Some alternative references for Math 115

Disquisitiones arithmeticae by Carl Friedrich Gauss.
This is the book that started it all!
An English edition was published in 1986 by
SpringerVerlag.

An introduction to the theory of numbers by
G. H. Hardy and E. M. Wright. Published by Oxford at the Clarendon
Press. This is an excellent book, a wonderful classic.
 Number theory for beginners by
André Weil, with the collaboration of Maxwell Rosenlicht
(an emeritus professor here at Berkeley).
This
Springer book, published in 1979,
was based on lectures given by Weil at the University of Chicago.
Although relatively terse, it is a model number theory book.
 A
classical introduction to modern number theory,
second edition,
by Kenneth Ireland and Michael Rosen.
This excellent book was used recently as a text in Math 115.

An
introduction to number theory by
Harold M. Stark,
MIT Press.
Highly recommended!
Although it has been used as a text for this course, it does
not cover quadratic reciprocity.
(The author
turned 60
just before the start of this semester.)
 The theory of numbers: a text and source book of problems
by Andrew Adler and John E. Coury, published in 1995 by
Jones and
Bartlett. This book is somewhat unusual in its approach in that it
presents the material of our course through problems. More precisely,
each chapter begins with a short exposition of fundamental results,
then presents a large number of problems with solutions, and then
finishes off with exercises that do not have solutions.
This might be a good book to look at if your aim is to do as many problems
as possible.

Elementary number theory by David M. Burton, published by
Wm. C. Brown. Now in its fourth edition
(dated 1998), it's a fairly popular textbook for courses like ours.
 Elements of the Theory of Numbers
by Thomas P. Dence and
Joseph B. Dence. This book was sent to me recently by Academic Press.
It is a plausible textbook for Math 115.

Introduction
to Number Theory by
Peter D. Schumer.
I've never seen this book, but I know that it has been used in several
places for courses like ours.

Elementary Number Theory and its Applications
by Kenneth H. Rosen, 3rd ed., AddisonWesley. Rosen was trained
as a number theorist (PhD student of Harold Stark) and writes well.
(His discrete math textbook is the standard book for Math 55.)
I remember liking his number theory book when it first came out,
but I haven't seen a copy lately.
 Elementary
number theory : a problem oriented approach by
Joe Roberts, a professor in the
Reed College math
department.
This book was published by
MIT Press in the late 1970s.
Visually, it's an amazing book: it is not typeset, but rather is
photographically reproduced from a handwritten manuscript.
The library has a copy (QA241.R61), but the
book is out of print.
Roberts has also written
The lure of the integers.

Number theory : an approach through history from Hammurapi to
Legendre by André Weil; published by Birkhäuser (1984).
There are copies in the math library and in Moffitt. This is the book
to consult if you want to see how the ancients did number theory.

Introduction to number theory by Hua Loo Keng, published by
Springer in 1982. This book
is a translation of Hua's 1956 treatise; it's great to browse through.
I especially like Hua's discussion of the Chinese Remainder Theorem.

A friendly
introduction to number theory by
Joseph H. Silverman,
published by Prentice Hall. An excellent book for a
more elementary course; I used it for Math 24 one year ago.
(Silverman just won the American Math Society's
prize
for exposition, for a pair of graduatelevel books on elliptic curves.)

The book of numbers by
John Horton Conway and
Richard K. Guy. This book is not about number theory per se, but it's
a lot of fun to read!
It is used frequently
in freshman seminars.
Kenneth A. Ribet
,
Math Department 3840, Berkeley CA 947203840
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