Mass Selecta

Author : Svetlana Katok,A. B. Sossinsky,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 43,6 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821872583

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MASS Selecta by Svetlana Katok,A. B. Sossinsky,Serge Tabachnikov Pdf

This book results from a unique and innovative program at Pennsylvania State University. Under the program, the ''best of the best'' students nationwide are chosen to study challenging mathematical areas under the guidance of experienced mathematicians. This program, Mathematics Advanced Study Semesters (MASS), offers an unparalleled opportunity for talented undergraduate students who are serious in the pursuit of mathematical knowledge. This volume represents various aspects of the MASS program over its six-year existence, including core courses, summer courses, students' research, and colloquium talks. The book is most appropriate for college professors of mathematics who work with bright and eager undergraduate and beginning graduate students, for such students who want to expand their mathematical horizons, and for everyone who loves mathematics and wants to learn more interesting and unusual material. The first half of the book contains lecture notes of nonstandard courses. A text for a semester-long course on $p$-adic analysis is centered around contrasts and similarities with its real counterpart. A shorter text focuses on a classical area of interplay between geometry, algebra and number theory (continued fractions, hyperbolic geometry and quadratic forms). Also provided are detailed descriptions of two innovative courses, one on geometry and the other on classical mechanics. These notes constitute what one may call the skeleton of a course, leaving the instructor ample room for innovation and improvisation. The second half of the book contains a large collection of essays on a broad spectrum of exciting topics from Hilbert's Fourth Problem to geometric inequalities and minimal surfaces, from mathematical billiards to fractals and tilings, from unprovable theorems to the classification of finite simple groups and lexicographic codes.

Author : Svetlana Katok
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 42,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842201

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$p$-adic Analysis Compared with Real by Svetlana Katok Pdf

The book gives an introduction to $p$-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. in addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity of isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and $p$-adic contexts of the book. The book is based on an advanced undergraduate course given by the author. The choice of the topic was motivated by the internal beauty of the subject of $p$-adic analysis, an unusual one in the undergraduate curriculum, and abundant opportunities to compare it with its much more familiar real counterpart. The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. Well written, with obvious care for the reader, the book can be successfully used in a topic course or for self-study.

Author : Paul C. Bell,Patrick Totzke,Igor Potapov
Publisher : Springer Nature
Page : 181 pages
File Size : 55,6 Mb
Release : 2021-10-25
Category : Computers
ISBN : 9783030897161

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Reachability Problems by Paul C. Bell,Patrick Totzke,Igor Potapov Pdf

This book constitutes the refereed proceedings of the 15th International Conference on Reachability Problems, RP 2021, held in Liverpool, UK in October 2021. The 6 full papers presented were carefully reviewed and selected from 27 submissions. In addition, 4 invited papers were included in this volume. The RP proceedings cover topics such as reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps; and new computational paradigms. Chapter ‘Recent Advances on Reachability Problems for Valence Systems’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Author : Enli Guo,Xiaohuan Mo
Publisher : Springer
Page : 154 pages
File Size : 43,7 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9789811315985

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The Geometry of Spherically Symmetric Finsler Manifolds by Enli Guo,Xiaohuan Mo Pdf

This book presents properties, examples, rigidity theorems and classification results of such Finsler metrics. In particular, this book introduces how to investigate spherically symmetric Finsler geometry using ODE or PDE methods. Spherically symmetric Finsler geometry is a subject that concerns domains in R^n with spherically symmetric metrics. Recently, a significant progress has been made in studying Riemannian-Finsler geometry. However, constructing nice examples of Finsler metrics turn out to be very difficult. In spherically symmetric Finsler geometry, we find many nice examples with special curvature properties using PDE technique. The studying of spherically symmetric geometry shows closed relation among geometry, group and equation.

Author : Michael H. Albert,Richard J. Nowakowski
Publisher : Cambridge University Press
Page : 577 pages
File Size : 42,6 Mb
Release : 2009-05-29
Category : Mathematics
ISBN : 9780521861342

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Games of No Chance 3 by Michael H. Albert,Richard J. Nowakowski Pdf

This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.

Author : Alexandre Borovik
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 47,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821847619

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Mathematics under the Microscope by Alexandre Borovik Pdf

Discusses, from a working mathematician's point of view, the mystery of mathematical intuition: Why are certain mathematical concepts more intuitive than others? And to what extent does the 'small scale' structure of mathematical concepts and algorithms reflect the workings of the human brain?

Author : Svetlana Katok,A. B. Sossinsky,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 54,6 Mb
Release : 2003
Category : Mathematics
ISBN : 0821833634

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MASS Selecta by Svetlana Katok,A. B. Sossinsky,Serge Tabachnikov Pdf

The Mathematics Advanced Study Semesters (MASS) program offers an opportunity for talented undergraduate students who are serious in the pursuit of mathematical knowledge. This book represents various aspects of the MASS program over its six-year existence, including core courses, summer courses, students' research, and colloquium talks.

Author : John Whitehead
Publisher : Unknown
Page : 582 pages
File Size : 45,7 Mb
Release : 1852
Category : Methodist Church
ISBN : UOM:39015064392551

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The Life of the Rev. John Wesley, M. A. by John Whitehead Pdf

Author : John Whitehead
Publisher : Unknown
Page : 584 pages
File Size : 50,5 Mb
Release : 1845
Category : Methodism
ISBN : HARVARD:32044026014811

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The Life of the Rev. John Wesley, M.A. Some Time Fellow of Lincoln College, Oxford by John Whitehead Pdf

Author : Anonim
Publisher : Unknown
Page : 892 pages
File Size : 50,5 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015082440762

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Mathematical Reviews by Anonim Pdf

Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 50,6 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9783031408465

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Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman Pdf

Author : Ralucca Gera,Stephen Hedetniemi,Craig Larson
Publisher : Springer
Page : 291 pages
File Size : 42,5 Mb
Release : 2016-10-19
Category : Mathematics
ISBN : 9783319319407

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Graph Theory by Ralucca Gera,Stephen Hedetniemi,Craig Larson Pdf

This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes.

Author : D. B. Fuks,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 55,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821843161

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Mathematical Omnibus by D. B. Fuks,Serge Tabachnikov Pdf

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Author : Eric Grinberg
Publisher : World Scientific
Page : 238 pages
File Size : 48,7 Mb
Release : 2006
Category : Science
ISBN : 9789812565136

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Proceedings of the International Conference Integral Geometry and Convexity by Eric Grinberg Pdf

Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.

Author : American Mathematical Society. Short Course
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 42,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821844663

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Applications of Knot Theory by American Mathematical Society. Short Course Pdf

Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.