• Mathematics

Abstract and Concrete Categories

The Joy of Cats
Author: Jiri Adamek,Jiří Adámek (ing.),Horst Herrlich,George E. Strecker
Publisher: N.A
ISBN: 9780486469348
Category: Mathematics
Page: 517
View: 3186
This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

    • Mathematics

Topoi

The Categorial Analysis of Logic
Author: R. Goldblatt
Publisher: Elsevier
ISBN: 148329921X
Category: Mathematics
Page: 565
View: 1407
The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''. The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

    • Mathematics

Models and Ultraproducts

An Introduction
Author: John Lane Bell,A. B. Slomson
Publisher: Courier Corporation
ISBN: 0486449793
Category: Mathematics
Page: 322
View: 8426
In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

    • Mathematics

The Red Book of Mathematical Problems


Author: Kenneth S. Williams,Kenneth Hardy
Publisher: Courier Corporation
ISBN: 0486151824
Category: Mathematics
Page: 192
View: 2313
Handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Preface to the First Edition. Sources. 1988 edition.

    • Technology & Engineering

Selected Papers on Noise and Stochastic Processes


Author: Nelson Wax
Publisher: Courier Corporation
ISBN: 0486798267
Category: Technology & Engineering
Page: 352
View: 9994
These six classic papers on stochastic process were selected to meet the needs of professionals and advanced undergraduates and graduate students in physics, applied mathematics, and engineering. Contents include: "Stochastic Problems in Physics and Astronomy" by S. Chandrasekhar from Reviews of Modern Physics, Vol. 15, No. 1 "On the Theory of Brownian Motion" by G. E. Uhlenbeck and L. S. Ornstein from Physical Review, Vol. 36, No. 3 "On the Theory of the Brownian Motion II" by Ming Chen Wang and G. E. Uhlenbeck from Reviews of Modern Physics, Vol. 17, Nos. 2 and 3 "Mathematical Analysis of Random Noise" by S. O. Rice from Bell System Technical Journal, Vols. 23 and 24 "Random Walk and the Theory of Brownian Motion" by Mark Kac from American Mathematical Monthly, Vol. 54, No. 7 "The Brownian Movement and Stochastic Equations" by J. L. Doob from Annals of Mathematics, Vol. 43, No. 2

    • Science

Some Mathematical Methods of Physics


Author: Gerald Goertzel,Nunzio Tralli
Publisher: Courier Corporation
ISBN: 0486780635
Category: Science
Page: 320
View: 952
Well-rounded, thorough treatment introduces basic concepts of mathematical physics involved in the study of linear systems, with emphasis on eigenvalues, eigenfunctions, and Green's functions. Topics include discrete and continuous systems and approximation methods. 1960 edition.

    • Science

Sapiens

A Brief History of Humankind
Author: Yuval Noah Harari
Publisher: Harper Collins
ISBN: 0062316109
Category: Science
Page: 464
View: 6181
New York Times Bestseller A Summer Reading Pick for President Barack Obama, Bill Gates, and Mark Zuckerberg From a renowned historian comes a groundbreaking narrative of humanity’s creation and evolution—a #1 international bestseller—that explores the ways in which biology and history have defined us and enhanced our understanding of what it means to be “human.” One hundred thousand years ago, at least six different species of humans inhabited Earth. Yet today there is only one—homo sapiens. What happened to the others? And what may happen to us? Most books about the history of humanity pursue either a historical or a biological approach, but Dr. Yuval Noah Harari breaks the mold with this highly original book that begins about 70,000 years ago with the appearance of modern cognition. From examining the role evolving humans have played in the global ecosystem to charting the rise of empires, Sapiens integrates history and science to reconsider accepted narratives, connect past developments with contemporary concerns, and examine specific events within the context of larger ideas. Dr. Harari also compels us to look ahead, because over the last few decades humans have begun to bend laws of natural selection that have governed life for the past four billion years. We are acquiring the ability to design not only the world around us, but also ourselves. Where is this leading us, and what do we want to become? Featuring 27 photographs, 6 maps, and 25 illustrations/diagrams, this provocative and insightful work is sure to spark debate and is essential reading for aficionados of Jared Diamond, James Gleick, Matt Ridley, Robert Wright, and Sharon Moalem.

    • Mathematics

Dialgebras and Related Operads


Author: J.-L. Loday,A. Frabetti,F. Chapoton,F. Goichot
Publisher: Springer
ISBN: 3540453288
Category: Mathematics
Page: 140
View: 6871

    • Mathematics

A Short Account of the History of Mathematics


Author: W. W. Rouse Ball
Publisher: Courier Corporation
ISBN: 0486157849
Category: Mathematics
Page: 560
View: 5853
This standard text treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.

    • Science

An Introduction to the Theory of Elasticity


Author: R. J. Atkin,N. Fox
Publisher: Courier Corporation
ISBN: 0486150992
Category: Science
Page: 272
View: 9806
Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.

    • Mathematics

A Book of Set Theory


Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Category: Mathematics
Page: 256
View: 5773
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

    • Mathematics

Axiomatic Set Theory


Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486136876
Category: Mathematics
Page: 265
View: 510
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

    • Science

Physics of Fully Ionized Gases

Second Revised Edition
Author: Lyman Spitzer
Publisher: Courier Corporation
ISBN: 0486151581
Category: Science
Page: 192
View: 4488
An introductory course in theoretical physics is the sole prerequisite for this general but simple introduction to the fields of plasma and fusion research. 1962 edition.

    • Mathematics

Introduction to Applied Numerical Analysis


Author: Richard W. Hamming
Publisher: Courier Corporation
ISBN: 0486485900
Category: Mathematics
Page: 331
View: 6392
"This book is appropriate for an applied numerical analysis course for upper-level undergraduate and graduate students as well as computer science students. Actual programming is not covered, but an extensive range of topics includes round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, Fourier series, and much more. 1989 edition"--Provided by publisher.

    • Mathematics

Complex Integration and Cauchy's Theorem


Author: G.N. Watson
Publisher: Courier Corporation
ISBN: 0486283569
Category: Mathematics
Page: 96
View: 5557
Brief monograph by a distinguished mathematician offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Includes applications to the calculus of residues. 1914 edition.

    • Mathematics

Set Theory and Logic


Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category: Mathematics
Page: 512
View: 5857
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

    • Science

Atomic Physics: 8th Edition


Author: Max Born
Publisher: Courier Corporation
ISBN: 0486318583
Category: Science
Page: 544
View: 1741
Nobel Laureate's lucid treatment of kinetic theory of gases, elementary particles, nuclear atom, wave-corpuscles, atomic structure and spectral lines, much more. Over 40 appendices, bibliography.

    • Mathematics

Mathematical Logic


Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 0486317072
Category: Mathematics
Page: 416
View: 2673
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

    • Mathematics

Curvature in Mathematics and Physics


Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 0486292711
Category: Mathematics
Page: 416
View: 1946
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

    • Mathematics

Galois Theory

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,
Author: Emil Artin
Publisher: Courier Corporation
ISBN: 048615825X
Category: Mathematics
Page: 86
View: 1087
Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.