Elements of Mathematics: Lie Groups and Lie Algebr...

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Title: Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7-9
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(Elements of Mathematics)
3540434054, Pages: 434

This is the English translation of Bourbaki's text Groupes et Algbres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (3-540-42650-7) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

http://linkgrabber.blogspot.com/2007/02/elements-of-mathematics.html
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Laws of Nature
3540240799, Pages: 376

The book is concerned with the laws of nature and in particular with the laws of physics. The authors discuss three important questions: First, whether the observed regularities are based on strict "laws of nature" that hold rigorously and without any exception. Second, what we call a "law of nature" is studied by comparing this concept with invariance principles, causality principles, teleological principles and means of predicting future events. Finally, on the basis of these investigations the authors treat the ambitious and intricate third question, why the laws of nature hold. Are there rational reasons for this largely unexplained phenomenon? This book addresses students as well as researchers. It will be an excellent reference for those interested in the philosophical foundations of the natural sciences.

http://linkgrabber.blogspot.com/2007/02/laws-of-nature.html
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Frontiers of Numerical Analysis: Durham 2004
3540239219, Pages: 266

This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

http://linkgrabber.blogspot.com/2007/02/frontiers-of-numerical-analysis.html
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Essential Topology
(Springer Undergraduate Mathematics Series)
1852337826, Pages: 224

Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and homology: the cornerstones of contemporary algebraic topology.

While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student, reflecting the fact that these are often the key examples behind current research.

With chapters on:

continuity and topological spaces
deconstructionist topology
the Euler number
homotopy groups including the fundamental group
simplicial and singular homology, and
fibre bundles

Essential Topology contains enough material for two semester-long courses, and offers a one-stop-shop for undergraduate-level topology, leaving students motivated for postgraduate study in the field, and well-prepared for it.

http://linkgrabber.blogspot.com/2007/02/essential-topology.html
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The Human Condition, 2nd Edition
0226025985, Pages: 370

A work of striking originality bursting with unexpected insights, The Human Condition is in many respects more relevant now than when it first appeared in 1958. In her study of the state of modern humanity, Hannah Arendt considers humankind from the perspective of the actions of which it is capable. The problems Arendt identified then--diminishing human agency and political freedom, the paradox that as human powers increase through technological and humanistic inquiry, we are less equipped to control the consequences of our actions--continue to confront us today. This new edition, published to coincide with the fortieth anniversary of its original publication, contains an improved and expanded index and a new introduction by noted Arendt scholar Margaret Canovan which incisively analyzes the book's argument and examines its present relevance. A classic in political and social theory, The Human Condition is a work that has proved both timeless and perpetually timely.

Hannah Arendt (1906-1975) was one of the leading social theorists in the United States. Her Lectures on Kant's Political Philosophy and Love and Saint Augustine are also published by the University of Chicago Press.

http://linkgrabber.blogspot.com/2007/02/human-condition-2nd-edition.html
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Conceptions of Truth
0199241317, Pages: 512

Truth is one of the most debated topics in philosophy; Wolfgang Kunne presents a comprehensive critical examination of all major theories. Conceptions of Truth is organized around a flow-chart comprising sixteen key questions, ranging from Is truth a property? to Is truth epistemically constrained? Kunne expounds and engages with the ideas of many thinkers, from Aristotle and the Stoics, to Continental analytic philosophers like Bolzano, Brentano, and Kotarbinski, to such leading figures in current debates as Dummett, Putnam, Wright, and Horwich. He explains many important distinctions (between varieties of correspondence, for example, between different conceptions of making true, between various kinds of eternalism and temporalism) which have so far been neglected in the literature. Kunne argues that it is possible to give a satisfactory 'modest' account of truth without invoking problematic notions like correspondence, fact, or meaning. And he offers a novel argument to support the realist claim that truth outruns justifiability. The clarity of exposition and the wealth of examples will make Conceptions of Truth an invaluable and stimulating guide for advanced students and scholars in metaphysics, epistemology and the philosophy of language.

http://linkgrabber.blogspot.com/2007/02/conceptions-of-truth.html
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Mathematical Circus (Spectrum)
0883855062, Pages: 296


The twenty chapters of this book are nicely balanced between all sorts of stimulating ideas, suggested by down-to-earth objects like match sticks and dollar bills as well as by faraway objects like planets and infinite random walks. We learn about ancient devices for arithmetic and about modern explanations of artificial intelligence. There are feasts here for the eyes and hands as well as for the brain.

Links

http://linkgrabber.blogspot.com/2007/02/mathematical-circus.html

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1. Ebooks list page : 507
2. Elements of Mathematics: Lie Groups and Lie Algebr...
3. Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)
4. Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7-9 (Elements of Mathematics)
5. Elements of Mathematics: Lie Groups and Lie Algebras: Chapters 7-9
6. Lie Groups (Graduate Texts in Mathematics)
7. Permutation Groups (Graduate Texts in Mathematics)
8. A Course in the Theory of Groups (Graduate Texts in Mathematics)
9. Topological Groups (Classics of Soviet Mathematics)
10. Groups and Symmetry: A Guide to Discovering Mathematics
11. 3-Transposition Groups (Cambridge Tracts in Mathematics)
12. Lie Groups (Graduate Texts in Mathematics) (Repost)
13. Groups and Symmetry: A Guide to Discovering Mathematics
14. Linear Algebraic Groups (Graduate Texts in Mathematics)
15. Linear Algebraic Groups (Graduate Texts in Mathematics)
16. Algebraic K-Groups as Galois Modules (Progress in Mathematics)