MATH 471             --            MATHEMATICS SEMINAR

MATHEMATICS FROM AN HISTORICAL PERPESPECTIVE

                                    Course Syllabus for Spring Semester, 2001 – prepared by Marie Vanisko

Professor and Office Hours:

Mrs. Marie Vanisko, Professor of Mathematics, 118 Science Building, 447-4451, mvanisko@carroll.edu

Office Hours:    MWF  (9-10, 11-11:30, 3-4 (MW)), Tues-Thurs  (9-9:30, 11-11:30, 2-4:30 (3:30 Th))

Class Schedule:  MA 117 (8-8:50 MWF), MA 122 (2-2:50 MWF), MA 471 (3:30-4:20 Th)

                           MA 334 (10-10:50 MWF and 9:30-10:45 TTh),

REQUIRED TEXT

Journey Through Genius by William Dunham, © 1990 by Wiley, published by Penguin Books

COURSE OVERVIEW

This is a required course for mathematics secondary-education majors. It is intended to give students an insight into some of the great masterpieces of mathematics, as seen in their historical contexts. Mathematics is an ever-growing discipline in which new ideas are built upon the old. Developing an understanding of the individuals who were the creators of mathematics helps one better appreciate their creations.

COURSE FORMAT

   1.      Each of the twelve chapters of the textbook will be the focus of discussion for the first seven weeks of the class. Students will be required to read each chapter and will take turns leading the discussion over each chapter.

   2.      The last half of the class will involve a look at twentieth century mathematics. By late February, students will select two 20^th century individuals who have contributed to the field of mathematics in a significant way (pure or applied). After investigating the life, times, and work, of the individuals selected, students will prepare two papers (3-4 pages each). These papers will be due on the day before the report is given.

GRADING

Students will be graded on a scale of  A(90-100), B(80-89), C(70-79), D(60-69),

F(below 60). The following weights will be used:

Class Participation 50%

Papers and Reports 50%

CONTENTS OF TEXT

Ch 1                 Hippocrates' Quadrature of the Lune

Ch 2                 Euclid's Proof of the Pythagorean Theorem

Ch 3                 Euclid and the Infinitude of Primes

Ch 4                 Archimedes' Determination of Circular Area

Ch 5                 Heron's Formula for Triangular Area

Ch 6                 Cardano and the Solution of the Cubic

Ch 7                 A Gem from Isaac Newton

Ch 8                 The Bernoullis and the Harmonic Series

Ch 9                 The Extraordinary Sums of Leonhard Euler

Ch 10               A Sampler of Euler's Number Theory

Ch 11               The Non-Denumerability of the Continuum

Ch 12               Cantor and the Transfinite Realm