 H3-3 §3-4: Three Construction Problems of Antiquity
Jan 28 H3-4 §3-5: The Quadratrix of Hippias
Jan 30 H3-5 §4-1,2: Euclid and the Elements, Euclidean Geometry
Jan 31 H4-1,2 §4-3: Euclid's Number Theory
Feb 4 First Project Due

H4-3



§4-4: Eratosthenes, the Wise Man of Alexandria
Feb 6 H4-4 §4-5: Archimedes
Feb 7 Midquarter Vacation Day No class
Feb 11 H4-5 §5-1,2: Decline of Alexandrian Mathematics, Arithmetica
Feb 13 Prepare for the test. TEST Chapters 1-4 [100 points]
Feb 14 H5-1,2 §5-3,4: Diophantine Equations, Later Commentators
Feb 18 H5-3,4 §5-5: Mathematics in the Near and Far East
Feb 20 H5-5 §6-1,2: Decline and Revival of Learning,

Liber Abaci and Liber Quadratorum

Feb 21 H6-1,2 §6-3: The Fibonacci Sequence
Feb 25 Second Project Due

H6-3

§7-1,2: Europe in the 14th & 15th Centuries,

Battle of the Scholars

Feb 27 H7-1,2 §7-3: Cardan's Ars Magna
Feb 28 H7-3 §7-4: More Ars Magna, Ferrari's Quartic Solution
Mar 4 H7-4 §8-1a: Dawn of Modern Mathematics
Mar 6 H8-1a §8-1b: Dawn of Modern Mathematics,continued
Mar 7 H8-1b §8-2: Descartes: The Discours de la Methode
Mar 11 H8-2 §8-3: Newton: Principia Mathematica
Mar 13 H8-3 §9-1: Origins of Probability Theory
Mar 14 H9-1 Review
Mar 18 Tuesday, 9:45 a.m. FINAL TEST Chapters 5-9 [100 points]