Paperback
Series: Mathematical Association of America Notes
ISBN: 9780883851876
Publication date: June 2011
120 pages
Dimensions: 247 x 174 mm
Weight: 0.72 kg
Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Relevant history-based activities for a wide range of undergraduate and secondary mathematics courses are included. Readers will find articles and activities from mathematics history that enhance the learning of topics typically associated with undergraduate or secondary mathematics curricula. Each capsule presents one topic, or perhaps a few related topics, or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide other teachers with the historical background, suggested classroom activities and further references and resources on the subject addressed. After reading a capsule, a teacher will have increased confidence in engaging students with at least one activity rich in the history of mathematics that will enhance student learning of the mathematical content of the course.
Preface
Part I: 1. The sources of algebra Roger Cooke
2. How to measure the Earth Lawrence D'Antonio
3. Numerical solution of equations Roger Cooke
4. Completing the square through the millennia Dick Jardine
5. Adapting the medieval 'rule of double false position' to the modern classroom Randy K. Schwartz
6. Complex numbers, cubic equations and sixteenth-century Italy Daniel J. Curtin
7. Shearing with Euclid Davida Fischman and Shawnee McMurran
8. The mathematics of measuring time: the sinking-bowl water-clock in India Kim Plofker
9. Clear sailing with trigonometry: navigating the seas in fourteenth-century Venice Glen Van Brummelen
10. Copernican trigonometry Victor Katz
11. Cusps: horns and beaks Robert E. Bradley
12. The latitude of forms area and velocity Daniel J. Curtin
13. Descartes' approach to tangents Daniel J. Curtin
14. Integration a la Fermat Amy Shell-Gellasch
Interlude: 15. Sharing the fun: student presentations Amy Shell-Gellasch and Dick Jardine
16. Web searches and scavenger hunts: letting students dig up history Betty Mayfield
17. Newton vs. Leibniz in one hour! Betty Mayfield
Part II: 18. Connections between Newton, Leibniz, and Calculus I Andrew B. Perry
19. A different sort of calculus debate Vicky Williams Klima
20. A symbolic history of the derivative Clemency Montelle
21. Leibniz's calculus (real retro calc) Robert Rogers
22. An 'impossible' problem, courtesy of Leonhard Euler Homer S. White
23. Multiple representations of functions in the history of mathematics Robert Rogers
24. The unity of all science: Karl Pearson, the mean, and the standard deviation Joe Albree
25. Finding the greatest common divisor and morec J. J. Tattersall
26. Negativo-affirmative figures and an alternative technique for multiplying two numbers J. J. Tattersall
27. Origins of the integrating factor Dick Jardine
28. Euler's method in Euler's words Dick Jardine
29. Newton's differential equation y/x=1-3x+y+xx+xy Huseyin Kocak
30. Roots, rocks, and Newton?Raphson algorithms for approximating 3000 years apart Clemency Montelle
31. Plimpton 322: the Pythagorean Theorem, more than a thousand years before Pythagoras Daniel E. Otero
32. Thomas Harriot's Pythagorean Triples: could he list them all? Janet L. Beery
33. Amo, Amas, Amat! What's the sum of that? Bernoulli's account of the divergent harmonic series in Latin Clemency Montelle
34. The harmonic series: a primer Adrian Rice
35. Learning to move with Dedekind Fernando Q. Gouvea.
Hardback
Series: Dolciani Mathematical Expositions (No. 44)
ISBN: 9780883853511
Publication date: July 2011
266 pages
Dimensions: 247 x 174 mm
Weight: 0.49 kg
Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups. Students in algebra, analysis and topology will all find much of interest and use to them and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.
Preface
1. Vector spaces and linear transformations
2. Coordinates
3. Determinants
4. The structure of a linear transformation I
5. The structure of a linear transformation II
6. Bilinear, sesquilinear, and quadratic forms
7. Real and complex inner product spaces
8. Matrix groups as Lie groups
A. Polynomials: A.1 Basic properties
A.2 Unique factorization
A.3 Polynomials as expressions and polynomials as functions
B. Modules over principal ideal domains: B.1 Definitions and structure theorems
B.2 Derivation of canonical forms
Bibliography
Index.
Hardback
Series: Cambridge Studies in Advanced Mathematics (No. 49)
ISBN: 9781107015425
ISBN: 9781107602625 (softcover)
165 b/w illus. 536 exercises
Dimensions: 228 x 152 mm
December 2011
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential
1. What is enumerative combinatorics?
2. Sieve methods
3. Partially ordered sets
4. Rational generating functions.
Paperback
Series: London Mathematical Society Lecture Note Series (No. 394)
ISBN: 9780521282741
5 b/w illus.
Dimensions: 228 x 152 mm
Not yet published - available from October 2011
The field of geometric variational problems is fast-moving and influential. These problems interact with many other areas of mathematics and have strong relevance to the study of integrable systems, mathematical physics and PDEs. The workshop 'Variational Problems in Differential Geometry' held in 2009 at the University of Leeds brought together internationally respected researchers from many different areas of the field. Topics discussed included recent developments in harmonic maps and morphisms, minimal and CMC surfaces, extremal Kahler metrics, the Yamabe functional, Hamiltonian variational problems and topics related to gauge theory and to the Ricci flow. These articles reflect the whole spectrum of the subject and cover not only current results, but also the varied methods and techniques used in attacking variational problems. With a mix of original and expository papers, this volume forms a valuable reference for more experienced researchers and an ideal introduction for graduate students and postdoctoral researchers.
1. Preface
2. The supremum of first eigenvalues of conformally covariant operators in a conformal class Bernd Ammann and Pierre Jammes
3. K-Destabilizing test configurations with smooth central fiber Claudio Arezzo, Alberto Della Vedova and Gabriele La Nave
4. Explicit constructions of Ricci solitons Paul Baird
5. Open iwasawa cells and applications to surface theory Josef F. Dorfmeister
6. Multiplier ideal sheaves and geometric problems Akito Futaki and Yuji Sano
7. Multisymplectic formalism and the covariant phase space Frederic Helein
8. Nonnegative curvature on disk bundles Lorenz J. Schwachhofer
9. Morse theory and stable pairs Richard A. Wentworth and Graeme Wilkin
10. Manifolds with k-positive Ricci curvature Jon Wolfson