MAA Press: An Imprint of the American Mathematical Society
Active engagement is the key to learning. You want your students doing something that stimulates
them to ask questions and creates a need to know. Teaching Mathematics Through Games presents
a variety of classroom-tested exercises and activities that provoke the active learning and curiosity
that you hope to promote. These games run the gamut from well-known favorites like SET and Settlers
of Catan to original games involving simulating structural inequality in New York or playing Battleship with functions.
The book contains activities suitable for a wide variety of college mathematics courses, including general
education courses, math for elementary education, probability, calculus, linear algebra, history of math,
and proof-based mathematics. Some chapter activities are short term, such as a drop-in lesson for a day,
and some are longer, including semester-long projects. All have been tested, refined, and include extensive implementation notes.
Teachers of undergraduate students interested in incorporating more active learning in their classrooms.
Ultimately, the book fulfills its promise of sharing the ways in which mathematics may be explored through play, in ways
that are engaging and thought-provoking to students. There were several games that were new and interesting
to the reviewer, and as a resource reference book (coupled with the online supplementary materials) it offers great
potential value to the mathematics instructor looking for something new to add to their active learning repertoire.
-- Dr. Cristina Runnalls, Cal Poly Pomona
Classroom Resource Materials, Volume: 65
2021; 160 pp; Softcover
MSC: Primary 00;
Print ISBN: 978-1-4704-6284-0
Product Code: CLRM/65
This book is a translation from Russian of Part II of the book Mathematics Through Problems: From Olympiads
and Math Circles to Profession. Part I, Algebra, was recently published in the same series. Part III, Combinatorics, will be published soon.
The main goal of this book is to develop important parts of mathematics through problems.
The authors tried to put together sequences of problems that allow high school students
(and some undergraduates) with strong interest in mathematics to discover and recreate
much of elementary mathematics and start edging into more sophisticated topics such as
projective and affine geometry, solid geometry, and so on, thus building a bridge between standard
high school exercises and more intricate notions in geometry.
Definitions and/or references for material that is not standard in the school curriculum are included.
To help students that might be unfamiliar with new material, problems are carefully arranged to provide
gradual introduction into each subject. Problems are often accompanied by hints and/or complete solutions.
The book is based on classes taught by the authors at different times at the Independent University of Moscow,
at a number of Moscow schools and math circles, and at various summer schools. It can be used by high school
students and undergraduates, their teachers, and organizers of summer camps and math circles.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other
disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series
as a service to young people, their parents and teachers, and the mathematics profession.
High school students and their mentors and teachers.
MSRI Mathematical Circles Library, Volume: 26
2021; 177 pp; Softcover
MSC: Primary 00; 51; 52; 14; 97;
Print ISBN: 978-1-4704-4879-0
Product Code: MCL/26
This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5,
covers the basic elements of the shock wave theory by analyzing the scalar conservation laws.
The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course
in multi-variable calculus, and can be used as a text for an undergraduate topics course.
In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws.
This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations.
The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models.
Potentially interesting questions and research directions are also raised in these chapters.
The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering,
and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.
Readership
Graduate students and researchers interested in hyperbolic PDE with applications to fluid dynamics.
Graduate Studies in Mathematics, Volume: 215
2021; 437 pp; Hardcover
MSC: Primary 35; 76;
Print ISBN: 978-1-4704-6567-4
Product Code: GSM/215
A Concise Introduction to Algebraic Varieties is designed for a one-term introductory course on algebraic varieties
over an algebraically closed field, and it provides a solid basis for a course on schemes and cohomology or on specialized topics,
such as toric varieties and moduli spaces of curves. The book balances generality and accessibility by presenting local
and global concepts, such as nonsingularity, normality, and completeness using the language of atlases, an approach that is most
commonly associated with differential topology. The book concludes with a discussion of the Riemann-Roch theorem, the Brill-Noether theorem, and applications.
The prerequisites for the book are a strong undergraduate algebra course and a working familiarity with basic point-set topology.
A course in graduate algebra is helpful but not required. The book includes appendices presenting useful background in complex
analytic topology and commutative algebra and provides plentiful examples and exercises that help build intuition and familiarity with algebraic varieties.
Undergraduate and graduate students interested in an introduction to fundamentals of algebraic geometry.
Graduate Studies in Mathematics, Volume: 216
2021; Hardcover
MSC: Primary 14;
ISBN: 978-1-4704-6013-6
Product Code: GSM/216
Expected publication date January 16, 2022
Not yet published - available from October 2021
FORMAT: Hardback ISBN: 9781108843300 Paperback ISBN: 9781108824231
Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years,
is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know:
the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium.
The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax
theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games
like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively
text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory
courses in mathematics, computer science, or economics departments.
A detailed, accessible introduction to the mathematics of games, written for students meeting the topic for the first time
Based on over 15 years of teaching experience, ensuring that it is ideal for both self-study and course use
Starts from examples and gives complete, self-contained and clear proofs
as well as numerous exercises, fostering a solid understanding of the fundamentals
of game theory
'This looks like a fine introduction to game theory, inter alia emphasizing methods for computing equilibria, and mathematical aspects in general.
Especially worthy of note is the chapter devoted to correlated equilibria, a topic of central importance not normally covered in introductory texts.'
Robert Aumann, The Hebrew University of Jerusalem
PUBLICATION PLANNED FOR: October 2021
FORMAT: Hardback ISBN: 9781108843300
LENGTH: 374 pages DIMENSIONS: 252 x 195 x 22 mm WEIGHT: 0.92kg
Part of Institute of Mathematical Statistics Textbooks
PUBLICATION PLANNED FOR: October 2021
FORMAT: Paperback ISBN: 9781108401173 Hardback ISBN: 9781108415323
Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems,
control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing.
These problems are too large and complex for exact solution, but their scale allows approximation.
This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text
presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies,
and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic,
by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality
and efficiency driven Halfin?Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.
80 figures and more than 300 challenging exercises
Extensive solutions manual for most exercises
Consolidates current research in the field and an overview of three key approaches in one text