A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here.
This important addition to the New Mathematical Library series pays careful attention to applications of game theory in a wide variety of disciplines. The applications are treated in considerable depth. The book assumes only high school algebra, yet gently builds to mathematical thinking of some sophistication. Game Theory and Strategy might serve as an introduction to both axiomatic mathematical thinking and the fundamental process of mathematical modelling. It gives insight into both the nature of pure mathematics, and the way in which mathematics can be applied to real problems.
Hard Problems is about the extraordinary gifted students who represented the United States in 2006 at the world's toughest math competition: the International Mathematical Olympiad (IMO). It is the story of six American high school students who competed with 500 others from 90 countries in Ljublijana, Slovenia. The film shows the dedication and perseverance of these remarkably talented students, the rigorous preparation they undertake, and the joy they get out of solving challenging math problems. It captures the spirit that infuses the mathematical quest at the highest level.
Where did math come from? Who thought up all those algebra symbols, and why? What's the story behind ? ...negative numbers? ...the metric system? ...quadratic equations? ...sine and cosine? The 25 independent sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that's accessible to teachers, students, and anyone who is curious about the history of mathematical ideas.
Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus (MAA, 1998), in that it combines the features of a textbook with those of a problem workbook. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed and reinforced by working through leading questions posed in the problems.
This is the ninth book of problems and solutions from the American Mathematics Competitions (AMC) contests. It chronicles 325 problems from the 13 AMC 12 contests given in the years 2001 through 2007. The authors were the joint directors of the AMC 12 and AMC 10 competitions during that period. The problems have all been edited to ensure that they conform to the current style of the AMC 12 competitions, the graphs and figures have been redrawn to make them more consistent in form and style, and the solutions to the problems have been both edited and supplemented.
In the year 2000, the Mathematical Association of America initiated the American Mathematics Competitions 10 (AMC 10) for students up to grade 10. The Contest Problem Book VIII is the first collection of problems from that competition covering the years 2001-2007. J. Douglas Faires and David Wells were the joint directors of the AMC 10 and AMC 12 during that period, and have assembled this book of problems and solutions.
This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences.
Number Theory Through Inquiry is an innovative textbook that leads students on a guided discovery of introductory number theory. The book has two equally significant goals. One goal is to help students develop mathematical thinking skills, particularly, theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for an independent study experience, or for a course designed as an introduction to abstract mathematics.
Written for the mathematically literate reader, this book provides a glimpse of Euler in action. Following an introductory biographical sketch are chapters describing his contributions to eight different topics—number theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry, and combinatorics. Each chapter begins with a prologue to establish the historical context and then proceeds to a detailed consideration of one or more Eulerian theorems on the subject at hand. Each chapter concludes with an epilogue surveying subsequent developments or addressing related questions that remain unanswered to this day.
Counting lies at the heart of much mathematics, and Niven's subtitle is-How to count without counting. This is the whole art of combinatorics: permutations, combinations, binomial coefficients, the inclusion- exclusion principle, combinatorial probability, partitions of numbers, generating polynomials, the pigeonhole principle, and much more.