Umfang:
Online-Ressource (XXV, 500p. 139 illus, digital)
ISBN:
9780817682958
Serie:
Modern Birkhäuser Classics
Inhalt:
Preface -- Preface to the Study Edition -- Acknowledgements -- Introduction -- Overture -- 1. The Mathematical Landscape -- 2. Varieties of Mathematical Experience -- 3. Outer Issues -- 4. Inner Issues -- 5. Selected Topics in Mathematics -- 6. Teaching and Learning -- 7. From Certainty to Fallibility -- 8. Mathematical Reality -- Glossary -- Bibliography -- Index -- Epilogue.
Inhalt:
Winner of the 1983 National Book Award, The Mathematical Experience presented a highly insightful overview of mathematics that effectively conveyed its power and beauty to a large audience of mathematicians and non-mathematicians alike. The study edition of the work followed about a decade later, supplementing the original material of the book with exercises to provide a self-contained treatment usable for the classroom. This softcover version reproduces the study edition and includes epilogues by the three original authors to reflect on the book's content 15 years after its publication, and to demonstrate its continued applicability to the classroom. Moreover, The Companion Guide to the Mathematical Experience—originally published and sold separately—is freely available online to instructors who use the work, further enhancing its pedagogical value and making it an exceptionally useful and accessible resource for a wide range of lower-level courses in mathematics and mathematics education. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto (elena.marchisottocsun.edu) upon request. Reviews [The authors] have tried to provide a book usable in a course for liberal arts students and for future secondary teachers. They have done much more! This course should be required of every undergraduate major employing the mathematical sciences. It differs from the “mathematics appreciation” courses—courses that are merely a collection of amusing puzzles and toy problems giving an illusion of a mathematical encounter—presently found in many institutions. Students of this course are introduced to the context in which mathematics exists and the incredible magnitude of words devoted to communicating mathematics (hundreds of thousands of theorems each year). How much mathematics can there be? they are asked. Instructors in a “Mathematical Experience” course must be prepared to respond to questions from students concerning the fundamental nature of the whole mathematical enterprise. Stimulated by their reading of the text, students will ask about the underlying logical and philosophical issues, the role of mathematical methods and their origins, the substance of contemporary mathematical advances, the meaning of rigor and proof in mathematics, the role of computational mathematics, and issues of teaching and learning. How real is the conflict between “pure” mathematics, as represented by G.H. Hardy’s statements, and “applied” mathematics? they may ask. Are there other kinds of mathematics, neither pure nor applied? This edition of the book provides a source of problems, collateral readings, references, essay and project assignments, and discussion guides for the course. I believe that it is likely that this course would be a challenge to many teachers and students alike, especially those teachers and students who are willing to follow their curiosity beyond the confines of this book and follow up on the many references that are provided. —Notices of the AMS (Kenneth C. Millett) This beautifully written book can be recommended to any cultivated person with a certain sophistication of thought, and also to the practicing mathematician who will find here a vantage point from which to make a tour d'horizon of his science. —Publ. Math. Debrecen This is an unusual book, being more a book about mathematics than a mathematics book. It includes mathematical issues, but also questions from the philosophy of mathematics, the psychology of mathematical discovery, the history of mathematics, and biographies of mathematicians, in short, a book about the mathematical experience broadly considered… The book found its way into "Much for liberal arts students" courses and into education courses directed at future teachers. Term paper topics, essay assignments, problems, computer applications, and suggested readings are included. This new material should greatly enhance the usefulness of this very creative book. The range of topics covered is immense and the contents cannot easily be summarized. The book makes excellent casual reading, would make a good textbook, or could easily be used as a supplement to nearly any course concerned with mathematics. —Zentralblatt MATH .
Anmerkung:
Description based upon print version of record
,
""The Mathematical Experience, Study Edition""; ""Contents""; ""Preface""; ""Preface to the Study Edition""; ""Acknowledgements""; ""Introduction""; ""Overture""; ""1 THE MATHEMATICAL LANDSCAPE""; ""What is Mathematics?""; ""Further Readings. See Bibliography""; ""Where is Mathematics?""; ""The Mathematical Community""; ""Further Readings. See Bibliography""; ""The Tools of the Trade""; ""Further Readings. See Bibliography""; ""How Much Mathematics Is Now Known?""; ""Further Readings. See Bibliography""; ""Ulam's Dilemma""; ""Further Readings. See Bibliography""
,
""How Much Mathematics Can There Be?""""Further Readings. See Bibliography""; ""Appendix A""; ""Appendix B""; ""Assignments and Problem Sets""; ""The Mathematical Landscape""; ""Topics to Explore""; ""Essay Assignments""; ""Computer Question""; ""Suggested Readings""; ""2 VARIETIES OF MATHEMATICAL EXPERIENCE""; ""The Current Individual and Collective Consciousness""; ""The Ideal Mathematician""; ""A Physicist Looks at Mathematics""; ""I. R. Shafarevitch t:lnd the New Neoplatonistn""; ""Further Readings. See Bibliography""; ""Unorthodoxies""; ""Further Readings. See Bibliography""
,
""The Individual and the Culture""""Further Readings. See Bibliography""; ""Assignments and Problem Sets""; ""Varieties of Mathematical Experience""; ""Topics to Explore""; ""Essay Assignments""; ""Problems""; ""Computer Problem""; ""Suggested Readings""; ""3 OUTER ISSUES""; ""Why Mathematics Works: A Conventionalist Answer""; ""Some Simple Instances of Mathematics by Fiat""; ""Fiat in the Physical Sciences?""; ""Further Readings. See Bibliography""; ""Mathematical Models""; ""Further Readings. See Bibliography""; ""Utility""; ""1. Varieties of Mathematical Uses""
,
""2. On the Utility of Mathematics to Mathematics.""""3. On the Utility of Mathematics to Other Scientific or Technological Fields.""; ""4. Pure vs. Applied Mathematics""; ""5. From Hardyism to Mathematical Maoism""; ""Further Readings. See Bibliography""; ""Underneath the Fig Leaf""; ""1. Mathematics in the Marketplace""; ""Further Readings. See Bibliography""; ""2. Mathematics and War""; ""Further Readings. See Bibliography""; ""3. Number Mysticism""; ""Further Readings. See Bibliography""; ""4. Hermetic Geometry""; ""Further Readings. See Bibliography""; ""5. Astrology""
,
""Further Readings. See Bibliography""""6. Religion""; ""Who wields the compass? God? Archimedes? John Dee?Or does the compass wield itself?""; ""Further Readings. See Bibliography""; ""Abstraction and Scholastic Theology""; ""Further Readings. See Bibliography""; ""Assignments and Problem Sets""; ""Outer Issues""; ""Topics to Explore""; ""Essay Assignments""; ""Problems""; ""Computer Problem""; ""Suggested Readings""; ""4 INNER ISSUES""; ""Symbols""; ""Further Readings. See Bibliography""; ""Abstraction""; ""(a) Abstraction as Idealization""; ""(b) Abstraction as Extraction""
,
""Further Readings. See Bibliography""
Weitere Ausg.:
ISBN 9780817682941
Weitere Ausg.:
Buchausg. u.d.T. Davis, Philip J., 1923 - 2018 The mathematical experience New York : Springer, 2012 ISBN 0817682945
Weitere Ausg.:
ISBN 9780817682941
Sprache:
Englisch
Fachgebiete:
Informatik
,
Mathematik
,
Philosophie
Schlagwort(e):
Mathematik
;
Philosophie
;
Mathematik
;
Geschichte
;
Mathematik
;
Philosophie
DOI:
10.1007/978-0-8176-8295-8
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Davis, Philip J. 1923-2018
Mehr zum Autor:
Hersh, Reuben 1927-2020
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