Pure and Applied Undergraduate Texts Volume: 38
2019; 302 pp; Hardcover
MSC: Primary 03; 97; 26;
Print ISBN: 978-1-4704-5144-8
Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering.
The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material?including an introduction to complex variables and Fourier series?to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects?many with hints?at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout.
Undergraduate and graduate students interested in real analysis, constructivism, and logic.
CBMS Regional Conference Series in Mathematics Volume: 132
2019; 152 pp; Softcover
MSC: Primary 68; 14; 15; 81;
Print ISBN: 978-1-4704-5136-3
Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication.
Undergraduate and graduate students and researchers interested in tensors, mathematical aspects of solid state physics, and quantum information theory.
Contemporary Mathematics Volume: 730
2019; 237 pp; Softcover
MSC: Primary 03; 13; 16; Secondary 18; 37
Print ISBN: 978-1-4704-4367-2
This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28-August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy.
Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.
Graduate students and research mathematicians interested in model theory and its connections with algebra.
2019; 116 pp; Softcover
MSC: Primary 97; 00;
Print ISBN: 978-1-4704-5090-8
This book presents nine variations on a classic and beloved puzzle type. Building upon the rules of Sudoku, the puzzles in this volume introduce new challenges by adding clues involving sums, differences, means, divisibility, and more. Each of the first eight chapters presents a rule system followed by a series of puzzles that progress in difficulty from easy to hard, allowing readers to develop and hone skills in logical problem solving, pattern discernment, and strategy building. In the final chapter, the eight puzzle variants are combined into a single complex puzzle type that puts all of the reader's new skills into play.
From beginners trying Sudoku for the first time to experts craving something new, this innovative collection will delight and satisfy puzzle lovers of all ages and levels!
For math lovers of all levels, ages 12 and up, interested in Sudoku puzzles.
Pure and Applied Undergraduate Texts Volume: 37
2019; 395 pp; Hardcover
MSC: Primary 91; Secondary 92
Print ISBN: 978-1-4704-5029-8
This book introduces game theory and its applications from an applied mathematician's perspective, systematically developing tools and concepts for game-theoretic modelling in the life and social sciences. Filled with down-to-earth examples of strategic behavior in humans and other animals, the book presents a unified account of the central ideas of both classical and evolutionary game theory. Unlike many books on game theory, which focus on mathematical and recreational aspects of the subject, this book emphasizes using games to answer questions of current scientific interest.
In the present third edition, the author has added substantial new material on evolutionarily stable strategies and their use in behavioral ecology. The only prerequisites are calculus and some exposure to matrix algebra, probability, and differential equations.
Undergraduate and graduate students interested in game theory and biological modelling.