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Book List
Posted:
Jun 2, 1995 11:16 PM


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 notes. Han Sah, sah@math.sunysb.edu
**************** BOOKLIST.3
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 tollfree directory information first: 18005551212
Academic Press (1): 18003215068 (publishes free Math Newsletter) Addison Wesley (0): 18004472226 Amer. Math. Soc. (2): 18003214AMS Birkhauser (0): 18007774643 Cambridge U.P. (0): 18008727423 Chapman Hall (2): 12122443336 Chelsea (0): 12128898095 Univ. Chicago P. (0): 13127020279 Marcel Dekker (1): 18002281160 Dover (0): 15162947000 Elsevier (2): 12126333803 W. H. Freeman (0): 12125769400 Harcourt B.& J. (1) 18002372665 D.C. Heath (0): 18002353565 Innovative Textbooks(1):17148545667 Kluwer (0): 16178716600 Math Assoc. Amer (0): 18003311622 McGrawHill (0): 18003383987 W.W.Norton (0): 18002232584 Oxford Univ. Press (0): 18004517556 A. K. Peters (2): 16172352210 Open Court Publ. (0): 18004356580 Princeton UP (0): 18007774726 Publish or Perish (2): (FAX) 7135236743 Roman Press (0): 17148545667 (Bull. of Math. Books, $24/yr) Schaum (0): 18003383987 Simon & Schuster (0): 18004427070 Soc. Ind. App. Math (2):18004477426 SpringerVerlag (0): 18007774643 John Wiley (0): 18002255945 World Scientific (0): 18002277562
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General
All of these should be accessible to 12th graders, some of the topics may be accessible to 9th 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.
*************** Magazines ***************
Quantum, the magazine of math and science. This is copublished 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 18007774643, 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 SpringerVerlag. 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 nonMAA members and Library. call 18003311622.
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: 7148545667. ******************************************************************** ********************************************************************
Puzzles, Recreations and General Interests. (Numbers, geometry, logic etc.)
Abraham, R. M., Easytodo 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. ISBN0486210960 ************ 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 ISBN0486610098. ************ Courant, R and Robbins, H. E., What is Mathematics? Oxford Univ. Press (paper) ISBN0195025172 ($19.95) ************ Dewdney, A. K., 200% of Nothing, Wiley, ISBN0471577766. ($19.95). ************ Dorrie, H., 100 Great Problems of Elementary Mathematics. Their History and Solution. Dover (1965). ISBN0486613488 ************ 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 ISBN0486207897. ************ Gamow, G., One, Two, Three, ..., Infinity, Bantam Books, 1971. ************ Gardiner, A., Mathematical Puzzling, Oxford U. P. 1987. ISBN0199142580 (paper) W. W. Norton ($14.95) ************ Gardner, M., Mathematical puzzles of Sam Lloyd, Dover. Knotted Doughnuts (and other mathematical entertainments), Freeman, (1986), ISBN0716717999 (paper). Aha, Aha, insight, Freeman (paperback), 1978. Aha, Gotcha, Freeman, 1982 Fads and Fallacies in the Name of Science, Dover, 1957. Sciencegood, bad and bogus, Prometheus, Buffalo, NY, 1961. Mathematics, Magic and Mystery, Dover, 1956. The ScientificAmerican book of math. puzzles and diversions, Simon and Schuster, 195961. More math. puzzles and diversions from Scientific American. Bell, London, 1963. New Math. diversions from Scientific American. Simons and Schuster 1966. 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 45th printing, (paper, $4.95). ISBN0195025172 45th 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 07167O4714 (paper), 0716704390 (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 ISBN0486203506 ************ MottSmith, G., Mathematical puzzles for beginners and enthusiasts, Dover. ************ Moritz, R. E., On Mathematics and Mathematicians, Dover. ISBN0486204898 ************ 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. ISBN0691023565 ************ 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. ISBN0486262421. An excellent source book of topics to pursue. ************ Singh, J., Great Ideas of Modern Mathematics, Their Nature and Use, Dover. ISBN00486205878. ************ Smullyan, R., The Lady or the Tiger, Random House, 1992 (paper), $10.00. ************ Stein, Sherman K.:MathematicsThe ManMade Universe, McGrawHill (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 19381964, 19651984, 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. (5th ed was published in 1983, there may be newer edition.) ISBN0030620643 ******** 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, 68 weeks backordered)
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. WC. Lun, Clarendon Press, Oxford, 1987. ISBN0198581815
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. III, 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. ISBN0271012382 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 17th 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.
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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. ISBN048661848X.
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******************* Number Theory *******************
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Andrews, George, E., Number Theory, Saunders, 1971, Dover 1994. ISBN0486682528 ($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 mathematicsthere is no Nobel Prize in mathematics).
********
Dickson, L. E., Introduction to the Theory of Numbers, Dover. ISBN0486603423
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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, 5th ed. (paper) ISBN198531710 ($32.95, but over 400 pages of goodies).
This is a classic. A number of the topics are accessible to 12th 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. ISBN0486602591
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Arithmetic and Algebra ***********
Bowers, Henry and Bowers, Joan E., Arithmetical Excursions: An Enrichment of Elementary Mathematics, Dover. ISBN0486207706
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Chrystal, G. Textbook of Algebra, 2 volumes, Dover.
This is a classic.
***********
Fine, Henry B., College Algebra, Dover (may be out of print). ISBN0486602117.
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, SpringerVerlag
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Volpel, M. C., Concepts and Methods of Arithmetic, Dover. ISBN0486612376.
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Geometry and Trignometry
********
Abbott, E. A., Flatland, Dover.
A classic.
********
Bonola, R., NonEuclidean Geometry, A Critical and Historical Study of Its Development, Dover. ISBN0486600270
********
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 CohnVossen, Geometry and the Imagination, Chelsea, 1952.
********
Hobson, E. W., A treatise on Plane Trigonometry, Dover.
********
Klein, F., Famous Problems of Elementary Geometry, Dover.
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Lang, S. and Morrow, Geometry, Springer
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Manning, Henry P., The Fourth Dimension Simply Explained, Dover ISBN0486207110
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Manning, Henry P., Introduction to nonEuclidean Geometry, Dover ISBN0486603105
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Row, T. Sundara, Geometric Exercise in Paper Folding, Dover ISBN0486215946
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Sommerville, D. M. Y., The Elements of NonEuclidean Geometry, Dover. ISBN0486604608
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Winger, Roy M. An Introduction to Projective Geometry, Dover. ISBN0486609499
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Calculus
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.
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Supplementary Texts to Courses
I. M. Gelfand, E.G. Glagoleva, A. A. Kirillov, The Method of Coordinates Birkhauser (1990), paperback. ISBN0817635335
I. M. Gelfand, E.G. Glagoleva, E. E. Shnol, Functions and Graphs Birkhauser (1990), paperback. ISBN0817635327
I. M. Gelfand, A. Shen, Algebra Birkhauser (1993), paperback. ISBN0817636773
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