Fundamentals of Mathematics, Vol. I: The Real Number System and Algebra

Description

Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in Mathematical Reviews, the work is “designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and ‘classical.’”
The outstanding pedagogical quality of this work was made possible only by the unique method by which it was written. There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system. (In a few cases, more than two authors have collaborated.) And the whole book has been coordinated in repeated conferences, involving altogether about 150 authors and coordinators.

Volume I opens with a section on mathematical foundations. It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials, rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn’s lemma.
Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology.
Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. An important concluding chapter examines “The Changing Structure of Modern Mathematics.”









RS Link (Vol. 1):
http://rapidshare.com/files/185026080/FuMathV1Num.rar
RS Link (Vol. 2):
http://rapidshare.com/files/185038578/FuMathV2Ge.rar
RS Link (Vol. 3):
http://rapidshare.com/files/185027207/FuMathV3An.rar

Disclaimer:
Contents of this page are indexed from the Internet. All actions are under your responsability. Email us to report illegal contents or external links and we'll remove them immediately.

Please check the description for download links if any or do a search to find alternative books.

Can't Download?
Please search mirrors if you can't find download links for "Fundamentals of Mathematics, Vol. I: The Real Number System and Algebra" in "Description" and someone else may update the links. Check the comments when back to find any updates.

Search Mirrors
Maybe some mirror pages will be helpful, search this book at top of this page or click here to find more info.

1. Ebooks list page : 2199
2. Geometric Methods in Algebra and Number Theory (Progress in Mathematics)
3. Certain Number-Theoretic Episodes In Algebra (Pure and Applied Mathematics)
4. Approximation of Additive Convolution-Like Operators: Real C*-Algebra Approach (Frontiers in Mathematics)
5. Transseries and Real Differential Algebra (Lecture Notes in Mathematics): Joris Van der Hoeven
6. A.Computational.Introduction.To.Number.Theory.And.Algebra
7. A Computational Introduction to Number Theory and Algebra
8. A Computational Introduction to Number Theory and Algebra
9. A Computational Introduction To Number Theory And Algebra
10. Symmetries in Algebra and Number Theory (SANT)
11. A Computational Introduction to Number Theory and Algebra
12. A Computational Introduction to Number Theory and Algebra
13. [share_ebook] A Computational Introduction to Number Theory and Algebra
14. A Computational Introduction to Number Theory and Algebra (Reupload)
15. Introduction to Statistics, Number Systems and Boolean Algebra
16. A Computational Introduction to Number Theory and Algebra by Victor Shoup