Modern Mathematics Through Discovery Series
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Modern Mathematics Through Discovery
Author | : Robert Lee Morton |
Publisher | : |
Total Pages | : 318 |
Release | : 1966 |
Genre | : Mathematics |
ISBN | : |
Modern Mathematics Through Discovery
Author | : Myron Frederick Rosskopf |
Publisher | : |
Total Pages | : 384 |
Release | : 1964 |
Genre | : Arithmetic |
ISBN | : |
Proofs and Refutations
Author | : Imre Lakatos |
Publisher | : Cambridge University Press |
Total Pages | : 190 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : 9780521290388 |
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Modern Classical Homotopy Theory
Author | : Jeffrey Strom |
Publisher | : American Mathematical Soc. |
Total Pages | : 862 |
Release | : 2011-10-19 |
Genre | : Mathematics |
ISBN | : 0821852868 |
The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Experimentation in Mathematics
Author | : Jonathan M. Borwein |
Publisher | : CRC Press |
Total Pages | : 372 |
Release | : 2004-04-12 |
Genre | : Mathematics |
ISBN | : 1439864195 |
New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of
Labyrinth of Thought
Author | : Jose Ferreiros |
Publisher | : Springer Science & Business Media |
Total Pages | : 472 |
Release | : 2001-11-01 |
Genre | : Mathematics |
ISBN | : 9783764357498 |
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
The Nature and Growth of Modern Mathematics
Author | : Edna Ernestine Kramer |
Publisher | : Princeton University Press |
Total Pages | : 790 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : 9780691023724 |
Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.