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Author : R. E. Edwards
Publisher : Springer Science & Business Media
ISBN 13 : 1461380960
Total Pages : 651 pages
Book Rating : 4.4/5 (613 download)
Download or read book A Formal Background to Mathematics 2a written by R. E. Edwards and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. E. Edwards
Publisher : Springer Science & Business Media
ISBN 13 : 1461299845
Total Pages : 968 pages
Book Rating : 4.4/5 (612 download)
Download or read book A Formal Background to Mathematics written by R. E. Edwards and published by Springer Science & Business Media. This book was released on 2013-12-18 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: §1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted).
Author : R. E. Edwards
Publisher : Springer
ISBN 13 : 9780387905136
Total Pages : 606 pages
Book Rating : 4.9/5 (51 download)
Download or read book A Formal Background to Mathematics 2a written by R. E. Edwards and published by Springer. This book was released on 1980-10-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert E. Edwards
Publisher :
ISBN 13 :
Total Pages : 486 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Formal Background to Mathematics written by Robert E. Edwards and published by . This book was released on 1979 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert E. Edwards
Publisher :
ISBN 13 :
Total Pages : 490 pages
Book Rating : 4.3/5 (97 download)
Download or read book A Formal Background to Mathematics: Logic, sets, and numbers. 2 v written by Robert E. Edwards and published by . This book was released on 1979 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1084 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arthur Jones
Publisher : Springer Science & Business Media
ISBN 13 : 1441985522
Total Pages : 191 pages
Book Rating : 4.4/5 (419 download)
Download or read book Abstract Algebra and Famous Impossibilities written by Arthur Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.
Author : Alexander J. Hahn
Publisher : Springer Science & Business Media
ISBN 13 : 146846311X
Total Pages : 296 pages
Book Rating : 4.4/5 (684 download)
Download or read book Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups written by Alexander J. Hahn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.
Author : Richard A. Holmgren
Publisher : Springer Science & Business Media
ISBN 13 : 1468402226
Total Pages : 213 pages
Book Rating : 4.4/5 (684 download)
Download or read book A First Course in Discrete Dynamical Systems written by Richard A. Holmgren and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to both topics in dynamical systems and mathematical thinking. In particular, the authors emphasize those parts of mathematical analysis necessary for understanding the intricacies of a discrete dynamical system. The organizing principle is the understanding of the parametrized family of functions h(x) = rx(1-x). Readers should have some background in calculus although extensive knowledge of proof-based mathematics is not necessary. Students will learn to understand periodic points, stable sets, bifurcations, symbolic dynamics, and chaos. The book includes rigorous proofs of important concepts in dynamics while remaining accessible to the typical advanced undergraduate.
Author : D.D. Bleecker
Publisher : Springer Science & Business Media
ISBN 13 : 1468406272
Total Pages : 467 pages
Book Rating : 4.4/5 (684 download)
Download or read book Topology and Analysis written by D.D. Bleecker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ ent mathematical approaches, and must have experience with their inter connections. The Atiyah-Singer Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrela tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many facetted and always new presentations of the material by M. F.
Author : Richard H. Hammack
Publisher :
ISBN 13 : 9780989472111
Total Pages : 314 pages
Book Rating : 4.4/5 (721 download)
Download or read book Book of Proof written by Richard H. Hammack and published by . This book was released on 2016-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author : Thomas E. Cecil
Publisher : Springer Science & Business Media
ISBN 13 : 1475740964
Total Pages : 219 pages
Book Rating : 4.4/5 (757 download)
Download or read book Lie Sphere Geometry written by Thomas E. Cecil and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie Sphere Geometry provides a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space. This book begins with Lie's construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres and Lie sphere transformation. The link with Euclidean submanifold theory is established via the Legendre map. This provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres. Of particular interest are isoparametric, Dupin and taut submanifolds. These have recently been classified up to Lie sphere transformation in certain special cases through the introduction of natural Lie invariants. The author provides complete proofs of these classifications and indicates directions for further research and wider application of these methods.
Author : Alexandru Dimca
Publisher : Springer Science & Business Media
ISBN 13 : 1461244048
Total Pages : 277 pages
Book Rating : 4.4/5 (612 download)
Download or read book Singularities and Topology of Hypersurfaces written by Alexandru Dimca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Joel L. Schiff
Publisher : Springer Science & Business Media
ISBN 13 : 1461209072
Total Pages : 241 pages
Book Rating : 4.4/5 (612 download)
Download or read book Normal Families written by Joel L. Schiff and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour. Since its inception early this century the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, and the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter that has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Basically, it asserts that a family of analytic (meromorphic) functions defined by a particular property, P, is likely to be a normal family if an entire (meromorphic in
Author : D.H. Luecking
Publisher : Springer Science & Business Media
ISBN 13 : 1461382955
Total Pages : 184 pages
Book Rating : 4.4/5 (613 download)
Download or read book Complex Analysis written by D.H. Luecking and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main idea of this book is to present a good portion of the standard material on functions of a complex variable, as well as some new material, from the point of view of functional analysis. The main object of study is the algebra H(G) of all holomorphic functions on the open set G, with the topology on H(G) of uniform convergence on compact subsets of G. From this point of vie~, the main theorem of the theory is Theorem 9.5, which concretely identifies the dual of H(G) with the space of germs of holomorphic functions on the complement of G. From this result, for example, Runge's approximation theorem and the global Cauchy integral theorem follow in a few short steps. Other consequences of this duality theorem are the Germay interpolation theorem and the Mittag-Leffler Theorem. The approach via duality is entirely consistent with Cauchy's approach to complex variables, since curvilinear integrals are typical examples of linear functionals. The prerequisite for the book is a one-semester course in com plex variables at the undergraduate-graduate level, so that the elements of the local theory are supposed known. In particular, the Cauchy Theorem for the square and the circle are assumed, but not the global Cauchy Theorem in any of its forms. The second author has three times taught a graduate course based on this material at the University of Illinois, with good results.
Author : Bernard Aupetit
Publisher : Springer Science & Business Media
ISBN 13 : 1461230489
Total Pages : 206 pages
Book Rating : 4.4/5 (612 download)
Download or read book A Primer on Spectral Theory written by Bernard Aupetit and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory. Topics include the basic results of functional analysis, bounded operations on Banach and Hilbert spaces, Banach algebras, and applications of spectral subharmonicity. Each chapter is followed by exercises of varying difficulty. Much of the subject matter, particularly in spectral theory, operator theory and Banach algebras, contains new results.
Author : Hans Samelson
Publisher : Springer Science & Business Media
ISBN 13 : 1461390141
Total Pages : 172 pages
Book Rating : 4.4/5 (613 download)
Download or read book Notes on Lie Algebras written by Hans Samelson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H.
