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Topic: Book List
Replies: 2   Last Post: Jun 20, 1995 11:21 AM

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Chih-Han sah

Posts: 75
Registered: 12/3/04
Book List
Posted: Jun 2, 1995 11:16 PM
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This is the "booklist". I compiled it for a local high school. I am
sure that everyone has their own "must have" list. I have edited out
a number of longer notes to myself and left behind only very short
Han Sah, sah@math.sunysb.edu


Phone Book of Book Publishers

Code: 0 = All levels; 1 = Collegiate and up; 2 = Professional.
The classification code is TENTATIVE.
To locate a phone number for a publisher, one may try
asking toll-free directory information first:

Academic Press (1): 1-800-321-5068 (publishes free Math Newsletter)
Addison Wesley (0): 1-800-447-2226
Amer. Math. Soc. (2): 1-800-321-4AMS
Birkhauser (0): 1-800-777-4643
Cambridge U.P. (0): 1-800-872-7423
Chapman Hall (2): 1-212-244-3336
Chelsea (0): 1-212-889-8095
Univ. Chicago P. (0): 1-312-702-0279
Marcel Dekker (1): 1-800-228-1160
Dover (0): 1-516-294-7000
Elsevier (2): 1-212-633-3803
W. H. Freeman (0): 1-212-576-9400
Harcourt B.& J. (1) 1-800-237-2665
D.C. Heath (0): 1-800-235-3565
Innovative Textbooks(1):1-714-854-5667
Kluwer (0): 1-617-871-6600
Math Assoc. Amer (0): 1-800-331-1622
McGraw-Hill (0): 1-800-338-3987
W.W.Norton (0): 1-800-223-2584
Oxford Univ. Press (0): 1-800-451-7556
A. K. Peters (2): 1-617-235-2210
Open Court Publ. (0): 1-800-435-6580
Princeton UP (0): 1-800-777-4726
Publish or Perish (2): (FAX) 713-523-6743
Roman Press (0): 1-714-854-5667 (Bull. of Math. Books, $24/yr)
Schaum (0): 1-800-338-3987
Simon & Schuster (0): 1-800-442-7070
Soc. Ind. App. Math (2):1-800-447-7426
Springer-Verlag (0): 1-800-777-4643
John Wiley (0): 1-800-225-5945
World Scientific (0): 1-800-227-7562



All of these should be accessible to 12-th graders, some of the topics
may be accessible to 9-th graders. Many of the "recreation" books are
accessible to students of ALL ages. University Presses typically will
send out free catalogs of their publications by fields. Many of them
have annual sales. It may be possible to work out a deal with them.

Suggestion: Paper bound books are much less expensive. If your
school has some sort of "Shop Courses". You might ask the teacher
if there is a way to bind the paper bound books with hard covers.
Teach this as a part of the course. Dover books are around
$12 per volume. Many are less than $10.

Suggestion: Go to garage sales and negotiate with the owners a donation
to the schools. Tactics to use: Tell the owners that schools do not
have much of a library budget. If this does not work, tell the owner
that you will come back at the end of the day and cart away all the
unsold books. Even better, ask students in your school to participate
in such "book hunting projects". The bonus is that the tactics will
make the public become more aware of the plight of the schools even if
you don't succeed in getting the free donation. You may adopt a more
aggressive approach: Go to garage sales and ASK the owner if they
have old books that they would like to donate to the school library.
Make this a project for the students. When the books have been collected,
make it a project for the students to help the teachers to sort them out
--put out the spare ones on sale during School Night, use the proceed
to buy needed books for the school library.


Quantum, the magazine of math and science.
This is co-published by National Science Teachers Association
(NSTA) and Quantum Bureau of the Russian Academy of Sciences
in conjunction with American Association of Physics Teachers
(AAPT) and National Council of Teachers of Mathematics (NCTM).
To order: call 1-800-777-4643, Ext 9 (this is Springer Verlag,
you may also ask them to put you on their mailing list, although
most of the publications are at the university level or higher,
they do have sales on some general science books that might be
of interest.)
The cost of a subscription are:
Library/Institution: $34, Special Personal Rate: $20 and
Super Student Rate (full time only): $15.

Mathematical Intelligencer: This is also published by Springer-Verlag.
It comes out 4 times a year. It is fine for college and
university students, but probably too advanced except for the
top high school students.

Math Horizons: This is primarily for undergraduate students in college
and universities. It is published 4 times a year by the Math
Assoc. of Amer. (MAA). The bulk subscription rate is 20 copies
minimum at the cost of $100 per year, additional in units of
10 copies for $50. Individual rate is $20 for MAA members,
$35 for non-MAA members and Library. call 1-800-331-1622.

The Bulletin of Mathematics Books: This is a newsletter published by
the Roman Press at a subscription cost of $24 a year (4 issues).
It provides telegraphic reviews of new as well old books.
It also reviews Computer Softwares. Phone: 714-854-5667.


Puzzles, Recreations and General Interests.
(Numbers, geometry, logic etc.)

Abraham, R. M., Easy-to-do entertainments and diversions with cards,
strings, coins, paper and matches. Dover.
-------, Diversions and Pastimes with cards, string, paper and
string. Dover.
Beck, A., Bleicher, M.N., and Crowe, D.W., Excursion into Mathematics
Worth Publ.
Beiler, A. H., Recreations in the theory of numbers: the queen of
mathematics. Dover. ISBN-0-486-21096-0
Burns and Hariston, I Hate Mathematics! Book, Little Brown Co. 1975.
Now called: The Brown Paper Bag Mathematics Book.
Good for 8 years olds or there abouts.
Carroll, Lewis, Symbolic Logic and the Game of Logic, Dover.
Coolidge, J. L., The Mathematics of the Great Amateurs, Dover
Courant, R and Robbins, H. E., What is Mathematics? Oxford Univ. Press
(paper) ISBN-0-19-502517-2 ($19.95)
Dewdney, A. K., 200% of Nothing, Wiley, ISBN-0-471-57776-6. ($19.95).
Dorrie, H., 100 Great Problems of Elementary Mathematics. Their
History and Solution. Dover (1965). ISBN-0-486-61348-8
Dudeney, H. E., Amusements in Mathematics, Dover.
536 puzzles and curious problems, edited by M. Gardner.
Scribner, 1967.
Frolichstein, J., Mathematical Fun, Games and Puzzles. Dover
Gamow, G., One, Two, Three, ..., Infinity, Bantam Books, 1971.
Gardiner, A., Mathematical Puzzling, Oxford U. P. 1987.
ISBN-0-19-914258-0 (paper) W. W. Norton ($14.95)
Gardner, M., Mathematical puzzles of Sam Lloyd, Dover.
Knotted Doughnuts (and other mathematical entertainments),
Freeman, (1986), ISBN-0-7167-1799-9 (paper).
Aha, Aha, insight, Freeman (paperback), 1978.
Aha, Gotcha, Freeman, 1982
Fads and Fallacies in the Name of Science, Dover, 1957.
Science--good, bad and bogus, Prometheus, Buffalo, NY, 1961.
Mathematics, Magic and Mystery, Dover, 1956.
The Scientific-American book of math. puzzles and diversions,
Simon and Schuster, 1959-61.
More math. puzzles and diversions from Scientific American.
Bell, London, 1963.
New Math. diversions from Scientific American. Simons and Schuster
Sixth book of math. games from Scientific American, Freeman, 1971.
Wheels, life and other math. amusements, Freeman, 1983.

In general, any item by Martin Gardner is worth reading.
Heath, R. V. Mathmagic, Dover.
Huff, Darrell, How to Lie with Statistics, W. W. Norton, 1982
45-th printing, (paper, $4.95). ISBN-0-19-502517-2
45-th printing is enough of a recommendation. It is a classic.
Jacobs, Harold R., Mathematics: A Human Endeavor. A Book for Those Who
Think They Don't Like the Subject. W. H. Freeman (1970)
ISBN 0-7167-O471-4 (paper), 0-7167-0439-0 (cloth).

An excellent source book to pursue a variety of
topics. There are beautiful pictures, graphs, cartoons, etc.
Kraitchik, M., Mathematical Recreations, Dover.
Merrill, Helen A., Mathematical Excursions, Dover
Mott-Smith, G., Mathematical puzzles for beginners and enthusiasts, Dover.
Moritz, R. E., On Mathematics and Mathematicians, Dover.
Phillips, H ("Caliban"), My best puzzles in mathematics, Dover.
--------, My best puzzles in logic and reasoning, Dover.
--------, and Shovelton, S. T, Marshall, G. S., Caliban's Problem
Book: Mathematical, inferential, and cryptographic puzzles. Dover.
Polya, G., How to Solve It, 2nd ed. (paper), Princeton U. Press, 1973.
Radamacher, Hans and Toeplitz, Otto, The Enjoyment of Mathematics: Selections
from Mathematics for the Amateur, Princeton University Press (1957).
Available as paperback from Dover for $6.95. ISBN-0-486-26242-1.
An excellent source book of topics to pursue.
Singh, J., Great Ideas of Modern Mathematics, Their Nature and Use, Dover.
Smullyan, R., The Lady or the Tiger, Random House, 1992 (paper), $10.00.
Stein, Sherman K.:Mathematics-The Man-Made Universe, McGraw-Hill (originally
Published by W. H. Freeman and Company).
Vilenkin, N. Ya, Combinatorics, Academic Press, 1971.
Whitworth, A, Choice and Chance, Hafner, (1959).

Problem Books

Hungarian Problem Book, Math. Assoc. of Amer.
The William Lowell Putnam Math. Competition Problems and Solutions
1938-1964, 1965-1984, Math. Assoc. of Amer.
USSR Olympiad Problem Book, Dover. Edited by Shklarsky, Chentzov
and Yaglom.

History of Mathematics
Boyer, Merzback, History of Mathematics, MAA.
Eves, Howard, An Introduction to the History of Mathematics, Saunders.
(5-th ed was published in 1983, there may be newer edition.)
Hogben, L. Mathematics in the Making, Double Day.
This has many beautiful color photographs. It has a short
Chapter 7, Oriental Contribution, that explains the role
played by the Arabian Empire and the Mongolian Empire.

Mathematics for the Million, Norton, (paperback).
Lam, Lay Yong and Ang, Tian Se, Fleeting Footsteps: Tracing
the Conception of Arithmetic and Algebra in Ancient
China, World Scientific, 1994. ($24, 6-8 weeks

This is a 150 page long pamphlet. Lam has written
a number of papers on history of Chinese mathematics
since 1970.
Li, Yan and Du, Shiran, Chinese Mathematics, A Concise History,
translated by J. N. Crossley and A. W-C. Lun, Clarendon
Press, Oxford, 1987.

It includes Chinese characters which are useful
because the transliteration of Chinese names to English
has changed several times. However, for many, the
Chinese characters may be a distraction. May be
useful as source book.
Mikami, Y., The Development of Mathematics in China and Japan,
Chelsea (reprint of 1913 ed.)

This book contains many examples of word problems extracted
from old Chinese and Japanese texts. The transliteration
was especially difficult.
Neugebauer, Otto, The Exact Sciences in Antiquity, Brown University Press.
1957. Dover, 1969

It also has a historical chart. This book only charts the
Western Heritage. Nothing is said about China and Japan.
Nevertheless, it gives very details analysis of a number of
issues. It is a classic on Western Mathematics.
Smith, D. E., A History of Mathematics, vol. I-II, Dover.
A best buy!
Struik, D. J., A Concise History of Mathematics, Dover.
Swetz, Frank J. and Kao, T. I., Was Pythagoras Chinese? The
Pennsylvania State Univ. Press, and NCTM, Reston, Virginia, 1977.
Conclusion: it is open.
van der Waerden, B. L., Science Awakening, Oxford University Prsee, 1961.
Paperback, Wiley, 1963.

This book provides a critical reading of the history of western
mathematics up to the 17-th century. The following statement
give a general flavor:

"In short, all the developments which converge in the work of
Newton, those of mathematics, of mechanics and of astronomy,
begin in Greece."

In a number of places, van der Waerden showed that many astounding
attributions may be based on inaccurate reading of the name of the
objects being considered. It is therefore important to go back
to original sources and consult experts of the ancient languages.

More specifically, on p. 124, van der Waerden stated:

"... What could only be surmised before, has now become
certainty, namely that the Babylonian tradition supplied the
material which the Greeks, the Pythagoreans in particular, used
in constructing their mathematics."

The book ends with the decay of Greek mathematics. The
external causes and inner causes were offered.


All of these books have extensive bibliographies. Together, they
cover most of the territories.


Number Systems and Number Theory

Number Systems

Menninger, Karl, Number Words and Number Symbols: A Cultural History
of Numbers, M.I.T. Press, Cambridge (1969).

An excellent source book. On p. 309, it recorded a contest
between a Japanese using the soroban (abacus) against an American
using an electric machine. The abacus won. This is quoted
directly from "Hands Down!" in Reader's Digest, vol. 50, March,
1947, p. 47.


Thurston, Hugh A., The Number System, Dover.


Number Theory


Andrews, George, E., Number Theory, Saunders, 1971, Dover 1994.
ISBN-0-486-68252-8 ($6.95)

A good source book. Many topics should be accessible
to high school students wishing to do projects.


Baker, Alan, A Concise Introduction to the Theory of Numbers,
Cambridge University Press.

A short paperback by a Fields Medalist (the equivalent
of Nobel Prize Winner in mathematics--there is no
Nobel Prize in mathematics).


Dickson, L. E., Introduction to the Theory of Numbers, Dover.


Dickson, L. E., Theory of Numbers, Chelsea (3 volumes)

This is the classic History of Number Theory in 3 volumes.
It is a good reference book for many problems. May be
too advanced for high school students. However, it is
a good source book.


Dudley, Underwood, Elementary Number Theory, Freeman.


Friedman, Richard, An adventurer's guide to number theory, ???


Hardy, G. H. and Wright, E. M., An Introduction to the Theory of
Numbers, Oxford University Press, 5-th ed. (paper)
ISBN-19-853171-0 ($32.95, but over 400 pages of goodies).

This is a classic. A number of the topics are accessible
to 12-th graders working on special projects in number theory.
A good source book on many classical problems in number theory.


Nagell, T., Number Theory, Chelsea.


Niven and Zuckerman, Introduction to Number Theory, Wiley.


Stark, H. M. An Introduction to Number Theory, MIT Press, 1978.
(available in paperback.)


Vinogradov, I. M. Elements of Number Theory, Dover.


Arithmetic and Algebra

Bowers, Henry and Bowers, Joan E., Arithmetical Excursions: An Enrichment
of Elementary Mathematics, Dover.


Chrystal, G. Textbook of Algebra, 2 volumes, Dover.

This is a classic.


Fine, Henry B., College Algebra, Dover (may be out of print).

This is a classic. Many College sophomores may have
trouble with this, even though it was first written
in the early 1900's for college Freshman at Princeton.


Lang, S, Basic Mathematics, Springer-Verlag


Volpel, M. C., Concepts and Methods of Arithmetic, Dover.


Geometry and Trignometry


Abbott, E. A., Flatland, Dover.

A classic.


Bonola, R., Non-Euclidean Geometry, A Critical and Historical Study
of Its Development, Dover.


Euclid. The Elements, 3 volumes. Dover.

This is for the History buff.


Hilbert, D. Foundations of Geometry, Open Court, 1971.

A classic. It straightened out the axioms for plane
Euclidean geometry after 2,200 years.

-------, and Cohn-Vossen, Geometry and the Imagination, Chelsea, 1952.


Hobson, E. W., A treatise on Plane Trigonometry, Dover.


Klein, F., Famous Problems of Elementary Geometry, Dover.


Lang, S. and Morrow, Geometry, Springer


Manning, Henry P., The Fourth Dimension Simply Explained, Dover


Manning, Henry P., Introduction to non-Euclidean Geometry, Dover


Row, T. Sundara, Geometric Exercise in Paper Folding, Dover


Sommerville, D. M. Y., The Elements of Non-Euclidean Geometry, Dover.


Winger, Roy M. An Introduction to Projective Geometry, Dover.



General Remark: There are an infinite number of calculus texts on the
market. Many of them should be termed "generic" as in "generic drugs".
Since this involves a huge market, hardbound cover texts tend to be
quite expensive. The list below excludes all textbooks.


Simmons, G. Calculus Gems, McGraw Hills.



Supplementary Texts to Courses

I. M. Gelfand, E.G. Glagoleva, A. A. Kirillov, The Method of Coordinates
Birkhauser (1990), paperback.

I. M. Gelfand, E.G. Glagoleva, E. E. Shnol, Functions and Graphs
Birkhauser (1990), paperback.

I. M. Gelfand, A. Shen, Algebra
Birkhauser (1993), paperback.


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