Michael Dummett - Frege: Philosophy of Mathematics

Michael Dummett - Frege: Philosophy of Mathematics
Publisher: Harvard University Press | 1995-04 | ISBN: 0674319362 | DJVU | 352 pages | 2.74 MB

No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments.
Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

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Topics in Finite and Discrete Mathematics

Sheldon M. Ross, "Topics in Finite and Discrete Mathematics"
Ca-ridge Univ-sity Press | 2000 | ISBN: 0521772591 | 278 pages | Djvu | 1,3 MB
Written for students in mathematics, computer science, operations research, statistics, and engineering, this text presents a concise lively survey of several fascinating non-calculus topics in modern applied mathematics. Sheldon Ross, noted textbook author and scientist, covers probability, mathematical finance, graphs, linear programming, statistics, computer science algorithms, and groups. He offers an abundance of interesting examples not normally found in standard finite mathematics courses: options pricing and arbitrage, tournaments, and counting formulas. The chapters assume a level of mathematical sophistication at the beginning calculus level, that is, a course in pre-calculus.

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Algebra: A Graduate Course (Mathematics) by I. Martin Isaacs

Algebra: A Graduate Course (Mathematics) by I. Martin Isaacs
Publisher: Brooks Cole; 1 edition (November 15, 1993) | ISBN: 0534190022 | Pages: 528 | PDF | 11.70 MB
Isaac's love for algebra and his more than 25 years of teaching experience in mathematics is evident throughout the book. In order to draw students into the material, Isaac's offers numerous examples and exercises and he seldom teaches a definition unless it leads to some interesting or exciting theorem. A number of specialized topics are included, so professors may design a course that is compatible with their own tastes. Students using this book should have knowledge of the basic ideas of group theory, ring theory, and field theory. They should know elementary linear algebra and matrix theory and they should be comfortable with mathematical proofs (how to read them, invent them, and write them).

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The Genius of Archimedes – 23 Centuries of Influence on Mathematics, Science and Engineering (Repost)

Stephanos A. Paipetis, Marco Ceccarelli, "The Genius of Archimedes – 23 Centuries of Influence on Mathematics, Science and Engineering: Proceedings of an International Conference held at Syracuse, Italy, June 8–10, 2010"
Publisher: S/r | ISBN: 9048190908 | September 11, 2010 | 696 pages | PDF | 15.9 MB
Archimedes is held in high esteem by mathematicians, physicists and engineers as one of the most brilliant scientists of all time. These proceedings contain original, unpublished papers with the primary emphasis on the scientific work of Archimedes and his influence on the fields of mathematics, science, and engineering. There are also papers dealing with archaeological aspects and the myths and legends about Archimedes and about the Archimedes Palimpsest. Papers on the following subjects form part of the book: Hydrostatics (buoyancy, fluid pressure and density, stability of floating bodies); Mechanics (levers, pulleys, centers of gravity, laws of equilibrium); Pycnometry (measurement of volume and density); Integral Calculus (Archimedes as the father of the integral calculus, method of exhaustion, approximation of pi, determination of areas and volumes); Mathematical Physics (Archimedes as the father of mathematical physics, Law of the Lever, Law of Buoyancy, Axiomatization of Physics); History of Mathematics and Mechanics (Archimedes’ influence in antiquity, the middle ages, the Renaissance, and modern times; his influence on Leonado da Vinci, Galileo, Newton, and other giants of science and mathematics); Ancient Machines and Mechanisms (catapults, water screws, iron hands, compound pulleys, planetaria, water clocks, celestial globes, the Antikythera Mechanism); Archimedean Solids (their rediscovery in the Rennaisance and their applications in materials science and chemistry); Archimedean Legends (how stories of golden crowns, eureka moments, naked runs, burning mirrors, steam cannons, etc., have influenced us through the ages, whether true or not); The Cattle Problem (how its 18th century rediscovery inspired the study of equations with integer solutions); Teaching the Ideas of Archimedes (how his life and works have influenced the teaching of science, mathematics, and engineering).

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