MAA Press: An Imprint of the American Mathematical Society
The soul of mathematics is the practice of skeptical inquiry: asking how and why things work, experimenting, exploring, and discovering. Estimation, analysis, computation, conjecture, and proof are the mathematical path to uncovering truth and we can use them in nearly every human pursuit. In this thoroughly charming and beguiling book, Shai Simonson applies mathematical tools in a variety of contexts that arise in everyday life to prove his claim that math is, literally, everywhere. Simonson applies his mathematical cast of mind to hiking, birthday parties, carnival games, lock picking, and kite flying. We see unexpected depths and connections when we look in the gwrongh places in the right way.
No advanced mathematical knowledge is required to travel with Simonson and share in his investigations. All a reader needs is an open and curious mind, an eagerness to ask questions, and a willingness to think deeply and carefully about seemingly mundane things. There is wonder and joy in quotidian life with Simonson as your guide.
Undergraduate students interested in seeing mathematics in unusual applications.
Spectrum
Volume: 104; 2022; 209 pp; Softcover
MSC: Primary 00; 05; 97;
Print ISBN: 978-1-4704-7012-8
Product Code: SPEC/104
This volume contains the proceedings of the virtual conference on Hypergeometry, Integrability and Lie Theory, held from December 7?11, 2020, which was dedicated to the 50th birthday of Jasper Stokman.
The papers represent recent developments in the areas of representation theory, quantum integrable systems and special functions of hypergeometric type.
Graduate students and research mathematicians interested in representation theory and quantum integrable systems.
Contemporary Mathematics
Volume: 780; 2022; 347 pp; Softcover
MSC: Primary 13; 16; 17; 33; 43; 60;
Print ISBN: 978-1-4704-6520-9
Product Code: CONM/780
This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the classical topic of quadratic forms with integer coefficients, a central topic of the book. Quadratic forms of this type in two variables have a very rich theory, developed mostly by Euler, Lagrange, Legendre, and Gauss during the period 1750?1800. In this book their approach is modernized by using the splendid visualization tool introduced by John Conway in the 1990s called the topograph of a quadratic form. Besides the intrinsic interest of quadratic forms, this theory has also served as a stepping stone for many later developments in algebra and number theory.
The book is accessible to students with a basic knowledge of linear algebra and arithmetic modulo n. Some exposure to mathematical proofs will also be helpful. The early chapters focus on examples rather than general theorems, but theorems and their proofs play a larger role as the book progresses.
Undergraduate students interested in number theory and topology.
2022; Softcover
MSC: Primary 11;
Print ISBN: 978-1-4704-5611-5
Product Code: MBK/145
This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course.
The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. O-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line.
Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in P3, and double planes, and it ends with applications of the Riemann-Roch Theorem.
Undergraduate and graduate students interested in learning and teaching algebraic geometry.
Graduate Studies in Mathematics
Volume: 222; 2022; 318 pp; Hardcover
MSC: Primary 14;
Print ISBN: 978-1-4704-6848-4
Product Code: GSM/222
Paperback ISBN: 9780443189128
Algebraic Theory for True Concurrency presents readers with the algebraic laws for true concurrency. Parallelism and concurrency are two of the core concepts within computer science. This book covers the different realms of concurrency, which enables programs, algorithms or problems to be broken out into order-independent or partially ordered components to improve computation and execution speed. There are two primary approaches for executing concurrency: interleaving concurrency and true concurrency. The main representative of interleaving concurrency is bisimulation/rooted branching bisimulation equivalences which is also readily explored. This work eventually founded the comprehensive axiomatization modulo bisimulation equivalence -- ACP (Algebra of Communicating Processes).The other approach to concurrency is true concurrency. Research on true concurrency is active and includes many emerging applications. First, there are several truly concurrent bisimulation equivalences, including: pomset bisimulation equivalence, step bisimulation equivalence, history-preserving (hp-) bisimulation equivalence, and hereditary history-preserving (hhp-) bisimulation equivalence, the most well-known truly concurrent bisimulation equivalence.
Part of Cambridge Tracts in Mathematics
Not yet published - available from October 2022
FORMAT: Hardback ISBN: 9781009254632
The fractional Sobolev spaces studied in the book were introduced in the 1950s by Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical Sobolev spaces. They provide a natural home for solutions of a vast, and rapidly growing, number of questions involving differential equations and non-local effects, ranging from financial modelling to ultra-relativistic quantum mechanics, emphasising the need to be familiar with their fundamental properties and associated techniques. Following an account of the most basic properties of the fractional spaces, two celebrated inequalities, those of Hardy and Rellich, are discussed, first in classical format (for which a survey of the very extensive known results is given), and then in fractional versions. This book will be an Ideal resource for researchers and graduate students working on differential operators and boundary value problems.
Gives the basic properties of fractional spaces; you do not have to search the vast literature
Provides up-to-date material including very extensive known results on two celebrated inequalities
Matches applications to theory. The reader will learn significant applications for celebrated inequalities
1. Preliminaries
2. Classical Sobolev spaces
3. Fractional Sobolev spaces
4. Eigenvalues of the fractional p-Laplacian
5. Classical (local) Hardy inequalities
6. Fractional analogues
7. Classical and fractional inequalities of Rellich type
References
Symbol index
Author index
Index of terms.
Part of Cambridge Studies in Advanced Mathematics
Not yet published - available from December 2022
FORMAT: Hardback ISBN: 9781108478588
Many researchers in geometric functional analysis are unaware of algebraic aspects of the subject and the advances they have permitted in the last half century. This book, written by two world experts on homological methods in Banach space theory, gives functional analysts a new perspective on their field and new tools to tackle its problems. All techniques and constructions from homological algebra and category theory are introduced from scratch and illustrated with concrete examples at varying levels of sophistication. These techniques are then used to present both important classical results and powerful advances from recent years. Finally, the authors apply them to solve many old and new problems in the theory of (quasi-) Banach spaces and outline new lines of research. Containing a lot of material unavailable elsewhere in the literature, this book is the definitive resource for functional analysts who want to know what homological algebra can do for them.
The first book presenting a comprehensive step-by-step approach to homological methods in Banach space theory
Includes many results old and recent that have never appeared in book form
Reworks in context deep results taken from about fifty papers of Kalton
Presents solutions to classical problems of functional analysis and formulates many new open problems for future research
1. Complemented subspaces of Banach spaces
2. The homological language
3. Quasilinear maps
4. The functor Ext and the homology sequences
5. Local methods in the theory of twisted sums
6. Fraisse limits by the pound
7. Extensions of operators, isomorphisms and isometries
8. Extension of C(K)-valued operators
9. Singular exact sequences
10. Back to Banach space theory.