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Language, Truth and Logic in Mathematics

Posted By: AvaxGenius
Language, Truth and Logic in Mathematics

Language, Truth and Logic in Mathematics by Jaakko Hintikka
English | PDF | 1998 | 257 Pages | ISBN : 0792347668 | 26.8 MB

One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer.

Geometric Constructions

Posted By: AvaxGenius
Geometric Constructions

Geometric Constructions by George E. Martin
English | PDF | 1998 | 210 Pages | ISBN : 0387982760 | 17.3 MB

Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations.

A First Course in Real Analysis

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A First Course in Real Analysis

A First Course in Real Analysis by Sterling K. Berberian
English | PDF | 1994 | 249 Pages | ISBN : 0387942173 | 16.6 MB

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers.

Tools for Computational Finance

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Tools for Computational Finance

Tools for Computational Finance by Rüdiger Seydel
English | PDF | 2004 | 256 Pages | ISBN : 3540406042 | 18.9 MB

This edition contains more material. The largest addition is a new section on jump processes (Section 1.9). The derivation of a related partial integro­ differential equation is included in Appendix A3. More material is devoted to Monte Carlo simulation. An algorithm for the standard workhorse of in­ verting the normal distribution is added to Appendix A7. New figures and more exercises are intended to improve the clarity at some places.

Punctured Torus Groups and 2-Bridge Knot Groups (I) (Repost)

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Punctured Torus Groups and 2-Bridge Knot Groups (I) (Repost)

Punctured Torus Groups and 2-Bridge Knot Groups (I) by Hirotaka Akiyoshi
English | PDF | 2007 | 293 Pages | ISBN : 3540718060 | 4.8 MB

This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory.

Trigonometry

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Trigonometry

Trigonometry by I. M. Gelfand
English | PDF,EPUB | 2001 | 236 Pages | ISBN : 0817639144 | 17.9 MB

In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science.

Algorithms: Main Ideas and Applications

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Algorithms: Main Ideas and Applications

Algorithms: Main Ideas and Applications by Vladimir Uspensky
English | PDF | 1993 | 280 Pages | ISBN : 079232210X | 29.53 MB

Today the notion of the algorithm is familiar not only to mathematicians. It forms a conceptual base for information processing; the existence of a corresponding algorithm makes automatic information processing possible.