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Combinatorial Extremization

Combinatorial Extremization Author Yuefeng Feng
ISBN-10 9789814723183
Release 2016-02-17
Pages 232
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In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.



Combinatorial Problems in Mathematical Competitions

Combinatorial Problems in Mathematical Competitions Author Yao Zhang
ISBN-10 9789812839497
Release 2011
Pages 289
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Annotation. This text provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions.



Probability and Expectation

Probability and Expectation Author Zun Shan
ISBN-10 9789813141513
Release 2016-07-14
Pages 208
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In China, lots of excellent students who are good at maths take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year. The author is one of the senior coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.



A First Step to Mathematical Olympiad Problems

A First Step to Mathematical Olympiad Problems Author Derek Holton
ISBN-10 9789814365253
Release 2009-07-30
Pages 292
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See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.



Solving Problems in Geometry

Solving Problems in Geometry Author Kim Hoo Hang
ISBN-10 9789814583763
Release 2017-05-19
Pages 356
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This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry. Request Inspection Copy



Lecture Notes on Mathematical Olympiad Courses

Lecture Notes on Mathematical Olympiad Courses Author Jiagu Xu
ISBN-10 9789814293570
Release 2010
Pages 376
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Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics. In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader''s practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers. Errata(s). Errata. Sample Chapter(s). Lecture 16: Quadratic Surd Expressions and Their Operations (183k). Request Inspection Copy. Contents.: Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Linear Inequality and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Solutions to Testing Questions; and other chapters. Readership: Mathematics students, school teachers, college lecturers, university professors; mathematics enthusiasts.



Methods and Techniques for Proving Inequalities

Methods and Techniques for Proving Inequalities Author Yong Su
ISBN-10 9789814696470
Release 2015-10-06
Pages 228
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In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The authors are coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.



Problems of Number Theory in Mathematical Competitions

Problems of Number Theory in Mathematical Competitions Author Hong-Bing Yu
ISBN-10 9789814271141
Release 2010
Pages 106
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Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.



Geometric Inequalities

Geometric Inequalities Author Gangsong Leng
ISBN-10 9789814696500
Release 2015-10-21
Pages 144
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In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.



104 Number Theory Problems

104 Number Theory Problems Author Titu Andreescu
ISBN-10 0817645616
Release 2007-04-05
Pages 204
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This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.



Geometric Inequalities

Geometric Inequalities Author Hayk Sedrakyan
ISBN-10 9783319550800
Release 2017-06-29
Pages 452
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This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.



A Walk Through Combinatorics

A Walk Through Combinatorics Author Mikl¢s B¢na
ISBN-10 9789814335232
Release 2011
Pages 546
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Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some the progress made in the area.



Design Theory

Design Theory Author
ISBN-10 9789814287432
Release 2009
Pages 234
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Design Theory has been writing in one form or another for most of life. You can find so many inspiration from Design Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Design Theory book for free.



Mathematical Olympiad In China 2011 2014 Problems And Solutions

Mathematical Olympiad In China  2011 2014   Problems And Solutions Author Xiong Bin
ISBN-10 9789813142954
Release 2018-03-21
Pages 368
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Mathematical Olympiad In China 2011 2014 Problems And Solutions has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Olympiad In China 2011 2014 Problems And Solutions also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Olympiad In China 2011 2014 Problems And Solutions book for free.



Automated Inequality Proving and Discovering

Automated Inequality Proving and Discovering Author Bican Xia
ISBN-10 9789814759137
Release 2016-06-21
Pages 344
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This is the first book that focuses on practical algorithms for polynomial inequality proving and discovering. It is a summary of the work by the authors and their collaborators on automated inequality proving and discovering in recent years. Besides brief introduction to some classical results and related work in corresponding chapters, the book mainly focuses on the algorithms initiated by the authors and their collaborators, such as real root counting, real root classification, improved CAD projection, dimension-decreasing algorithm, difference substitution, and so on. All the algorithms were rigorously proved and the implementations are demonstrated by lots of examples in various backgrounds such as algebra, geometry, biological science, and computer science. Contents: PrefaceBasics of Elimination MethodZero Decomposition of Polynomial SystemTriangularization of Semi-Algebraic SystemReal Root CountingReal Root IsolationReal Root ClassificationOpen Weak CADDimension-Decreasing AlgorithmSOS DecompositionSuccessive Difference SubstitutionProving Inequalities Beyond the Tarski Model Readership: Researchers and graduate students in computational real algebraic geometry, optimization and artificial intelligence.



Strong Uniformity And Large Dynamical Systems

Strong Uniformity And Large Dynamical Systems Author Beck Jozsef
ISBN-10 9789814740760
Release 2017-07-07
Pages 460
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It is the first book about a new aspect of Uniform distribution, called Strong Uniformity. Besides developing the theory of Strong Uniformity, the book also includes novel applications in the underdeveloped field of Large Dynamical Systems.



Algebraic Geometry Modeling in Information Theory

Algebraic Geometry Modeling in Information Theory Author Edgar Martínez-Moro
ISBN-10 9789814335751
Release 2013
Pages 325
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Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.