Math 100 The Story of Mathematics/WI

Course Syllabus

• Description
• Objectives
• Syllabus
• Technology
• Assessment
• Text
• Instructor

Description

An overview of the mathematics necessary for our modern technological society. Topics include the origins of mathematics, number systems, geometry, number theory, logic, algebra, calculus, probability and current mathematical topics. Presented from an historical perspective that includes biographies of important mathematicians and their ideas.

Objectives

The primary goal of the math 100 course is to provide a liberal arts major with a thorough review of the major ideas of mathematics and their relationship to our society.

On completion of the course students should be able to:

• Be familiar with the spectrum of mathematical ideas and their origins;
• Know the prominent mathematicians and their contributions;
• Understand the emergence of mathematical ideas within the context of the societies in which they first appeared;
• Understand the nature of proof and its relationship to mathematics;
• Understand what is referred to as the beauty of mathematics;
• Understand the importance of mathematics to science and modern society.

Syllabus

1. Foundations

What is mathematics? The origins of mathematics. Space shape and symmetry. From moon tallies to calendars. Accounting Tokens.

2. Ancient Mathematics.

Systems of numeration. The emergence of geometry. Measurement. Ancient mathematical mileposts.

3. Greek mathematics

Thales and the Greek Mystery. Pythagoras and arithmetica. Logica. The Elements of Euclid. Archimedes and the gang. The infinite.

4. The Transition

Al-jabr and the mathematics of Islam. Mathematics in medieval Europe.

5. Renaissance Mathematics.

Galileo, Kepler and the book of Nature. Fermat and Descartes' Coordinate geometry. Isaac Newton, Gottfreid Leibnitz and the creation of the Calculus. Probability. Euler. Differential equations. Gauss. Number Theory.

6.19th Century Mathematics

Non-Euclidean geometries. The infinite. The mathematics of symmetry.

7. Modern Thresholds

Topics from contemporary mathematics: Topology, fractals , graph theory, cellular automata, the millennium problems.

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Technology

You will need a computer with an internet browser to access the online text and assignments. Student computer accounts are available through the library. You will use the computer to take class notes and print them out at the end of each class.

Assessment

Your Journal

Your grade for the course will be determined by your class jounal, a notebook containing all of your work. On the first Monday of each week you will turn in all the work completed for the previous week for grading including 1) class notes, 2) Journal entires and 3) Assigned Homework. At any time in the semester you can visit my office and check on grade. Roughly your grade is:

Class notes(based on attendance) (20%)

Journal entries: Your reflections and research on the lectures (40%)

Homework Assignments (30%)

Final Notebook (10%)

In order to recieve full credit for your class notes and corresponding journal entires, you must diligently attend class. Late work is accepted as arranged with the professor. Extra credit is given for exceptional work and by arrangement.

Texts

The Story of Mathematics
Edited by Robert Garry
Online: http:\\isolatium.uhh.hawaii.edu

Instructor

Robert Garry
College Hall 8a
University of Hawaii- Hilo
933-0814
rgarry@hawaii.edu

Effective for Fall 2009.