Main Title |
The mathematical experience / |
Author |
Davis, Philip J.,
|
Other Authors |
|
Publisher |
Houghton Mifflin, |
Year Published |
1982 |
OCLC Number |
08194064 |
ISBN |
039532131X; 9780395321317; 0395321573; 9780395321577 |
Subjects |
Mathematics--Philosophy ;
Mathematics--History ;
Mathematics--Study and teaching
|
Holdings |
Library |
Call Number |
Additional Info |
Location |
Last Modified |
Checkout Status |
EHAM |
QA8.4.D37 1982 |
|
Region 1 Library/Boston,MA |
07/23/2004 |
|
Collation |
xix, 440 pages : illustrations ; 24 cm |
Notes |
Reprint. Originally published: Boston : Birkhäuser, 1981. Includes bibliographical references (pages 417-434) and index. |
Contents Notes |
Traces the history of mathematics, offers profiles of major mathematicians and their discoveries, and looks at the philosophy of mathematics. 1. The mathematical landscape -- What is mathematics? -- Where is mathematics? -- The mathematical community -- The tools of the trade -- How much mathematics is now known? -- Ulam's dilemma -- How much mathematics can there be? -- 2. Varieties of mathematical experience -- The current individual and collective consciousness -- The ideal mathematician -- A physicist looks at mathematics -- I.R. Shafarevitch and the new neoplatonism -- Unorthodoxies -- The individual and the culture -- 3. Outer issues -- Why mathematics works: A conventionalist answer -- Mathematical models -- Utility -- Abstraction and scholastic theory -- 4. Inner issues -- Symbols -- Abstraction -- Generalization -- Formalization -- Mathematical objects and structures; Existence -- Proof -- Infinity, or the miraculous jar of mathematics -- The stretched string -- The coin of Tyche -- The aesthetic component -- Pattern, order, and chaos -- Algorithmic vs. dialectic mathematics -- The drive to generality and abstraction -- The Chinese remainder theorem: A case study -- Mathematics as enigma -- Unity within diversity -- 5. Selected topics in mathematics -- Group theory and the classification of finite simple groups -- The prime number theorem -- Non-Euclidean geometry -- Non-Cantorian set theory -- 6. Teaching and learning -- Confessions of a prep school math teacher -- The classic classroom crises of understanding and pedagogy -- Pólya's craft of discovery -- The creation of new mathematics: An application of the Lakatos heuristic -- Comparative aesthetics -- Nonanalytic aspects of mathematics -- 7. From certainty to fallibility -- Platonism, formalism, constructivism -- The philosophical plight of mathematics -- Lakatos and the philosophy of dubitability -- 8. Mathematical reality -- The Riemann hypothesis -- [pi] and [ãpi] -- Mathematical models, computers, and Platonism -- Why should I believe a computer? -- Classification of finite simple groups -- Intuition -- Four-dimensional intuition -- True facts about imaginary objects. |
Place Published |
Boston : |
PUB Date Free Form |
1982, c1981. |
BIB Level |
m |
Cataloging Source |
OCLC/T |
LCCN |
81020304 |
OCLC Time Stamp |
20040721115835 |
Language |
eng |
Origin |
OCLC |
Type |
CAT |
OCLC Rec Leader |
00974pam 2200301 a 45010 |