**Text**: *History of Mathematics*, David
M. Burton, Fourth Edition

Prerequisites: MTH 142 or 132

**Exams and Grading**: There will be two exams,
some homework assignments, and the

presentations.

TWO HOUR TESTS: 40 percent

PRESENTATIONS AND HOMEWORK: 40 percent

FINAL EXAM: 20 percent

**Aims and Objectives-Short Version**

The course aims to illustrate the following:

1. How mathematics has been, and still is, a developing subject.

2. How advances in mathematics are driven
by problem solving and how initial formulations

often lacked rigour.

3. How good mathematical notation is vital to the development of the subject.

4. How mathematical ideas that are considered "elementary" today have great level of sophistication.

5. To teach you how to use the library and technology, especially the internet.

6. To improve your oral and written communication skills in a technical setting.

By the end of the course students are expected to be able to:

1. understand, describe, compare and contrast
the main ideas and methods studied in the

course.

2. apply the methods to given examples.

3. develop a broad historical appreciation of the development of mathematics.

4. understand that even very abstract results of pure mathematics affect everyday lives.

5. have effective presentation style in
a technical setting.

**Objectives-Detailed Version**

The main aim of this course is to introduce the study of the history of mathematics. This means both telling the story of the development of mathematics in the past, and practicing the historical judgements and methods that enable the story to be told. The course should also deepen your understanding of the role the mathematics has played in society.

**Topics**

The course is intended for interested people from a variety of backgrounds: students of mathematics who want more understanding of its historical development, teachers of mathematics at all levels, who will find such material enriching to their students' learning, and people who have a general interest in social and cultural history.

Our approach is based on texts and the materials that can be found on the Internet.

The major topics that will be covered are:

** Mathematics in the ancient
world** moves from the
earliest evidence for mathematical activity, before the time of the Egyptians
and Babylonians, through the achievements of classical Greece to Euclid's

** Through the Middle Ages to
the seventeenth century .** We follow the development
of the algebraic approach through Muslim culture and then the rediscovery
in Europe of classical Greek texts at the end of the sixteenth century,
which helped lead to a flowering of mathematics in the next century. We
look at the time of Napier (logarithms) in Scotland; Descartes (algebraic
geometry) in France; Kepler in Germany and Galileo in Italy applying mathematics
to the world; and the invention of the calculus.

** The seventeenth and eighteenth
centuries. **The calculus was invented, independently
and in rather different ways, by Newton and Leibniz (building on the work
of many earlier mathematicians). What were the consequences of this? We
trace some developments through the eighteenth century, and examine how
algebraic concerns reached almost their modern form in the work of the
great Swiss mathematician Leonhard Euler.

** Topics in nineteenth-century
mathematics.** Is Euclid's 'parallel postulate' necessarily
true, or can other logically consistent geometries be devised? Can a formula
be found for solving equations of the fifth degree or, if not, why not?
Were the foundations of the calculus secure - if not, what to do about
it? Can calculation be mechanized, and at what cost? Can you 'prove'
a theorem by using a computer? These are some of the questions discussed
in this survey of characteristic topics of nineteenth-century mathematics
that are the basis for many of the concerns and approaches of mathematics
in the twentieth century.

* Topics in twentieth century
mathematics. *This part is based
on John L. Casti book,

**Instructor**: Dr. M. Kulenovic, Tyler 216, X44436,

e-mail: *kulenm@math.uri.edu*

**Online information**: *www.math.uri.edu/courses
*or *www.math.uri.edu/~kulenm*
**Office hours**: MWF: 10-11

**Time**: MWF: 12-1
**Room:**