Series: Classroom Resource Materials
Hardback (ISBN-13: 9780883857519)
2 tables 105 exercises 3 worked examples
Page extent: 130 pages
Size: 228 x 152 mm
This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for independent study, or for a course designed as an introduction to abstract mathematics. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors’ materials explain the instructional method, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.
? Teaches students to think independently and develop their own ideas ? Ideal for mathematics or related disciplines, teachers, and anyone interested in exploring mathematical ideas on their own ? Contains over 100 exercises
Contents
0. Introduction; 1. Divide and conquer; 2. Prime time; 3. A modular world; 4. Fermat’s Little theorem and Euler’s theorem; 5. Public key cryptography; 6. Polynomial congruences and primitive roots; 7. The golden rule: quadratic reciprocity; 8. Pythagorean triples, sums of squares, and Fermat’s Last Theorem; 9. Rationals close to irrationals and the Pell equation; 10. The search for primes; Appendix A. Mathematical induction: the domino effect; Index.
Series: Practical Guides to Biostatistics and Epidemiology
Paperback (ISBN-13: 9780521719377)
Hardback (ISBN-13: 9780521895194)
79 tables 99 exercises
Page extent: 296 pages
This practical guide to survival data and its analysis for readers with a minimal background in statistics shows why the analytic methods work and how to effectively analyze and interpret epidemiologic and medical survival data with the help of modern computer systems. The introduction presents a review of a variety of statistical methods that are not only key elements of survival analysis but are also central to statistical analysis in general. Techniques such as statistical tests, transformations, confidence intervals, and analytic modeling are presented in the context of survival data but are, in fact, statistical tools that apply to understanding the analysis of many kinds of data. Similarly, discussions of such statistical concepts as bias, confounding, independence, and interaction are presented in the context of survival analysis and also are basic components of a broad range of applications. These topics make up essentially a ‘second-year’, one-semester biostatistics course in survival analysis concepts and techniques for non-statisticians.
? Examples of computer code in the text give an introduction to survival analysis computer techniques ? Contains the source data used to create the illustrations, allowing the reader to verify or extend text examples ? A single continuous example (data from the AIDS epidemic) provides a real, in depth example
Contents
1. Rates and their properties; 2. Life tables; 3. Two especially useful estimation tools; 4. Product-limit estimation; 5. Exponential survival time probability distribution; 6. Weibull survival time probability distribution; 7. Analysis of two-sample survival data; 8. General hazards model: parametric; 9. General hazards model: nonparametric.
Series: Mathematical Sciences Research Institute Publications (No. 55)
Hardback (ISBN-13: 9780521895279)
The three main themes of this book, probability theory, differential geometry, and the theory of integrable systems, reflect the broad range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the seventeen papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems in these areas. The topics are often combined in an unusual and interesting fashion to give solutions outside of the standard methods. The papers contain some exciting results and offer a guide to the contemporary literature on these subjects.
? Novel interplay between different mathematical topics
Contents
1. Direct and inverse problems for systems of differential equations Damir Arov and Harry Dym; 2. Turbulence of a unidirectional flow Bjorn Birnir; 3. Riemann?Hilbert problem in the inverse scattering for the Camassa?Holm equation on the line Anne Boutet de Monvel and Dimtry Shepelsky; 4. The Riccati map in random Schrodinger and matrix theory Santiago Cambronero, Jose Ramirez and Brian Rider; 5. SLE6 and CLE6 from critical percolation Federico Camia and Charles M. Newman; 6. Global optimization, the gaussian ensemble and universal ensemble equivalence Marius Costeniuc, Richard S. Ellis, Hugo Touchette and Bruce Turkington; 7. Stochastic evolution of inviscid Burger fluid Paul Malliavin and Ana Bela Cruzeiro; 8. A quick derivation of the loop equations for random matrices N. M. Ercolani and K. D. T-R McLaughlin; 9. Singular solutions for geodesic flows of Vlasov moments J. Gibbons, D. D. Holm and C. Tronci; 10. Reality problems in soliton theory Petr G. Grinevich and Sergei P. Novikov; 11. Random walks and orthogonal polynomials; some challenges F. Alberto Grunbaum; 12. Integration of pair flows of the Camassa?Holm hierarchy Enrique Loubet; 13. Landen survey Dante V. Manna and Victor H. Moll; 13. Lines on abelian varieties Emma Previato; 14. Integrable models of waves in shallow water Harvey Segur; 15. Nonintersecting brownian motions, integrable systems and orthogonal polynomials Pierre Van Moerbeke; 16. Homogenization of random Hamilton?Jacobi?Bellman equations S. R. S. Varadhan.
Series: London Mathematical Society Lecture Note Series (No. 352)
Paperback (ISBN-13: 9780521714679)
12 line diagrams 4 half-tones 26 tables 18 figures 4 colour figures 4 worked examples
Page extent: 360 pages
Size: 228 x 152 mm
Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book’s contents reflect the quality of the meeting. Topics covered include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure and its generalisations, the merit factor problem, Barker sequences, K3-surfaces, self-inversive polynomials, Newman’s inequality, algorithms for sparse polynomials, the integer transfinite diameter, divisors of polynomials, non-linear recurrence sequences, polynomial ergodic averages, and the Hansen-Mullen primitivity conjecture. With surveys and expository articles presenting the latest research, this volume is essential for graduates and researchers looking for a snapshot of current progress in polynomials and number theory.
? An invaluable resource to both students and experts in this area, with survey articles on the most important topics in the field ? Expository articles introduce graduate students to some problems of active interest ? The inclusion of new results from leading experts in the field provides a snapshot of current progress
Contents
Preface; Index of authors; List of participants; Conference photograph, with key; The trace problem for totally positive algebraic integers Julian Aguirre and Juan Carlos Peral, with an appendix by Jean-Pierre Serre; Mahler's measure: from Number Theory to Geometry Marie Jose Bertin; Explicit calculation of elliptic fibrations of K3-surfaces and their Belyi-maps Frits Beukers and Hans Montanus; The merit factor problem Peter Borwein, Ron Ferguson and Joshua Knauer; Barker sequences and flat polynomials Peter Borwein and Michael Mossinghoff; The Hansen-Mullen primitivity conjecture: completion of proof Stephen Cohen and Mateja Pre?ern; An inequality for the multiplicity of the roots of a polynomial Art?ras Dubickas; Newman's inequality for increasing exponential sums Tamas Erdelyi; On primitive divisors of n2 + b Graham Everest and Glyn Harman; Irreducibility and greatest common divisor algorithms for sparse polynomials Michael Filaseta, Andrew Granville and Andrzej Schinzel; Consequences of the continuity of the monic integer transfinite diameter Jan Hilmar; Nonlinear recurrence sequences and Laurent polynomials Andrew Hone; Conjugate algebraic numbers on conics: a survey James McKee; On polynomial ergodic averages and square functions Radhakrishnan Nair; Polynomial inequalities, Mahler's measure, and multipliers Igor E. Pritsker; Integer transfinite diameter and computation of polynomials Georges Rhin and Qiang Wu; Smooth divisors of polynomials Eira Scourfield; Self-inversive polynomials with all zeros on the unit circle Christopher Sinclair and Jeffrey Vaaler; The Mahler measure of algebraic numbers: a survey Chris Smyth.
Hardback (ISBN-13: 9780521841030)
23 line diagrams 2 half-tones 146 tables 96 exercises
Page extent: 240 pages
Experimental data can often be associated with or indexed by certain symmetrically interesting structures or sets of labels that appear, for example, in the study of short symbolic sequences in molecular biology, in preference or voting data, in (corneal) curvature data, and in studies of the handedness and entropy of symbolic sequences and elementary images. The symmetry studies introduced in this book describe the interplay among symmetry transformations that are characteristic of these sets of labels, their resulting classification, the algebraic decomposition of the data indexed by them, and the statistical analysis of the invariants induced by those decompositions. The overall purpose is to facilitate and guide the statistical study of the structured data from both a descriptive and inferential perspective. The text combines notions of algebra and statistics and develops a systematic methodology to better explore the interplay between symmetry-related research questions and their statistical analysis.
? Describes a new methodology for the analysis of data and planning 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 experimental results
Contents
1. Symmetry, classification and the analysis of structured data, 2. Sorting the labels: groups actions and orbits, 3. Connecting symmetries and data: linear representations, 4. Data reduction and inference: the canonical projections and their invariants, 5. Examples and techniques, 6. Symmetry studies of short symbolic sequences, 7. Symmetry studies of curvature data, 8. Symmetry studies of planar chirality.