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Other Books on the Subject of Proofs and Mathematical Writing 175An interesting and useful book for a quick review of mathematicalterms is the well-known Mathematics Dictionary by Glenn James andRobert C. James (Chapman & Hall, 1992).A book that goes to the roots of mathematical words is Vie Wordsof Mathematics: An Etymological Dictionary of Mathematical Terms Usedin English, by Steven Schwartzman (The Mathematical Association ofAmerica, 1994).The following books offer suggestions on writing mathematical material:Alley, M., The Craft of Scientific Writing, Springer-Verlag, Berlin/New York,1996.Countryman, J., Writing To l£arn Mathematics, Heinemann, Portsmouth,NH, 1992.Gerver, R., Writing Research Papers: Enrichment for Math Enthusiasts,Key Curriculum Press, 1997.Gillman, L., Writing Mathematics Well, Mathematical Association ofAmerica, Washington, D.C., 1987.Higham, N. J., Handbook of Writing for the Mathematical Sciences, Societyfor Industrial and Applied Mathematics, Philadelphia, PA, 1993.Knuth, D. E., Larrabee, T., and Roberts, P. M., Mathematical Writing,Mathematical Association of America, Washington, D.C., 1989.Levine, A., Discovering Higher Mathematics: Four Habits of Highly EffectiveMathematicians, Academic Press, San Diego, CA, 2000. (This is a bookthat focuses on the processes of experimentation, conjecture, proof, andgeneralization, by using material form number theory, discrete mathematics,and combinatorics. The author also addresses some issues inwriting mathematics.)A multitude of books are available on how to use the tools of logic to solveproblems. Here is a brief (and thus incomplete) hst of them:Daepp, U. and Garkin, P., Reading, Writing and Proving: A Closer look atMathematics, Springer-Verlag, Beriin/New York, 2003.Engel, A., Problem Solving Strategies, Springer-Verlag, Berlin/New York,1998.Larson, L.C., Problem Solving Through Problems, Springer-Verlag,Berlin/New York, 1983.Lozansky, E. and Rousseau, C, Winning Solutions, Problem Books inMathematics, Springer-Verlag, Berhn/New York, 1996.Vakil, R., A Mathematical Mosaic: Patterns and Problem Solving,Brendan Kelly PubUshing, 1997.
176 The Nuts and Bolts of Proof, Third EditionWilliams, K. S. and Hardy, K., The Red Book of Mathematical Problems,Dover, New York, 1996.Williams, K. S., Hardy, K. The Green Book of Mathematical Problems,Dover, New York, 1997.Zeitz, P., The Art and Craft of Problem Solving, John Wiley & Sons,New York, 1999.A book to enjoy after mastering the basics of mathematical proofsis Proofs from the Book, 3rd ed., by M. Aigner and G. Ziegler(Springer-Verlag, 2003).
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The Nuts and Bolts of ProofsThird E
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The Nuts and Bolts of ProofsThird E
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List of SymbolsNatural or counting
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List of Symbolsvii(relatively prime
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ContentsList of Symbols vPreface xi
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PrefaceThis book is addressed to th
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Introduction and BasicTerminologyHa
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Introduction and Basic Terminology
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General SuggestionsThe first step,
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Basic Techniques To ProveIf/Then St
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special Kinds of TheoremsThere are
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Special Kinds of Theorems 37Parti.
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Special Kinds of Theorems39Diagram
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Special Kinds of Theorems 41anda <
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Special Kinds of Theorems 43Suppose
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Special Kinds of Theorems 45and^aix
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Special Kinds of Theorems 47EXAMPLE
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Special Kinds of Theorems 493. Usin
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Special Kinds of Theorems 51use the
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Special Kinds of Theorems 53As both
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Special Kinds of Theorems 55Using t
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Special Kinds of Theorems 57If we s
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Special Kinds of Theorems 59B. Ther
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Special Kinds of Theorems 61EXERCIS
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Special Kinds of Theorems 63EXAMPLE
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Special Kinds of Theorems 65If /c >
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Special Kinds of Theorems 67for all
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Special Kinds of Theorems 69conside
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Special Kinds of Theorems 71To cons
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Special Kinds of Theorems 73We will
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Special Kinds of Theorems 75both A
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Special Kinds of Theorems 773. Prov
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Special Kinds of Theorems 79(For de
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Special Kinds of Theorems 81This im
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Special Kinds of Theorems 83Let us
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Special Kinds of Theorems 85Indeed,
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Special Kinds of Theorems 87of the
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Special Kinds of Theorems 89where p
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Special Kinds of Theorems 91which h
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Special Kinds of Theorems 93Thus, w
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Special Kinds of Theorems 95The exi
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Special Kinds of Theorems 97Thus,\x
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Special Kinds of Theorems2n-lpEXAMP
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Special Kinds of Theorems 101that l
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Review ExercisesDiscuss the truth o
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Review Exercises 10519. Let y4 be a
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Exercises Without SolutionsDiscuss
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Exercises Without Solutions 10922.
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Exercises Without Solutions 111(b)
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Exercises Without Solutions 113(Thi
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Collection of ProofsThe following c
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Collection of Proofs 117Alleged Pro
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Collection of Proofs 119where k is
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Collection of Proofs 121THEOREM 10.
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Solutions for the Exercises atthe E
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Page 190 and 191: IndexAlgorithms, Division, 16Argume
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