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A dictionary of quotations in mathematics

Author: Robert A Nowlan
Publisher: Jefferson, North Carolina : McFarland & Company, Inc., Publishers, [2002] ©2002
Edition/Format:   Print book : English
Summary:
Presents nearly three thousand quotations from the history of mathematics, arranged in thirty-eight categories including the God hypothesis, the origins of mathematics, mathematical people, and philosophy.
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Details

Genre/Form: Quotations
Quotations, maxims, etc
Document Type: Book
All Authors / Contributors: Robert A Nowlan
ISBN: 0786412844 9780786412846
OCLC Number: 49531279
Description: xiv, 314 pages ; 26 cm
Contents: Acknowledgments --
Preface --
[pt]. 1. The God hypothesis, religion and mathematics --
1. In the beginning : God the creator --
2. The mathematical nature of God --
3. Discovering God's thoughts --
4. Mathematical evidence of the existence of God --
5. God's universe --
playing dice or order and harmony? --
6. Religion, theology and mathematics --
[pt]. 2. The nature of mathematics 1 --
1. What is mathematics? --
2. The essence of mathematics --
3. Characteristics of mathematics --
4. Mathematics is ... --
5. Mathematics as an intellectual activity --
6. Analogies of mathematics --
7. Mathematics as a tool --
8. The misunderstanding of the nature of mathematics --
9. Other views of the nature of mathematics --
10. Mathematics as art --
11. mathematics as a game --
12. Mathematics as language. [pt]. 3. The nature of mathematics 2 --
1. Mathematics as science --
2. Appreciation for mathematics --
3. Aptitude for mathematics --
4. The attraction of mathematics --
5. Ignorance of mathematics --
6. Mathematics and the imagination --
7. Mathematical ideals and idealization --
[pt]. 4. The development of mathematics 1 --
1. Growth of new mathematical ideas --
2. The process of mathematical development --
3. Mathematical thinking --
4. Intuition --
5. Experiments and empiricism --
6. Induction --
7. Deduction --
[pt]. 5. The development of mathematics 2 --
1. Definitions --
2. Hypothesis in mathematics --
3. Mathematical analogies --
4. Abstraction --
5. General principles and generalizations --
6. Revolutions in mathematics --
7. Modern mathematics. [pt]. 6. The Historical origins of mathematics --
1. History of mathematics --
2. Oriental mathematics --
3. Egyptian mathematics --
4. Sumerian and Babylonian mathematics --
5. Chinese mathematics --
6. Japanese mathematics --
7. Mayan mathematics --
8. Greek mathematics --
9. Roman mathematics --
10. Hindu mathematics --
11. Arabic mathematics --
12. Hindu-Arabic numerals --
13. Decimal system of numeration --
14. The rebirth of mathematics in the West --
[pt]. 7. Language, e linguistics and mathematics --
1. Rhetoric and mathematics --
2. Making explanations --
3. Language and mathematics --
4. The science of mathematical linguistics --
5. Mathematical notation --
6. Mathematical symbols and symbolic language --
7. Mathematical terminology --
[pt]. 8. Mathematics : creation, discovery or invention? --
1. Creating mathematics --
2. Discovering mathematics --
3. Inventing mathematics --
4. Mathematical existence --
5. Discovering mathematical patterns --
6. Principles of mathematics --
7. Mathematical structures --
8. mathematical reasoning. [pt]. 9. The sciences and mathematics I --
1. The relationship between science and mathematics --
2. Experimentation --
3. Experience --
4. Physics and mathematics --
5. Mechanics --
[pt]. 10. The sciences and mathematics II --
1. Gravity and gravitation --
2. Relativity --
3. Quantum theory --
4. Astronomy and mathematics --
5. The sun and other stars --
6. Biology, medicine, chemistry and mathematics --
[pt]. 11. Mathematics and the arts --
1. Aesthetics : mathematical beauty --
2. Harmony and order --
3. Proportion --
4. Symmetry --
5. The arts and mathematics --
6. Architecture and mathematics --
7. Music and mathematics --
8. Painting and mathematics --
9. Perspective --
10. Poetry and mathematics --
11. Stories, myth and mysticism --
[pt]. 12. Mathematics and the social sciences --
1. Social sciences : sociology, anthropology and mathematics --
2. Economics and mathematics --
3. Psychology and mathematics --
4. Game theory. [pt]. 13. Teaching and learning mathematics --
1. The importance of examples --
2. Learning and mathematics --
3. Lectures and lecturing --
4. Clarity in teaching and learning mathematics --
5. On writing mathematics --
6. Reading and mathematics --
7. The study of mathematics --
8. Teaching and mathematics --
9. Professors, universities and mathematics --
[pt]. 14. The nature of infinity --
1. Understanding infinity --
2. The infinite and the finite --
3. Numbers and infinity --
4. The infinitely large : the infinitely small --
5. Fear and loathing of infinity --
6. Theories of infinity --
7. Nature and infinity --
8. Infinity is ... definitions, sort of --
[pt]. 15. Pure mathematics and applied mathematics --
1. Applied mathematics and mathematicians --
2. Pure mathematics and mathematicians --
3. Differences between pure and applied mathematics --
4. Partnership of pure and applied mathematics --
5. Uses and usefulness of mathematics --
6. Values of mathematics. [pt]. 16. Mathematicians --
1. Mathematicians on mathematicians --
2. Non-mathematicians on mathematicians --
3. Women an mathematics --
[pt]. 17. Some mathematical people 1 --
1. Niels Abel --
2. maria Gaetana Agnesi --
3. Ibn Musa al-Khowarizmi --
4. Apollonius of Perga --
5. Archimedes of Syracuse --
6. Charles Babbage --
7. Daniel Bernoulli --
8. Jacob Bernoulli --
9. Johann Bernoulli --
10. George David Birkhoff --
11. Ralph Boas, Jr. --
12. Janos Bolyai --
13. Bernard Bolzano --
14. George Boole --
15. "Nicolas Bourbaki" --
16. Georg Cantor --
17. Girolamo Cardano --
18. :Lewis Carroll" --
Charles Lutwidge Dodgson --
19. Augustin-Louis Cauchy --
20. Arthur Cayley --
21. Emilie de Breteuil, Marquise du Chatelet --
22. William Kingdon Clifford --
23. Nicolaus Copernicus --
24. Jean Le Rond d'Alembert --
25. Julius Wilhelm Richard Dedekind --
26. Rene Descartes --
27. Diophantus --
28. Paul Erdos --
29. Euclid --
30. Leonhard Euler. [pt]. 18. Some mathematical people 2 --
1. Pierre Fermat --
2. Joseph Fourier --
3. Gottlob Frege --
4. Galileo Galilei --
5. Evariste Galois --
6. Carl Friedrich Gauss --
7. Sophie Germain --
8. Kurt Goedel --
9. John Graunt --
10. Sir William Rowan Hamilton --
11. Godfrey H. Hardy --
12. Hermann von Helmholtz --
13. Charles Hermite --
14. David Hilbert --
15. Hipparchus of Rhodes --
16. Christiaan Huygens --
17. Hypatia --
18. Johannes Kepler --
19. Omar Khayyam --
20. Felix Klein --
21. Sonja Sophie Kovalevsky --
22. Leopold Kronecker --
23. Joseph-Louis Lagrange --
24. Imre Lakatos --
25. Pierre-Simon de Laplace --
26. Henri Lebesque --
27. Solomon Lefschetz --
28. Adrien-Marie Legendre --
29. Gottfried Wilhelm von Leibniz --
30. Marius Sophus Lie --
31. John Edensor Littlewood --
32. Nikolai Lobachevski --
33. Gosta Magnus Mittag-Leffler --
34. Gaspard Monge --
35. John Napier. [pt]. 19. Some mathematical people 3 --
1. Sir Isaac Newton --
2. Emmy Noether --
3. Pappus --
4. Blaise Pascal --
5. Benjamin Peirce --
6. Charles Sanders Peirce --
7. Jules Henri Poincare --
8. George Polya --
9. Ptolemy --
10. Pythagoras and the Pythagoreans --
11. Srinivasa Ramanujan --
12. Robert Recorde --
13. George Friedrich Bernhard Riemannn --
14. Lord Bertrand Russell --
15. Takakazu Seki (Kowa) --
16. Mary Somerville --
17. Hugo Steinhaus --
18. James Joseph Sylvester --
19. Thales --
20. Alan Turing --
21. Stanislaw Ulam --
22. John Von Neumann --
23. Karl Weierstrass --
24. Alfred North Whitehead --
25. Norbert Wiener --
26. Christopher Wren --
27. Zeno of Elea --
[pt]. 20. Problems and problem solving --
1. The three problems of antiquity --
2. Fermat's last theorem --
3. Other mathematical problems --
4. Posing mathematical problems and questions --
5. Complicated and unsolved problems --
6. Solving problems --
7. Learning and teaching problem solving --
8. Puzzles. [pt]. 21. Mathematics and nature --
1. Nature interpreted by mathematics --
2. Laws of mathematics --
3. Laws of motion --
4. Laws of nature --
[pt]. 22. Philosophy, mathematics, truth and certainty --
1. Philosophy and mathematics --
2. Philosophy of mathematics --
3. Metaphysics and metamathematics --
4. The nature of mathematical truth --
5. The certainty of mathematics --
[pt]. 23. Logic and foundations --
1. The nature of logic --
2. Symbolic logic --
3. Logic and mathematics --
4. Common sense --
5. Postulates, axioms and the axiomatic method --
6. The possible and the impossible --
7. Contradictions and paradoxes --
8. Syllogisms and validity --
9. Foundations of mathematics --
[pt]. 24. Proof and mathematics --
1. Mathematical arguments --
2. Mathematical demonstrations --
3. Cause and effect --
4. The role of assumptions in mathematics --
5. That which is obvious --
6. The nature of proof --
7. Mathematical proofs --
8. Rigor in mathematical proofs --
9. Elegant mathematical proofs --
10. mathematical propositions and theorems. [pt]. 25. Sets, relations and functions --
1. Sets and set theory --
2. Equality and equivalence --
3. Mathematical relations --
4. Functions and function theory --
5. Special functions --
[pt]. 26. Space : real and idealized --
1. Real and mathematical space --
2. Curvature of space --
3. The universe --
4. The world --
[pt]. 27. Numbers : the heart of mathematics --
1. The nature and development of numbers --
2. Number in verse --
3. The notion of quantity --
4. Cardinal and ordinal numbers --
5. Counting --
6. Whole numbers --
natural numbers --
7. Fractions --
8. Negative numbers --
9. Integers --
10. Irrational numbers --
11. Zero. [pt]. 28. Numbers and number theory --
1. Even and odd numbers --
2. Real and rational numbers --
3. Imaginary numbers --
4. Complex numbers --
5. Algebraic and transcendental numbers --
6. "e" --
7. "pi" --
8. Quaternions --
9. Transfinite numbers --
10. Number theory --
11. Continued fractions --
12. Divisibility --
13. Perfect numbers --
14. Prime numbers --
15. Magic squares --
16. Bistromathics --
[pt]. 29. Arithmetic --
1. The nature of arithmetic --
2. The fundamental operations of arithmetic --
3. Calculation and computation --
4. Logarithms --
[pt]. 30. Algebra and trigonometry --
1. Elementary algebra --
2. Exponents --
3. Formulas --
4. Unknowns and variables --
5. Equations and their solutions --
6. Fundamental theorem of algebra --
7. Trigonometry --
8. Abstract algebra --
9. Linear algebra --
10. Groups and group theory --
11. Transformation groups --
12. Invariants of groups. [pt]. 31. The art of measurement --
1. Measure and measurement --
2. Measurement and mathematics --
3. Weights and measures --
4. The measurable and the unmeasurable --
5. Measurement inverse --
6. Length, area and volume --
7. Measuring devices and techniques --
8. Approximations --
9. Longitude and latitude --
10. The metric system --
11. Time --
[pt]. 32. Geometry 1 --
1. The history of geometry --
2. The science of geometry --
3. Geometry and art --
4. Points, lines and planes --
5. Commensurability --
6. Curves --
7. Size and shapes --
8. Geometric constructions --
9. Angles and triangles --
10. Polygons and polyhedrons --
11. Circles --
12. The other conic sections --
13. Spheres --
14. Solid geometry. [pt. 33]. Geometry 2 --
1. Pythagorean theorem --
2. Flatland --
3. Dimensions and dimension theory --
4. Analytic or analytical geometry --
5. Algebraic geometry --
6. Differential geometry --
7. Distance --
metric geometry --
8. Parallel lines and the parallel postulate --
9. Non-Euclidean geometry --
10. Projection --
11. Projective geometry --
12. Duality --
13. Modern geometry --
14. Chaos --
15. Fractal geometry --
[pt]. 24. Topology and graph theory --
1. Origins of analysis situs [topology] --
2. The nature of topology --
3. Rubber sheet geometry --
4. Set-theoretic topology --
5. Topology, algebra and algebraic topology --
6. Königsberg bridge problem --
7. Graph theory --
8. The Moebius strop --
9. The Klein bottle --
10. Four color problem --
11. Knot theory. [pt]. 35. Analysis and calculus --
1. Analytical methods in mathematics --
2. Calculus of variations --
3. Continuity --
4. Infinitesimals --
5. The limit concept --
6. The calculus --
7. Derivatives and differentiation --
8. Maximum and minimum values --
9. Mean value theorem --
10. Integrals and integration --
11. Series --
12. Differential equations --
[pt]. 36. Computers, algorithms and mathematical models --
1. The history and development of computers --
2. Computers and mathematics --
3. Humans and machines --
4. Miscellaneous views of computers --
5. Cybernetics --
6. Combinatorics and combinatorial analysis --
7. Algorithms --
8. Linear programming --
9. Operations research --
10. Mathematical models. [pt]. 37. The theory of probability --
1. Calculating probabilities --
2. Probability, ignorance and certainty --
3. Miscellaneous views of probability --
4. Chance --
5. Gambling --
6. Permutations and combinations --
7. Discrete mathematics --
8. Making predictions --
[pt]. 38. Statistics and statisticians --
1. Statisticans --
2. The science of statistics --
3. Statistics and lies --
4. Miscellaneous views on statistics --
5. Samples and sampling --
6. Data --
7. Average values --
8. Decison-making --
Bibliography --
Author index --
Keyword index.
Responsibility: compiled and edited by Robert A. Nowlan.

Abstract:

This work contains 3000 quotations in mathematics, divided into 38 chapters and 389 sections that present quotations over a spectrum from God and religion to the nature of infinity.  Read more...
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"a wide array of mathematical topics...intriguing...carefully designated subject headings...quotations are fully credited...extensive bibliography...you can count on this book"--Booklist; "a massive Read more...

 
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