MSRI Mathematical Circles Library, Volume: 10
2012; 208 pp; softcover
Expected publication date is December 27, 2012.
This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K-8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals because of their importance in the classroom curriculum. The standard topics are covered in detail, but are arranged in an order that is slightly different from the usual one. Multiplication is treated first, and with that in hand, common denominators and equivalent fractions are more readily understood and are available for use when discussing addition.
The book is intended for the professional development of teachers. It is appropriate for teacher education programs as well as for enrichment programs such as Mathematical Circles for Teachers. There are numerous activities in each seminar that teachers can bring into their classrooms.
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.
Undergraduate students, graduate students, research mathematicians, and teachers interested in K-8 arithmetic.
MSRI Mathematical Circles Library, Volume: 11
2012; 335 pp; softcover
ISBN-13: 978-0-8218-8745-5
Expected publication date is January 26, 2013.
Early middle school is a great time for children to start their mathematical circle education. This time is a period of curiosity and openness to learning. The thinking habits and study skills acquired by children at this age stay with them for a lifetime. Mathematical circles, with their question-driven approach and emphasis on creative problem-solving, have been rapidly gaining popularity in the United States. The circles expose children to the type of mathematics that stimulates development of logical thinking, creativity, analytical abilities and mathematical reasoning. These skills, while scarcely touched upon at school, are in high demand in the modern world.
This book contains everything that is needed to run a successful mathematical circle for a full year. The materials, distributed among 29 weekly lessons, include detailed lectures and discussions, sets of problems with solutions, and contests and games. In addition, the book shares some of the know-how of running a mathematical circle. The curriculum, which is based on the rich and long-standing Russian math circle tradition, has been modified and adapted for teaching in the United States. For the past decade, the author has been actively involved in teaching a number of mathematical circles in the Seattle area. This book is based on her experience and on the compilation of materials from these circles.
The material is intended for students in grades 5 to 7. It can be used by teachers and parents with various levels of expertise who are interested in teaching mathematics with the emphasis on critical thinking. Also, this book will be of interest to mathematically motivated children.
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.
Undergraduate students, graduate students, and research mathematicians interested in teaching extracurricular math to school children.
Preliminaries
Session plans
Introduction
How to solve a problem
Knights and liars
How to turn lies into truth
Mathematical auction
Word problems and common sense
More word problems
Odd and even numbers I. Magic paper cups
Odd and even numbers II. Definitions and properties
Halloween math hockey I
Odd and even numbers III. Alternations
Weighings an counterfeit coins
Mathematical olympiad I
Meet the cube. First lesson in 3d geometry
Cross sections. Second lesson in 3d geometry
Mathematical auction
Combinatorics I
Combinatorics II
Mathematical hockey II
Numerical puzzles I. Runaway digits
Numerical puzzles II. Encrypted problems
Mathematical olympiad II
Divisibility I. Definition and properties
Divisibility II. Prime numbers and prime factorization
Mathematical auction
Divisibility III. Divisibility rules
Divisibility IV. Relatively prime numbers
Mathematical games of strategy I
Mathematical games of strategy II
Mathematical olympiad III
Mathematical contests and competitions
Mathematical contests
Mathematical auction
Mathematical hockey
Mathematical olympiads
Short entertaining math games
More teaching advice
How to be a great math circle teacher
Math circle day-to-day
More questions?
Solutions
Solutions
Bibliography
CRM Monograph Series, Volume: 31
2013; approx. 248 pp; hardcover
ISBN-13: 978-0-8218-9441-5
Expected publication date is February 23, 2013.
The trace formula for an arbitrary connected reductive group over a number field was developed by James Arthur. The twisted case was the subject of the Friday Morning Seminar at the Institute for Advanced Study in Princeton during the 1983-1984 academic year. During this seminar, lectures were given by Laurent Clozel, Jean-Pierre Labesse and Robert Langlands. Having been written quite hastily, the lecture notes of this seminar were in need of being revisited. The authors' ambition is to give, following these notes, a complete proof of the twisted trace formula in its primitive version, i.e., its noninvariant form. This is a part of the project of the Parisian team led by Laurent Clozel and Jean-Loup Waldspurger. Their aim is to give a complete proof of the stable form of the twisted trace formula, and to provide the background for the forthcoming book by James Arthur on twisted endoscopy for the general linear group with application to symplectic and orthogonal groups.
Graduate students and research mathematicians interested in automorphic representations and the Arthur-Selberg Trace formula.
Geometrie et combinatoire
Racines et convexes
Espaces tordus
Theorie de la reduction
Theorie spectrale, troncatures et noyaux
Loperateur de troncature
Formes automorphes et produits scalaires
Le noyau integral
Decomposition spectrale
La formule des traces grossere
Formule des traces: etat zero
Developpement geometrique
Developpement spectral grossier
Formule des traces: proprietes formelles
Forme explicite des termes spectraux
Introduction d'une fonction B
Calcul de AT(B)
Formules explicites
Bibliographie
Index des notations
Student Mathematical Library, Volume: 66
2013; approx. 353 pp; softcover
ISBN-13: 978-0-8218-9396-8
Expected publication date is February 14, 2013.
Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas.
This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology. The first chapter on conics is appropriate for first-year college students (and many high school students). Chapter 2 leads the reader to an understanding of the basics of cubic curves, while Chapter 3 introduces higher degree curves. Both chapters are appropriate for people who have taken multivariable calculus and linear algebra. Chapters 4 and 5 introduce geometric objects of higher dimension than curves. Abstract algebra now plays a critical role, making a first course in abstract algebra necessary from this point on. The last chapter is on sheaves and cohomology, providing a hint of current work in algebraic geometry.
Undergraduate students interested in algebraic geometry.
Conics
Cubic curves and elliptic curves
Higher degree curves
Affine varieties
Projective varieties
The next steps: Sheaves and cohomology
Bibliography
Index
Pure and Applied Undergraduate Texts, Volume: 20
2013; 362 pp; hardcover
ISBN-13: 978-0-8218-9141-4
Expected publication date is March 5, 2013.
This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in "AP Calculus", possibly followed by a routine course in multivariable calculus and a computational course in linear algebra.
There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.
The foundational material contained in this book is published separately as Paul Sally's, "Tools of the Trade: Introduction to Advanced Mathematics," also available from the AMS.
Undergraduate and graduate students interested in learning and teaching real analysis.
The construction of real and complex numbers
Metric and Euclidean spaces
Complete metric spaces
Normed linear spaces
Differentiation
Integration
Fourier analysis on locally compact abelian groups
Sets, functions, and other basic ideas
Linear algebra
Bibliography
Index of terminology
Index of notation definitions