The book review (due March 2)
These are things to keep in mind when choosing your book.
Subject matter
The book should contain a nontrivial amount of history and a
nontrivial amount of mathematics.
That leaves open a variety of possibilities. The book can be
- a biography of a mathematician, such as
S. Nasar, A Beautiful Mind
- a history of a branch of mathematics, such as
A. Weil, Number Theory: An Approach through History
- a history of a particular period of mathematics, such as
T. Heath, A History of Greek Mathematics
- a study of mathematical thinking in non-Western cultures, such as
J. F. Hamill, Ethno-Logic: The Anthropology of Human Reasoning
- an (advanced) textbook with a strong historical component, such as
E. Hairer and G. Wanner, Analysis by Its History
- a mathematical treatise with a strong historical component, such as
H. M Edwards, Riemann's Zeta Function
The examples were chosen at random. (I happen to own them all and had
them in my house on the afternoon in 2003 when I wrote the previous
version of these instructions. I've read 2 1/2 of the 6 and used
another (Heath) for reference in teaching this course.)
More extensive lists appear on the course pages of my predecessors:
Unlike them, I do not require you all to choose different books.
A list of specialty online bookstores is on the
Links page.
Level
Dr. Allen said the book should be "scholarly, not a popularization"
-- but he also encouraged biographies, which are usually written for
a general audience and hence are limited in how deeply they can treat the
mathematics.
I don't know where to draw the line between scholarly and popular books,
especially if asked about a book I've never seen.
I must trust you to choose a book that you think is respectable for a
graduate student to be reading for academic credit.
Further:
- Most of you are teachers or parents or both. If you read a book
intended for a popular or juvenile audience, write your review from the
perspective "I do/don't recommend this book for students at level X."
- A book like A Beautiful Mind contains references that delve into
the mathematics at a more technical level (for example, John Nash's actual
research papers).
Maybe you could follow up some of those leads.