A publication of the Societe Mathematique de France
Asterisque, Volume: 406
2018; 382 pp; Softcover
MSC: Primary 11; 14;
Print ISBN: 978-2-85629-896-1
This work is dedicated to the discovery, the definition, and the study of the fundamental curve in pp-adic Hodge theory. The authors define and study the pp-adic period rings as rings of holomorphic functions of the variable pp. Then they classify the vector bundles on the curve, a theorem that generalizes in some sense the classification theorem of vector bundles on the projective line. As an application, they give geometric proofs of the two main theorems in pp-adic Hodge theory: weakly admissible implies admissible and de Rham implies potentially semi-stable.
Graduate students and research mathematicians.
A publication of Hindustan Book Agency
Hindustan Book Agency, Volume: 77
2019; 252 pp; Hardcover
MSC: Primary 28;
Print ISBN: 978-93-86279-77-4
This book deals with topics usually studied in a master's or graduate level course on the theory of measure and integration. It starts with the Riemann integral and points out some of its shortcomings which motivate the theory of measure and the Lebesgue integral.
Starting with abstract measures and outer-measures, the Lebesgue measure is constructed and its important properties are highlighted. Measurable functions, different notions of convergence, the Lebesgue integral, the fundamental theorem of calculus, product spaces, and signed measures are studied. There is a separate chapter on the change of variable formula and one on LpLp-spaces.
Most of the material in this book can be covered in a one-semester course. The prerequisite for following this book is familiarity with basic real analysis and elementary topological notions, with special emphasis on the topology of the NN-dimensional euclidean space. Each chapter is provided with a variety of exercises.
Graduate students interested in the theory of measure and integration.
MAA Press: An Imprint of the American Mathematical Society
Dolciani Mathematical Expositions, Volume: 21
1998; 141 pp; Softcover
MSC: Primary 03;
Print ISBN: 978-1-4704-5113-4
Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra.
MAA Press: An Imprint of the American Mathematical Society
Problem Books, Volume: 31
2006; 183 pp; Softcover
Print ISBN: 978-1-4704-4970-4
This is the seventh book of problems and solutions from the Mathematics Competitions. Contest Problem Book VII chronicles 275 problems from the American Mathematics Contests (AMC 12 and AMC 10 for the years 1995 through 2000, including the 50th Anniversary AHSME issued in 1999). Twenty-three additional problems with solutions are included. A Problem Index classifies the 275 problems in to the following subject areas: Algebra, Complex Numbers, Discrete Mathematics (including Counting Problems), Logic, and Discrete Probability, Geometry (including Three Dimensional Geometry), Number Theory (including Divisibility, Representation, and Modular Arithmetic), Statistics, and Trigonometry. For over 50 years many excellent exams have been prepared by individuals throughout our mathematical community in the hope that all secondary school students will have an opportunity to participate in these problem solving and enriching mathematics experiences. The American Mathematics Contests are intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school.
MAA Press: An Imprint of the American Mathematical Society
Dolciani Mathematical Expositions, Volume: 54
1997; 90 pp; Softcover
MSC: Primary 11; Secondary 01
Print ISBN: 978-1-4704-5048-9
This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus?a person whose very existence has long been doubted by most historians of mathematics?will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman, who notes the most recent developments including the proof of Fermat's Last Theorem.