I have placed four books on 3-hour reserve in Carlson Library. (Under the Library tab at the MyUT portal you will see the Course Reserves search box.)

*The Crest of the Peacock*, by George Gheverghese Joseph.

This important book takes an important first step towards filling a large gap in the literature on the history of mathematics. Most books accessible to undergraduates pay scant attention to the mathematics that was not developed in Europe. Although far from comprehensive, Joseph gives a good account not only of how other cultures developed mathematical ideas centuries before they were rediscovered in Europe, but also why their approach was often subtly different than the European approach.*Journey through Genius*, by William Dunham.

Dunham believes that just as a course in the history of art would be meaningless unless you look carefully at the art produced by the greatest artists, so a course in the history of mathematics would be meaningless unless you look at the mathematics produced by the greatest mathematicians. Dunham looks at works of genius, from Thales to Cantor. He walks you through the proofs of major theorems as originally given by their discoverers, using the tools available at the time. He also includes biographical sketches and broader historical context. In many ways it would be profitable to read this book in parallel with our textbook.*Mathematics and Its History*, by John Stillwell.

I include it for the obvious reason that its author also wrote our textbook. It offers further historical and mathematical insight into the topics we will cover. However Stillwell is not a historian and you should compare and contrast his treatment with those of other authors.*Math through the Ages*, expanded edition, by William Berlinghoff and Fernando Gouvêa.

The NCTM standards call for the integration of the history of math into K-12 curriculum, and so this book was written with K-12 teachers in mind. It has two parts. In the first part they provide a sweeping overview of the history of mathematics. In the second they look in depth at individual topics. They try to answer questions such as where our arithmetic symbols came from, or how our concept of fractions evolved.

There are many websites with historical accounts, mathematical and otherwise. Here I mention only two.

- MacTutor.

For us this site is by far the most valuable. Here you will find biographies, maps, timelines, and much, much more. - Wikipedia.

This site is extremely important, and extremely flawed. You should not let the flaws deter you, but neither should you ignore them. Use Wikipedia as a starting point. Need to learn about Cyrus the Great or the Counter-reformation? Wikipedia is a great place to start. But don't stop there! read the article then follow-up by heading to some of the references listed in the end. Always verify information found at Wikipedia against other sources.

There is one other textbook which may be helpful, although Carlson Library does not have a copy:

*A History of Mathematics*, second edition, by Victor Katz.

This is a fairly comprehensive undergraduate treatment of the history of mathematics. You may find it particularly useful when we discuss topics such as the Egyptian method of arithmetic (section 1.3); Iraqi sexagesimals (section 1.3); Bhaskara's solutions of Pell's equation (section 6.7); Cardano's formulas (section 9.3); projective geometry (sections 10.1 and 11.5); and many others.

There are some BBC radio programs that help give us a glimpse of life
in the ancient world, and in particular the role of science and
mathematics. (Look for the *Listen Now* buttons on the pages
listed below.)

- Babylon.

They begin with a high-level view of 3000 years of ancient Iraqi history, focusing on the empires based at Babylon. There is a discussion of Babylonian science and mathematics beginning around the 28-minute mark. - There is a series entitled
*A history of the world in 100 objects*. Each 15-minute episode focuses on a single object from the British Museum. Here are a few that relate directly to our course.- Cuneiform tablets.

The tablet featured here records an allotment of beer, the currency of ancient Iraq, before money was invented. The object illustrates how writing was invented by the accountants, and only later exploited by the poets and mathematicians. - Rhind papyrus.

Unlike Iraq very few written objects survive from ancient Egypt. This episode describes one of the most important. It is in essence a self-study guide for the civil service exams, and hence illustrates the main goal of math education for the past 5000 years. - Rosetta stone.

How can we read objects such as the Rhind papyrus today, when the language it was written in has not been spoken for 2000 years? Because of the Rosetta stone. (You can read more about the deciphering of the Rosetta stone in chapter 5 of*The Code Book*, by Simon Singh.) How can we read the clay tablets from ancient Iraq, whose languages have been extinct even longer?

- Cuneiform tablets.

One of the voices you will hear frequently at the BBC is that of
Eleanor Robinson. She has a fabulous article in the *American Mathematical
Monthly* which shows what can go wrong when mathematicians try
their hand at historical reconstruction. This piece concerns the most
famous mathematical tablet from ancient Iraq, the so-called
Plimpton 322.

Karen Hunger Parshall provides a good survey of early algebra in her The art of algebra from al-Khwarizmi to Viète: a study in the natural selection of ideas.

There is a useful atlas with which you can trace, for example, the flow of european history starting in year 400, just before the fall of the western Roman Empire.

Charlie Gunn's view inside hyperbolic space.