2004, IV, 637 p., Hardcover
ISBN: 1-4020-2546-7
Due: August 2004
About this book
This handbook focuses on some important topics from Number Theory
and Discrete Mathematics. These include the sum of divisors
function with the many old and new issues on Perfect numbers;
Euler's totient and its many facets; the Moebius function along
with its generalizations, extensions, and applications; the
arithmetic functions related to the divisors or the digits of a
number; the Stirling, Bell, Bernoulli, Euler and Eulerian
numbers, with connections to various fields of pure or applied
mathematics. Each chapter is a survey and can be viewed as an
encyclopedia of the considered field, underlining the
interconnections of Number theory with Combinatorics, Numerical
mathematics, Algebra, or Probability theory. This reference work
will be useful to specialists in number theory and discrete
mathematics as well as mathematicians or scientists who need
access to some of these results in other fields of research.
Table of contents
Preface. Basic Symbols. Basic Notations. 1. Perfect Numbers: Old
and New Issues: Perspectives. 2. Generalizations and Extensions
of the Mobius Function. 3. The many Facets of Euler’s Totient.
4. Special Arithmetic Function connected with the Divisors, or
with the Digits of a Number. 5. Sterling, Bell, Bernoulli, Euler
and Eulerian Numbers. Reference. Index.
Series : New ICMI Study Series , Vol. 8
2004, XIV, 373 p., Hardcover
ISBN: 1-4020-8130-8
About this book
This book presents a wide-ranging, international perspective on
the state of the field of algebra from invited participants to
the 12th ICMI Study conference held in Melbourne, Australia in
2001. The authors are renowned academics from all around the
world who have written individual chapters associated with the
teaching and learning of algebra that relate to their particular
areas of research and teaching expertise. The book includes
information about different approaches to the teaching and
learning of algebra - from early algebra to tertiary algebra, the
impact of tools and technology (including Computer Algebra
Systems), the role of symbols and language, teachers of algebra,
and the history of algebra.
Table of contents
Solving the Problems with Algebra.- The Core of Algebra:
Reflections on its Main Activities.- Responses to 'The Core of
Algebra'.- The Early Development of Algebraic Reasoning: The
Current State of the Field.- A Toolkit for Analysing Approaches
to Algebra.- Research on the Role of Technological Environments
in Algebra Learning and Teaching.- Computer Algebra Systems and
Algebra: Curriculum, Assessment, Teaching, and Learning.- The
History of Algebra in Mathematics Education.- Symbols and
Language.- Teachers' Knowledge and the Teaching of Algebra.- The
Teaching and Learning of Tertiary Algebra.- Goals and Content of
an Algebra Curriculum for the Compulsory Years of Schooling.-
Algebra: A World of Difference.- Conference Participants.- Index
of Authors.- Index.
2004, XIII, 585 p., Hardcover
ISBN: 1-4020-2341-3
About this book
In Fourier Analysis and Approximation of Functions basics of
classical Fourier Analysis are given as well as those of
approximation by polynomials, splines and entire functions of
exponential type. In Chapter 1 which has an introductory nature,
theorems on convergence, in that or another sense, of integral
operators are given. In Chapter 2 basic properties of simple and
multiple Fourier series are discussed, while in Chapter 3 those
of Fourier integrals are studied. The first three chapters as
well as partially Chapter 4 and classical Wiener, Bochner,
Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be
interesting and available to all familiar with fundamentals of
integration theory and elements of Complex Analysis and Operator
Theory. Applied mathematicians interested in harmonic analysis
and/or numerical methods based on ideas of Approximation Theory
are among them. In Chapters 6-11 very recent results are
sometimes given in certain directions. Many of these results have
never appeared as a book or certain consistent part of a book and
can be found only in periodics; looking for them in numerous
journals might be quite onerous, thus this book may work as a
reference source. The methods used in the book are those of
classical analysis, Fourier Analysis in finite-dimensional
Euclidean space Diophantine Analysis, and random choice.
Table of contents
Dedication. Preface. 1: Representation Theorems. 1.1. Theorems on
representation at a point. 1.2. Integral operators. Convergence
in Lp-norm and almost everywhere. 1.3. Multidimensional case. 1.4.
Further problems and theorems. 1.5. Comments to Chapter 1. 2:
Fourier Series. 2.1. Convergence and divergence. 2.2. Two
classical summability methods. 2.3. Harmonic functions and
functions analytic in the disk. 2.4. Multidimensional case. 2.5.
Further problems and theorems. 2.6. Comments to Chapter 2. 3:
Fourier Integral. 3.1. L-Theory. 3.2. L2 Theory. 3.3.
Multidimensional case. 3.4. Entire functions of exponential type.
The Paley-Wiener theorem. 3.5. Further problems and theorems. 3.6.
Comments to Chapter 3. 4: Discretization. Direct and Inverse
Theorems. 4.1. Summation formulas of Poisson and Euler-Maclaurin.
4.2. Entire functions of exponential type and polynomials. 4.3.
Network norms. Inequalities of different metrics. 4.4. Inverse
theorems. Constructive characteristics. Embedding theorems. 4.6.
Moduli of smoothness. 4.7. Approximation on an interval. 4.8.
Further problems and theorems. 4.9. Comments to Chapter 4. 5:
Extremal Problems of Approximation Theory. 5.1. Best
approximation. 5.2. The space Lp. Best approximation. 5.3. Space
C. The Chebyshev alternation. 5.4. Extremal properties for
algebraic polynomials and splines. 5.5. Best approximation of a
set by another set. 5.6. Further problems and theorems. 5.7.
Comments to Chapter 5. 6: A Function as the Fourier Transform of
a Measure. 6.1. Algebras A and ￡Ii￡. The Wiener Tauberian
theorem. 6.2. Positive definate and completely monotone functions.
6.3. Positive definate functions depending only on a norm. 6.4.
Sufficient conditions for belonging to Ap
Series : Kluwer Texts in the Mathematical Sciences , Vol. 29
2004, IX, 326 p., Hardcover
ISBN: 1-4020-2695-1
About this textbook
This book presents in great detail all the results one needs to
prove the Morse Homology Theorem using classical techniques from
algebraic topology and homotopy theory. Most of these results can
be found scattered throughout the literature dating from the mid
to late 1900's in some form or other, but often the results are
proved in different contexts with a multitude of different
notations and different goals. This book collects all these
results together into a single reference with complete and
detailed proofs. The core material in this book includes CW-complexes,
Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the
Stable/Unstable Manifold Theorem), transversality theory, the
Morse-Smale-Witten boundary operator, and Conley index theory.
More advanced topics include Morse theory on Grassmann manifolds
and Lie groups, and an overview of Floer homology theories. With
the stress on completeness and by its elementary approach to
Morse homology, this book is suitable as a textbook for a
graduate level course, or as a reference for working
mathematicians and physicists.
Table of contents
Preface.- Introduction.- The CW-Homology Theorem.- Basic Morse
Theory.- The Stable/Unstable Manifold Theorem.- Basic
Differential Topology.- Morse-Smale Functions.- The Morse
Homology Theorem.- Morse Theory on Grassmann Manifolds.- An
Overview of Floer Homology Theories.- Hints and References for
Selected Problems.- Bibliography.- Symbol Index.- Index.
Published October 2004
568 pages 49 line diagrams
Hardback | In stock
ISBN:0-88385-547-X
This biography of Gauss, by far the most comprehensive in
English, is the work of a professor of German, G. Waldo
Dunnington, who devoted most of his scholarly career to studying
the life of Germany's greatest mathematician. The author was
inspired to pursue this project at the age of twelve when he
learned from his teacher in Missouri that no full biography of
Gauss existed at the time. His teacher was Gauss’s great
granddaughter, Minna Waldeck Gauss. Long out of print and almost
impossible to find on the used book market, this valuable piece
of scholarship is being reissued in an augmented form with
introductory remarks, an expanded and updated bibliography, and a
commentary on Gauss’s mathematical diary, by the eminent
British mathematical historian, Jeremy Gray.
Contents
1. Introduction: family background; 2. The enchanted boyhood; 3.
Student days; 4. The young man; 5. Astronomy and matrimony; 6.
Further activity; 7. Back to Gottingen; 8. Labour and sorrow; 9.
The young professor: a decade of discovery, 1812?1822; 10.
Geodesy and bereavement: the transitional decade, 1822?1832; 11.
Alliance with Weber: strenuous years; 12. The electromagnetic
telegraph; 13. Magnetism: physics dominant; 14. Surface theory,
crystallography, and optics; 15. Germination: non-Euclidean
geometry; 16. Trials and triumphs: experiencing conflict; 17.
Milestones on the highways and byways; 18. Senex mirabilis; 19.
Monarch of mathematics in Europe; 20. The doyen of German
science, 1832?1855; 21. Gathering up the threads: a broad
horizon; 22. Religio Scientiae: a profession of belief from the
philosopher and lover of truth; 23. Sunset and eventide:
renunciation; 24. Epilogue: 1. Apotheosis: orations of Ewald and
Sartorious; 2. Valhalla: posthumous recognition and honours;
Appendices; Index.