Series: Spectrum
Hardback (ISBN-13: 9780883855690)
Page extent: 440 pages
Size: 253 x 177 mm
This book picks up the history of mathematics from where Sherlock Holmes
in Babylon left it. The 40 articles of Who Gave You the Epsilon* continue
the story of the development of mathematics into the nineteenth and twentieth
centuries. The articles have all been published in the Mathematical Association
of America journals and are in many cases written by distinguished mathematicians
such as G. H. Hardy and B. van der Waerden. The articles are arranged thematically
to show the development of analysis, geometry, algebra and number theory
through this period of time. Each chapter is preceded by a foreword, giving
the historical background and setting and the scene, and is followed by
an afterword, reporting on advances in our historical knowledge and understanding
since the articles first appeared. This book is ideal for anyone wanting
to explore the history of mathematics.
Introduction; Part I. Analysis: 1. Who gave you the epsilon* Cauchy and
the origins of rigorous calculus Judith V. Grabiner; 2. Evolution of the
function concept: a brief survey Israel Kleiner; 3. S. Kovalevsky: a mathematical
lesson Karen D. Rappaport; 4. Highlights in the history of spectral theory
L. A. Steen; 5. Alan Turing and the central limit theorem S. L. Zabell;
6. Why did George Green write his essay of 1828 on electricity and magnetism*
I. Grattan-Guinness; 7. Connectivity and smoke-rings: Greenfs second identity
in its first fifty years Thomas Archibald; 8. The history of Stokesf theorem
Victor J. Katz; 9. The mathematical collaboration of M. L. Cartwright and
J. E. Littlewood Shawnee L. McMurran and James J. Tattersall; 10. Dr David
Harold Blackwell, African American pioneer Nkechi Agwu, Luella Smith and
Aissatou Barry; Part II. Geometry, Topology and Foundations: 11. Gauss
and the non-Euclidean geometry George Bruce Halsted; 12. History of the
parallel postulate Florence P. Lewis; 13. The rise and fall of projective
geometry J. L. Coolidge; 14. Notes on the history of geometrical ideas
Dan Pedoe; 15. A note on the history of the Cantor set and Cantor function
Julian F. Fleron; 16. Evolution of the topological concept of econnectedf
R. L. Wilder; 17. A brief, subjective history of homology and homotopy
theory in this century Peter Hilton; 18. The origins of modern axiomatics:
Pasch to Peano H. C. Kennedy; 19. C. S. Peircefs philosophy of infinite
sets Joseph W. Dauben; 20. On the development of logics between the two
world wars I. Grattan-Guinness; 21. Dedekindfs theorem: ã2 ~ ã3 = ã6
David Fowler; Part III. Algebra and Number Theory: 22. Hamiltonfs discovery
of quaternions B. L. van der Waerden: 23. Hamilton, Rodrigues, and the
quaternion scandal Simon L. Altmann; 24. Building an international reputation:
the case of J. J. Sylvester (1814*1897) Karen Hunger Parshall and Eugene
Seneta; 25. The foundation period in the history of group theory Josephine
E. Burns; 26. The evolution of group theory: a brief survey Israel Kleiner;
27. The search for finite simple groups Joseph A. Gallian; 28. Genius and
biographers: the fictionalization of Evariste Galois Tony Rothman; 29.
Hermann Grassmann and the creation of linear algebra Desmond Fearnley-Sander;
30. The roots of commutative algebra in algebraic number theory Israel
Kleiner; 31. Eisensteinfs misunderstood geometric proof of the quadratic
reciprocity theorem Reinhard C. Laubenbacher and David J. Pengelley; 32.
Waringfs problem Charles Small; 33. A history of the prime number theorem
L. J. Goldstein; 34. A hundred years of prime numbers Paul T. Bateman and
Harold G. Diamond; 35. The Indian mathematician Ramanujan G. H. Hardy;
36. Emmy Noether Clark H. Kimberling; 37. eA marvellous prooff Fernando
Q. Gouv*ea; Part IV. Surveys: 38. The international congress of mathematicians
George Bruce Halsted; 39. A popular account of some new fields of thought
in mathematics G. A. Miller; 40. A half-century of mathematics Hermann
Weyl; 41. Mathematics at the turn of the millennium Philip A. Griffiths;
Index.
Series: Dolciani Mathematical Expositions
Hardback (ISBN-13: 9780883853429)
Page extent: 250 pages
Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they donft possess the richness and variety that one finds with inequalities. The objective of this book is to illustrate how use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and we would like to convince you that the same is true when working with inequalities. We show how to produce figures in a systematic way for the illustration of inequalities; and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument can not only show two things unequal, but also help the observer see just how unequal they are.
* Demonstrates methods for creating pictures to illustrate (or even prove)
inequalities * Contains many examples and applications of the methods discussed
* Each chapter ends with a collection of challenges that the reader may
work through in order to better understand the methodology of the chapter
Preface; Introduction; 1. Representing positive numbers as lengths of segments; 2. Representing positive numbers as areas or volumes; 3. Inequalities and the existence of triangles; 4. Using incircles and circumcircles; 5. Using reflections; 6. Using rotations; 7. Employing non-isometric transformations; 8. Employing graphs of functions; 9. Additions topics; Solutions to the challenges; Selected open challenges for visualizing inequalities; Symbols and notation; References; Index.
Series: Dolciani Mathematical Expositions
Hardback (ISBN-13: 9780883853412)
Page extent: 282 pages
This text serves as a tour guide to little known corners of the mathematical landscape, not far from the main byways of algebra, geometry, and calculus. It is for the seasoned mathematical traveller who has visited these subjects many times and, familiar with the main attractions, is ready to venture abroad off the beaten track. For the old hand and new devotee alike, this book will surprise, intrigue, and delight readers with unexpected aspects of old and familiar subjects. In the first part of the book all of the topics are related to polynomials: properties and applications of Horner form, reverse and palindromic polynomials and identities linking roots and coefficients, among others. Topics in the second part are all connected in some way with maxima and minima. In the final part calculus is the focus.
* Designed to surprise, intrigue, and delight readers by presenting unexpected
aspects of the mathematics surrounding the standard curriculum * For anyone
who appreciates the intrinsic fascination of mathematics beyond its applicability
and utility * Further reading and the history of the topic being discussed
is found at the end of every chapter
Preface; Part I. The Province of Polynomia: 1. Hornerfs foam; 2. Polynomial potpourri; 3. Polynomial roots and coefficients; 4. Solving polynomial equations; Part II. Maxministan: 5. Leveling with Lagrange; 6. A maxmini miscellany; 7. Envelopes and the ladder problem; 8. Deflections on an ellipse; Part III. The Calculusian Republic: 9. A generalized logarithm for exponential-linear equations; 10. Envelopes and asymptotes; 11. Derivatives without limits; 12. Two calculusian miracles.
Series: MAA Problem Book Series
Hardback (ISBN-13: 9780883858288)
Page extent: 266 pages
When one thinks of mathematical problems posed over the past 30 years, one name automatically leaps to the fore - Murray Klamkin. In this book Andy Liu and Bruce Shawyer present problems that he proposed over his career. It contains the equickiesf (problems with quick and neat solutions) he proposed in eCrux Mathematicorum,f his longer problems, and also problems which were posed in tribute to him after he died. Solutions are provided in the second half of the book.
* A great way to improve your problem-solving * Problems are from a wide
range of topics including combinatorics, calculus and inequalities * Solutions
are provided in the second half of the book
Preface; Introduction; Part I. Problems: 1. Quickies; 2. Klamkinfs problems
in Crux Mathematicorum; 3. The Klamkin tribute problems 2005; Part II.
Solutions: 4. Quickies; 5. Klamkinfs problems in Crux Mathematicorum;
6. The Klamkin tribute problems 2005.
Series: Lecture Notes in Logic
Hardback (ISBN-13: 9780521110815)
Page extent: 384 pages
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.
* Describes a new methodology for the analysis of data and planing of experiments
* Combines solid, well-known, results in algebra and statistics into a
systematic, step-by-step method * Leads to descriptive, inferential, and
broadly qualitative analysis of the experimental results
1. Definability and elementary equivalence in the Ershov difference hierarchy Marat M. Arslanov; 2. A unified approach to algebraic set theory Benno van den Berg and Leke Moerdijk; 3. Brief introduction to unprovability Andrey Bovykin; 4. Higher-order abstract syntax in type theory Venanzio Capretta and Amy P. Felty; 5. An introduction to b-minimality Raf Cluckers; 6. The sixth lecture on algorithmic randomness Rod Downey; 7. The inevitability of logical strength: strict reverse mathematics Harvey M. Friedman; 8. Applications of logic in algebra: examples from clone theory; 9. On infinite imaginaries Ehud Hrushovski; 10. Strong minimal covers and a question of Yates: the story so far Andrew E. M. Lewis; 10. Embeddings into the Turing degrees Antonio Montalban; 11. Randomness - beyond Lebesgue measure Jan Reimann; 12. The derived model theorem J. R. Steel; 13. Forcing axioms and cardinal arithmetic Boban Velivckovic; 14. Hrushovski's amalgamation construction Frank O. Wagner.