More Books

Our textbook is the book by Burton, but you may be interested in looking at some other books as well. I'll be supplementing Burton's book with some material that I'll distribute in class; much of it will come from the following books -- especially from the first few books listed below.

Howard Eves, An Introduction to the History of Mathematics (with cultural connections). Apparently the most recent edition is the 6th -- Saunders College Publishing (a part of Harcourt Brace), Philadelphia, 1990.
Victor J. Katz, A History of Mathematics: An Introduction. Second edition. Addison Wesley, Reading, Massachusetts, 1998.
Howard Eves, Great Moments in Mathematics, in two volumes: Before 1650 and After 1650. Mathematical Association of America. Dolciani Mathematical Exposition Series, volumes 5 and 7 respectively.
R. Laubenbacher and D. Pengelley, Mathematical Expeditions: Chronicles by the Explorers. Springer, 1998. 285 pages. Perhaps trying to cover all of mathematical history is too ambitious, so this book just focuses on 5 of the most exciting stories in mathematical history:
- Geometry: The Parallel Postulate.
- Set Theory: Taming the Infinite.
- Analysis: Calculating Areas and Volumes.
- Number Theory: Fermat's Last Theorem.
- Algebra: The Search for an Elusive Formula
I like this choice of topics very much, and in fact I will attempt to cover a similar selection of topics in my course. However, I decided not to use the Laubenbacher-Pengelley textbook because I felt that its style of exposition and its style of homework problems were not well suited for the students that I expect to have.
John Stillwell, Mathematics and Its History, Springer, 1989. I believe Stillwell will have a new edition ready soon.
William Dunham, Journey through Genius: Great Theorems of Mathematics. Wiley, 1990. "Seventeen landmarks spanning 2,300 years and representing ten mathematicians." Presents results in modern style rather than original sources.
Morris Kline, Mathematics: The Loss of Certainty , Oxford University Press, New York, 1980. This book is not really a textbook, but I might decide to use it for supplemental reading. It sketches the entire history of mathematics, but it devotes particular attention to the history of human confidence in mathematics, which rose to great heights when Newton explained celestial mechanics, and which -- according to Kline -- began to decline when Gödel's Incompleteness Theorems demonstrated inherent limitations to mathematical certainty. I'm not sure I agree with Kline's conclusions about the end of certainty, but I thoroughly enjoyed what came before that.
There are a few books that are commonly used as history sourcebooks -- i.e., collections of original articles. I haven't looked through many of these yet. One that I might use is Classics of Mathematics, by Ronald Calinger, published by Prentice-Hall.
Charles R. Hadlock, Field Theory and its Classical Problems, 1978 Carus Monograph number 19, Mathematical Association of America. This book has 4 chapters, and much of it is too advanced and too specialized for our history course, but we might cover Chapter 1. That chapter introduces three problems that the ancient Greek geometers posed but could not solve -- doubling the cube, trisecting the angle, squaring the circle. All three constructions were proved impossible using field theory in the 19th century; these impossibility proofs are also given (in slightly more modern language) in Chapter 1.
Gregory H. Moore. Zermelo's Axiom of Choice; Its Origins, Development, and Influence. Springer-Verlag, 1982. This book is too advanced and specialized for me to ask the whole class to look at it, but I'm going to put it on reserve, and I may have some students look at parts of it -- particularly if I assign writing projects. See my remarks about controversy over the Axiom of Choice. Apparently this book is out of print.
Dover Publications prints many books at very low prices -- generally by reprinting old editions whose copyrights have expired or at least gone down in price. I haven't had a chance to look through these yet, but I may end up choosing one or more of the following. Prices are from last year; some may have risen slightly since then.
- Jane Muir. Of Men and Numbers: The Story of the Great Mathematicians. 256 pages, $7.95.
- Jacob Klein. Greek Mathematical Thought and the Origin of Algebra. 360 pages, $11.95.
- L. Bunt, P. Jones, and J. Bedient. The Historical Roots of Elementary Mathematics. 320 pages, $8.95.
- David E. Smith. History of Mathematics. Total of 1355 pages in two volumes, $13.95 each.
- David E. Smith. A Source Book in Mathematics. 217 pages, $15.95.
- W. W. R. Ball. A Short Account of the History of Mathematics. 522 pages, $13.95.
- Roberto Bonola. Non-Euclidean Geometry. 432 pages, $11.95.
- E. T. Bell. The Development of Mathematics. 637 pages. $14.95.
- Dirk J. Struik. A Concise History of Mathematics. 205 pages. $8.95.
M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History. 3rd edition, 1993. W. H. Freeman and Co. This book is the best I've seen for introducing, at an elementary level, the idea of non-Euclidean geometries -- a concept which was crucial in the development of modern mathematics (and not just geometry, but other fields of math too).