How to Prepare for Math Olympiads


Book Description

This book is intended as a teacher's manual and a self-study handbook for high-school or college students, and mathematical competitors. It consists mainly of problems created by the authors, with author-prepared-solutions, which were used in different national and international Mathematical Olympiads from 1984 to 2019. The book is arranged by topic and difficulty level. The book gives a broad view of mathematics and goes well beyond the elementary mathematics by providing deeper treatments of the following topics: Geometry and Trigonometry, Number theory, Algebra, Combinatorics and Calculus.




Mathematical Circles


Book Description

Suitable for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. This book contains vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.




Problem-Solving Strategies


Book Description

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.




Euclidean Geometry in Mathematical Olympiads


Book Description

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.




The IMO Compendium


Book Description

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.




Microprediction


Book Description

How a web-scale network of autonomous micromanagers can challenge the AI revolution and combat the high cost of quantitative business optimization. The artificial intelligence (AI) revolution is leaving behind small businesses and organizations that cannot afford in-house teams of data scientists. In Microprediction, Peter Cotton examines the repeated quantitative tasks that drive business optimization from the perspectives of economics, statistics, decision making under uncertainty, and privacy concerns. He asks what things currently described as AI are not “microprediction,” whether microprediction is an individual or collective activity, and how we can produce and distribute high-quality microprediction at low cost. The world is missing a public utility, he concludes, while companies are missing an important strategic approach that would enable them to benefit—and also give back. In an engaging, colloquial style, Cotton argues that market-inspired “superminds” are likely to be very effective compared with other orchestration mechanisms in the domain of microprediction. He presents an ambitious yet practical alternative to the expensive “artisan” data science that currently drains money from firms. Challenging the machine learning revolution and exposing a contradiction at its heart, he offers engineers a new liberty: no longer reliant on quantitative experts, they are free to create intelligent applications using general-purpose application programming interfaces (APIs) and libraries. He describes work underway to encourage this approach, one that he says might someday prove to be as valuable to businesses—and society at large—as the internet.




Math Storm Olympiad Problems


Book Description

This is a book on Olympiad Mathematics with detailed and elegant solution of each problem. This book will be helpful for all the students preparing for RMO, INMO, IMO, ISI and other National & International Mathematics competitions.The beauty of this book is it contains “Original Problems” framed by authors Daniel Sitaru( Editor-In-Chief of Romanian Mathematical Magazine) & Rajeev Rastogi (Senior Maths Faculty for IIT-JEE and Olympiad in Kota, Rajasthan)




Introduction to Math Olympiad Problems


Book Description

Introduction to Math Olympiad Problems aims to introduce high school students to all the necessary topics that frequently emerge in international Math Olympiad competitions. In addition to introducing the topics, the book will also provide several repetitive-type guided problems to help develop vital techniques in solving problems correctly and efficiently. The techniques employed in the book will help prepare students for the topics they will typically face in an Olympiad-style event, but also for future college mathematics courses in Discrete Mathematics, Graph Theory, Differential Equations, Number Theory and Abstract Algebra. Features: Numerous problems designed to embed good practice in readers, and build underlying reasoning, analysis and problem-solving skills Suitable for advanced high school students preparing for Math Olympiad competitions




The Mathematical Olympiad Handbook


Book Description

Olympiad problems help able school students flex their mathematical muscles. Good Olympiad problems are unpredictable: this makes them worthwhile but it also makes them seem hard and even unapproachable. The Mathematical Olympiad Handbook contains some of the problems and solutions from the British Mathematical Olympiads from 1965 to 1996 in a form designed to help bright students overcome this barrier.




First Steps for Math Olympians


Book Description

A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of 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 preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.