Series: London Mathematical Society Lecture Note Series (No. 362)
Paperback (ISBN-13: 9780521757683)
Page extent: 456 pages
This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras, and on their modules. But there are also some new results and some new proofs. Their approach presents a formal alternative to the use of bocses (bimodules over categories with coalgebra structure) with underlying additive categories and pull-back reduction constructions. Professional mathematicians working in representation theory and related fields, and graduate students interested in homological algebra will find much of interest in this book.
* Includes central results not covered in existing books * Suitable for
professional mathematicians and graduate students with only a basic knowledge
of module theory * Contains over 90 exercises for the reader to test their
understanding
Preface; 1. t-algebras and differentials; 2. Ditalgebras and modules; 3. Bocses, ditalgebras and modules; 4. Layered ditalgebras; 5. Triangular ditalgebras; 6. Exact structures in A-Mod; 7. Almost split conflations in A-Mod; 8. Quotient ditalgebras; 9. Frames and Roiter ditalgebras; 10. Product of ditalgebras; 11. Hom-tensor relations and dual basis; 12. Admissible modules; 13. Complete admissible modules; 14. Bimodule ltrations and triangular admissible modules; 15. Free bimodule ltrations and free ditalgebras; 16. AX is a Roiter ditalgebra, for suitable X; 17. Examples and applications; 18. The exact categories P(Λ), P1(Λ) and Λ-Mod; 19. Passage from ditalgebras to finite dimensional algebras; 20. Scalar extension and ditalgebras; 21. Bimodules; 22. Parametrizing bimodules and wildness; 23. Nested and seminested ditalgebras; 24. Critical ditalgebras; 25. Reduction functors; 26. Modules over non-wild ditalgebras; 27. Tameness and wildness; 28. Modules over non-wild ditalgebras revisited; 29. Modules over non-wild algebras; 30. Absolute wildness; 31. Generic modules and tameness; 32. Almost split sequences and tameness; 33. Varieties of modules over ditalgebras; 34. Ditalgebras of partially ordered sets; 35. Further examples of wild ditalgebras; 36. Answers to selected exercises; References; Index.
Series: The New Martin Gardner Mathematical Library (No. 3)
Hardback (ISBN-13: 9780521756075)
Paperback (ISBN-13: 9780521747011)
Page extent: 296 pages
Packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll. These and other mathematical diversions return to readers with updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries. Read about Knuth’s Word Ladders program and the latest developments in the digits of pi. Once again these timeless puzzles will charm readers while demonstrating principles of logic, probability, geometry, and other fields of mathematics.
* Contains extensive updated material by Gardner not found in any other
editions of these books, plus and new bibliographies * The first complete
collection of Martin Gardner’s Mathematical Library which encompasses
the entire 25 year run of his Scientific American columns
1. The binary system; 2. Group theory and braids; 3. Eight problems; 4. The games and puzzles of Lewis Carroll; 5. Paper cutting; 6. Board games; 7. Sphere packing; 8. The transcendental number Pi; 9. Victor Eigen, mathemagician; 10. The four-color map theorem; 11. Mr. Apollinax visits New York; 12. Nine problems; 13. Polyominoes and fault-free rectangles; 14. Euler’s spoilers: the discovery of an Order-10 Graeco-Latin square; 15. The ellipse; 16. The 24 color squares and the 30 color cubes; 17. H. S. M. Coxeter; 18. Bridg-it and other games; 19. Nine more problems; 20. The calculus of finite differences.
2009年2月発刊 税込価格 6400円 ／ 送料 340円
本書は，２００７年６月に京都で開催された柏原正樹教授の還暦を記念する研究集会``Algebraic Analysis and Around''の報告集である． -加群，超局所解析，表現論，可積分系を主な内容として，上記研究集会における招待講演に基づいた研究論文を中心に，１１編の論文・論説が収められている．現在に至るまで，-加群の理論は大いに発展して数学の諸分野に対して多大な影響を与えている．本書は，その発展と影響を体現しつつ，ひいては未来の数学の萌芽となるような珠玉の論文・論説からなっている．
目次 (pdf file)
ISBN: 978-81-7319-933-2
Publication Year: 2008
Pages: 266
Binding: Hard Back
About the book
The Riemann, Lebesgue and Generalized Riemann Integrals aims at the definition and development of the Henstock-Kurzweil integral and those of the McShane integral in the real line. The developments are as simple as the Riemann integration and can be presented in introductory courses. The Henstock-Kurzweil integral is of super Lebesgue power while the McShane integral is of Lebesgue power. For bounded functions, however, the Henstock-Kurzweil, the McShane and the Lebesgue integrals are equivalent. Owing to their simple construction and easy access, the Generalized Riemann integrals will surely be familiar to physicists, engineers and applied mathematicians. Each chapter of the book provides a good number of solved problems and counter examples along with selected problems left as exercises.
Preface / The Riemann Integral / The Lebesgue Measure / The Lebesgue Integral / Functions of Bounded Variation / Semi-continuous Functions / Tagged Gauge Partitions / The Henstock-Kurzweil Integral / The Absolute Integrals / The Riemann Integral Revisited / The HK-Integral on Sets / Author’s Related Publications / Bibliography / Index.
Honorable Mention,
Paper | 2009
248 pp. | 6 x 9 | 6 halftones. 74 line illus.
The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest background in mathematics, this biography of e brings out that number's central importance in mathematics and illuminates a golden era in the age of science.
Eli Maor is the author of Venus in Transit, Trigonometric Delights, To Infinity and Beyond, and The Pythagorean Theorem: A 4,000-Year History (all Princeton). He teaches the history of mathematics at Loyola University in Chicago and at the Graham School of General Education at the University of Chicago.
Preface
1 John Napier, 1614 3
2 Recognition 11
3 Financial Matters 23
4 To the Limit, If It Exists 28
5 Forefathers of the Calculus 40
6 Prelude to Breakthrough 49
7 Squaring the Hyperbola 58
8 The Birth of a New Science 70
9 The Great Controversy 83
10 e[superscript x]: The Function That Equals its Own Derivative 98
11 e[superscript theta]: Spira Mirabilis 114
12 (e[superscript x] + e[superscript -x])/2: The Hanging Chain 140
13 e[superscript ix]: "The Most Famous of All Formulas" 153
14 e[superscript x + iy]: The Imaginary Becomes Real 164
15 But What Kind of Number Is It* 183
App. 1. Some Additional Remarks on Napier's Logarithms 195
App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity] 197
App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus 200
App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0 202
App. 5. An Alternative Definition of the Logarithmic Function 203
App. 6. Two Properties of the Logarithmic Spiral 205
App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions 208
App. 8. e to One Hundred Decimal Places 211
Bibliography 213
Index