These titles are available as free samples. This selection is subject to change - check back regularly to see new sample titles.
Visit our About the eReader page to learn about the features of our eBook reader.
These titles are available as free samples. This selection is subject to change - check back regularly to see new sample titles.
Visit our About the eReader page to learn about the features of our eBook reader.
Finite group theory is remarkable for the simplicity of its
statements—and the difficulty of their proofs. It is essential in
several branches of mathematics, notably number theory.
Finite Groups: An Introduction is an elementary textbook on finite group theory. Written by the eminent French mathematician Jean-Pierre Serre (a principal contributor to algebraic geometry, group theory, and number theory), this textbook is based upon a course given by Serre at l'École Normale Supérieure de Jeunes Filles, Paris, in 1978–1979.
Each of the ten chapters is followed by a series of exercises.
A publication of International Press of Boston, Inc. Distributed worldwide by the American Mathematical Society.
College students, graduate students, and researchers interested in finite groups.
Traditionally, \(p\)-adic \(L\)-functions have
been constructed from complex \(L\)-functions via special
values and Iwasawa theory. In this volume, Perrin-Riou presents a
theory of \(p\)-adic \(L\)-functions coming directly
from \(p\)-adic Galois representations (or, more generally,
from motives). This theory encompasses, in particular, a construction
of the module of \(p\)-adic \(L\)-functions via the
arithmetic theory and a conjectural definition of the
\(p\)-adic \(L\)-function via its special values.
Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.
Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.
Graduate students and research mathematicians interested in number theory.
Written in a concise but readable style and can be recommended to readers interested in this rapidly growing subject.
-- European Mathematical Society Newsletter
This book has three main goals. First, it
explores a selection of topics from the early period of the theory of
relativity, focusing on particular aspects that are interesting or
unusual. These include the twin paradox; relativistic mechanics and
its interaction with Maxwell's laws; the earliest triumphs of general
relativity relating to the orbit of Mercury and the deflection of
light passing near the sun; and the surprising bizarre metric of Kurt
Gödel, in which time travel is possible. Second, it provides an
exposition of the differential geometry needed to understand these
topics on a level that is intended to be accessible to those with just
two years of university-level mathematics as background. Third, it
reflects on the historical development of the subject and its
significance for our understanding of what reality is and how we can
know about the physical universe. The book also takes note of
historical prefigurations of relativity, such as Euler's 1744 result
that a particle moving on a surface and subject to no tangential
acceleration will move along a geodesic, and the work of Lorentz and
Poincaré on space-time coordinate transformations between two
observers in motion at constant relative velocity.
The book is aimed at advanced undergraduate mathematics, science, and engineering majors (and, of course, at any interested person who knows a little university-level mathematics). The reader is assumed to know the rudiments of advanced calculus, a few techniques for solving differential equations, some linear algebra, and basics of set theory and groups.
Undergraduate and graduate students and general readers interested in mathematical aspects of relativity.
This volume is a collection of papers presented at the XIII
International Workshop on Real and Complex Singularities, held from
July 27–August 8, 2014, in São Carlos, Brazil, in honor
of María del Carmen Romero Fuster's 60th birthday.
The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries).
This book is published in cooperation with Real Sociedad Matemática Española (RSME)
This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Undergraduate students interested in abstract algebra.
Pushing Limits: From West Point to Berkeley and Beyond challenges the myth that mathematicians lead dull and ascetic lives. It recounts the unique odyssey of a noted mathematician who overcame military hurdles at West Point, Army Ranger School and the Vietnam War, and survived many civilian escapades—hitchhiking in third-world hotspots, fending off sharks in Bahamian reefs, and camping deep behind the forbidding Iron Curtain. From ultra-conservative West Point in the ’60s to ultra-radical Berkeley in the ’70s, and ultimately to genteel Georgia Tech in the ’80s, this is the tale of an academic career as noteworthy for its offbeat adventures as for its teaching and research accomplishments. It brings to life the struggles and risks underlying mathematical research, the unparalleled thrill of making scientific breakthroughs, and the joy of sharing those discoveries around the world. Hill's book is packed with energy, humor, and suspense, both physical and intellectual. Anyone who is curious about how a maverick mathematician thinks, who wants to relive the zanier side of the ’60s and ’70s, who wants an armchair journey into the third world, or who seeks an unconventional viewpoint about some of our more revered institutions, will be drawn to this book.
… captivating memoir reveals an intriguing character who is part Renaissance Man, part Huckleberry Finn. Fast-paced and often hilarious … provides some penetrating and impious insights into some of our more revered institutions.
—Rick Atkinson, three-time Pulitzer Prize winner, author of The Long Gray Line
Ted Hill is unique in having both a very exciting internal mathematical life … and an action-filled, adventurous, external life. … his natural gift, very rare for mathematicians, of story-telling, [makes this] a page-turner.
—Doron Zeilberger, Rutgers University, winner of MAA Ford Prize, AMS Steele Prize, and ICA Euler Medal
Thoughtful, funny, evocative, Ted Hill, takes us through a life well-lived … an intensely personal story that will appeal to every profession—and to every generation!
—General Wesley Clark, former NATO Supreme Commander
Ted Hill is an original. Mathematician. Adventurer. Activist. His life has seen both his mind and body tested to extremes … insightful, entertaining and—in a very good way—unlike any other book you will ever read by a mathematician.
—Alex Bellos, author of Here's Looking at Euclid and The Grapes of Math
General readers interested in mathematics careers and education, adventure travel, military life, the 1960s-70s, and how all this combines together; mathematics educators, students, and graduates, especially those of West Point, Stanford, and Berkeley.
A fascinating journey from pure adventurism...through West Point and the Vietnam War to the highest intellectual accomplishments. At the center is a beautiful portrayal of the tedious, but highly rewarding road from graduate school to becoming a substantial research mathematician. A joy to read.
-- David Gilat, Professor Emeritus, School of Mathematical Sciences, Tel Aviv University
It is well known that math is boring and that mathematicians are dull individuals lacking both social skills and common sense. Wait a minute.Ted Hill might change your mind. His almost mathemagical life experiences are like a platter of petit fours: sample one and you'd want a second, then a third and soon you're addicted.
-- Christian Houdré , Professor of Mathematics, Georgia Institute of Technology
I loved the book. Extraordinary job of making scenes come alive...with great energy and really good dialog.
-- David Ignatius, Columnist and Associate Editor at The Washington Post, author of Body of Lies
Most people think that mathematics has nothing to do with daily life. These folks need to spend a few hours with Ted. He sees life through a mathematical lens and brings excitement and adventure to everything he comes in contact with.
-- Martin Jones, Professor of Mathematics, College of Charleston
Spell-binding accounts of events actually experienced... Ted Hill...challeng(es) normative value systems in startling ways but of impish consequences.
-- Michael Klass, Professor of Mathematics and Statistics, U.C. Berkeley
The first adjectives...when thinking about a mathematician...are likely to [be] words such as: eccentric, reclusive, nerd. Ted Hill amply demonstrates that, at least in his case, nothing could be further from the truth, as he offers us a glimpse of the fascinating world of an accomplished mathematician.
-- Mario Livio, author of The Golden Ratio and the upcoming Why?
Ted Hill's fascinating and raucous memoir...is proof that life in the exotic world of theoretical mathematics doesn't preclude and in fact benefits from passionate engagement with the real world.
-- Jack Miller, Physicist, Lawrence Berkeley National Laboratory
Ted Hill is the Indiana Jones of mathematics. A West Point graduate, [he] served in Vietnam, swam with sharks in the Caribbean, and has resolutely defied unreasoned authority. With this same love of adventure, he has confronted the sublime challenges of mathematics. Whether it's discovering intellectual treasures or careening down jungle trails, this real life Dr. Jones has done it all.
-- Michael Monticino, Professor of Mathematics and Special Assistant to the President, U. North Texas
Straddling the military and the mathematical worlds, Ted Hill's life is full of contradictions, daring exploits and accomplishments, and outright fun and adventure. A fascinating read...
-- John Allen Paulos, Professor of Mathematics at Temple University, author of Innumeracy and A Mathematician Reads the Newspaper
This [memoir]...will thrill and perplex the reader, by the seamless mixture of mind-adventure and body adventure, and for the unconventional academic path traveled by its author. Hill perpetually runs into trouble with authorities...[but] befriends mathematicians all over the world... With verve and nerve, Hill writes the story of...a life that touches on the highly exceptional, rich in friendship, thought, and humane warmth.
-- Mircea Pitici, Cornell University, Editor of Best Writing on Mathematics
Ted Hill has led an exciting life, and his vivid stories shed light on some remarkable times and places. Mathematicians will especially appreciate his chapters on graduate school and his early professional life; he brings our shared experiences to life in a way that only an outstanding writer can do.
-- Walter Stromquist, past Editor of Mathematics Magazine
Ted Hill paints vivid pictures of his life in the military and academia. From West Point and Vietnam to Berkeley and Georgia Tech, his trials and hair-raising adventures are highly entertaining and informative.
-- Bill Sudderth, Professor Emeritus of Statistics, U. of Minnesota
Ted Hill took a very unusual route to...mathematics: a military start and a stint in Vietnam, followed by a first-rate degree at one of the top programs in the world (Berkeley) and a highly successful career. This path, in addition to providing him with many adventures, has allowed him to look at thing(s) a little differently than most mathematicians...
-- Stan Wagon, Macalester College, winner of MAA Ford Prize, author of The Banach-Tarski Paradox
The fame of the Polish school at Lvov rests
with the diverse and fundamental contributions of Polish
mathematicians working there during the interwar years. In
particular, despite material hardship and without a notable
mathematical tradition, the school made major contributions to what is
now called functional analysis. The results and names of Banach, Kac,
Kuratowski, Mazur, Nikodym, Orlicz, Schauder, Sierpiński, Steinhaus,
and Ulam, among others, now appear in all the standard textbooks.
The vibrant joie de vivre and singular ambience of Lvov's once scintillating social scene are evocatively recaptured in personal recollections. The heyday of the famous Scottish Café—unquestionably the most mathematically productive cafeteria of all time—and its precious Scottish Book of highly influential problems are described in detail, revealing the special synergy of scholarship and camaraderie that permanently elevated Polish mathematics from utter obscurity to global prominence.
This chronicle of the Lvov school—its legacy and the tumultuous historical events which defined its lifespan—will appeal equally to mathematicians, historians, or general readers seeking a cultural and institutional overview of key aspects of twentieth-century Polish mathematics not described anywhere else in the extant English-language literature.
Undergraduate, graduate, and research mathematicians interested in the history of mathematics and the Polish history of sciences.
This eagerly awaited translation of the book Pearls describes a world-class Polish school of mathematics at Lvov (now the Ukrainian Lviv) that thrived during the interwar period and has left an enduring legacy that remains part of the folklore today. Published in English translation after a somewhat protracted period of negotiation, this important work fills a niche in the history of science and should become a standard source of mathematics in Poland, especially the genesis of functional analysis during its Golden Age, 1918-1939. Moreover, the translator, Oxford's Daniel Davies, explains material that is unlikely to be familiar to readers outside Poland.
-- Isis, A Journal of the History of Science Society
Many journal articles have been devoted to various aspects of mathematics in Lwów or to biographies of Lwów mathematicians, but Duda's book is the first comprehensive exposition. It is a must-read for everyone interested in the history of functional analysis or of mathematics in Poland, where the original Polish edition from 2007 ... has been highly successful. There is good reason to assume that the English version will be likewise successful.
-- Dirk Werner, ZMATH
This book gives the history of Lvov as a mathematical center, from pre-WWI to Soviet and Ukrainian times, looking especially at the interwar golden age and the special favorable environment for mathematical scholarship. The author also describes the ways in which the Soviets and Germans destroyed this rich environment. The book includes a list, with biographical sketches, of mathematicians associated with Lvov, and a Lvov biography. It was a special time and place for mathematics, disrupted by war and politics and oppression and murder, and one wonders what more could have been achieved in a peaceful environment.
-- CHOICE Reviews
The book under review is well and carefully written. The translation from Polish into English is polished and lively. ... I highly recommend the book for all university libraries, and I recommend it to those interested in the history of mathematics. The general mathematical reader will find it an entertaining and informative story about mathematicians and a truly extraordinary mathematical community.
-- Henry Heatherly, MAA Reviews
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Get the Ultimate Companion to A Comprehensive Course in Analysis free with any purchase of the complete set.
Researchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, graduate students who need any kind of analysis in their work.
There is no doubt that graduate students and seasoned analysts alike will find a wealth of material in this project and appreciate its encyclopedic nature.
-- Fritz Gesztesy, Mathematical Reviews
There is no need to belabor the point that this is a fabulous set of texts and will be a smash hit in graduate programs with good taste and good students willing to work hard and ready for exposure to mathematical culture of a wonderful sort. In addition to being a fine mathematician and teacher of mathematics, Simon is something of a raconteur (in the best sense of the word) with a strong interest in history. The books are peppered with historical asides and human interest material, and this feature adds to their readability. Indeed, they are beautifully and clearly written and certainly make for a major contribution to the literature at the intended level and beyond. When I learned that the AMS (which is to be congratulated with this publication) was launching this series by Barry Simon, I, of course, expected a great deal. I was by no means disappointed; these books are terrific.
-- MAA Online
The subject of this book is the theory of
operads and colored operads, sometimes called symmetric
multicategories. A (colored) operad is an abstract object which
encodes operations with multiple inputs and one output and relations
between such operations. The theory originated in the early 1970s in
homotopy theory and quickly became very important in algebraic
topology, algebra, algebraic geometry, and even theoretical physics
(string theory). Topics covered include basic graph theory, basic
category theory, colored operads, and algebras over colored operads.
Free colored operads are discussed in complete detail and in full
The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.
Graduate students and researchers in mathematics and other sciences where operads and colored operads are used.
An introductory undergraduate course in abstract algebra is sufficient as a prerequisite for almost all of the material covered in the book. One impressive feature of the book is the emphasis on motivating new concepts as they are introduced and providing numerous graphical illustrations to clarify their geometric significance; there are also numerous exercises collected at the ends of the chapters. The author also provides a list of references to related literature to assist the reader who wishes to continue the study of operads beyond the topics covered in this book.
-- Murray R. Bremner, Mathematical Reviews
The book contains much valuable information and detail, which can potentially save a struggling newcomer into operad land many hours of frustration.
-- Ittay Weiss, MAA Reviews