- Paperback: 500 pages
- Publisher: World Scientific Publishing Company; 2 edition (May 6, 2015)
- Language: English
- ISBN-10: 9814571849
- ISBN-13: 978-9814571845
- Product Dimensions: 6.6 x 1.1 x 9.3 inches
- Shipping Weight: 1.5 pounds (View shipping rates and policies)
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
- Amazon Best Sellers Rank: #3,458,778 in Books (See Top 100 in Books)
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Doing Mathematics : Convention, Subject, Calculation, Analogy (2nd Edition) 2nd Edition
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Reviews of the First Edition:
"The book Doing Mathematics, by Martin Krieger is truly a masterpiece. He has not only explained ways of doing mathematical work to aspiring mathematicians and the intelligent laymen, but has also shown how various pieces of research work are related to each other. Even experts may not have realized such inter-relations. The cases studied include, especially, the stability of matter and the Ising model, two topics of great depth. Such clear explanations cannot be found anywhere else. Furthermore, his style of writing makes the book exceptionally enjoyable to read." -- T T Wu, Gordon McKay Professor of Applied Physics, Professor of Physics, Harvard University, USA
"This is the first time I have seen a mathematician deal substantively with the issue of mathematics as culturally based, and he does it superbly and mathematically … Although this book is no easy read, it is well worth the effort, and I am sure it will stimulate and inform, perhaps even surprise, the most sophisticated of mathematical readers. It is refreshing to find such a book being published." -- Mathematical Reviews
"Both challenging and provocative reading, Doing Mathematics sheds bright light on some of the main characteristics of the mathematical quest." -- Library of Science
"Krieger has made some effort to accommodate different levels of readers; for example, structuring his text so that lay readers are alerted to sections that can be safely skipped and paragraphs that provide nontechnical summaries." -- Mathematical Association of America
From the Inside Flap
Doing Mathematics discusses some ways mathematicians do their work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians, all depend on mathematics what will work out and what won't. And how mathematics, as it is done, is shaped and supported, or not, by convention, subject matter, calculation, and analogy. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, rigorous proofs of the stability of matter, solutions to the two-dimensional Ising model of ferromagnetism, and their connection to the Langlands program in number theory and representation theory and a relationship of number theory, function theory, and analysis begun by Dedekind.
This second edition deepens each chapter: mathematical rigor and the philosophy of mathematics; finance and big data in statistics; the need for perseverance and the inevitable inelegance in a first proof; the recurrent appearance of the Bethe Ansatz and Hopf algebras in these lattice models; solutions of the Kondo model as epitomizing these themes; analogies between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics; Edward Frenkel's use of the Weil threefold-analogy in the geometric Langlands program; the warehouse of mathematical objects and how it is enlarged; and how recent developments in set theory are analogous with developments in systematic theology as attempts to be articulate about what others take as vague or beyond analysis.
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