Studyguide For A Primer For Mathematics Competitions By Zawaira Alex

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A Primer for Mathematics Competitions

Author : Alexander Zawaira
Publisher : OUP Oxford
ISBN 13 : 0191561703
Total Pages : 368 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis A Primer for Mathematics Competitions by : Alexander Zawaira

Download or read book A Primer for Mathematics Competitions written by Alexander Zawaira and published by OUP Oxford. This book was released on 2008-10-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.

102 Combinatorial Problems

Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 0817682228
Total Pages : 125 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis 102 Combinatorial Problems by : Titu Andreescu

Download or read book 102 Combinatorial Problems written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

Number Theory

Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 0817646450
Total Pages : 383 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Number Theory by : Titu Andreescu

Download or read book Number Theory written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

The Art of Mathematics

Author : Béla Bollobás
Publisher : Cambridge University Press
ISBN 13 : 1139936662
Total Pages : 392 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis The Art of Mathematics by : Béla Bollobás

Download or read book The Art of Mathematics written by Béla Bollobás and published by Cambridge University Press. This book was released on 2006-09-14 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.

Graphs, Colourings and the Four-Colour Theorem

Author : Robert A. Wilson
Publisher : OUP Oxford
ISBN 13 : 019158360X
Total Pages : 153 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Graphs, Colourings and the Four-Colour Theorem by : Robert A. Wilson

Download or read book Graphs, Colourings and the Four-Colour Theorem written by Robert A. Wilson and published by OUP Oxford. This book was released on 2002-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.

Introduction to Complex Analysis

Author : H. A. Priestley
Publisher : OUP Oxford
ISBN 13 : 0191037206
Total Pages : 344 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Introduction to Complex Analysis by : H. A. Priestley

Download or read book Introduction to Complex Analysis written by H. A. Priestley and published by OUP Oxford. This book was released on 2003-08-28 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.

From Calculus to Chaos

Author : David Acheson
Publisher :
ISBN 13 : 9780198500773
Total Pages : 284 pages
Book Rating : 4.5/5 (7 download)

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Book Synopsis From Calculus to Chaos by : David Acheson

Download or read book From Calculus to Chaos written by David Acheson and published by . This book was released on 1997 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e., of how--and why--things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by focusing on the many important and interesting ideas which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and some of its liveliest applications.

Probability

Author : Geoffrey Grimmett
Publisher : OUP Oxford
ISBN 13 : 0191019933
Total Pages : 319 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Probability by : Geoffrey Grimmett

Download or read book Probability written by Geoffrey Grimmett and published by OUP Oxford. This book was released on 2014-08-21 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

A Path to Combinatorics for Undergraduates

Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 081768154X
Total Pages : 235 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A Path to Combinatorics for Undergraduates by : Titu Andreescu

Download or read book A Path to Combinatorics for Undergraduates written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.

A First Course in Coding Theory

Author : Raymond Hill
Publisher : Oxford University Press
ISBN 13 : 9780198538035
Total Pages : 268 pages
Book Rating : 4.5/5 (38 download)

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Book Synopsis A First Course in Coding Theory by : Raymond Hill

Download or read book A First Course in Coding Theory written by Raymond Hill and published by Oxford University Press. This book was released on 1986 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

Invitation to Discrete Mathematics

Author : Jiří Matoušek
Publisher : Oxford University Press
ISBN 13 : 0198570430
Total Pages : 462 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Invitation to Discrete Mathematics by : Jiří Matoušek

Download or read book Invitation to Discrete Mathematics written by Jiří Matoušek and published by Oxford University Press. This book was released on 2009 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates.

Visual Complex Analysis

Author : Tristan Needham
Publisher : Oxford University Press
ISBN 13 : 9780198534464
Total Pages : 620 pages
Book Rating : 4.5/5 (344 download)

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Book Synopsis Visual Complex Analysis by : Tristan Needham

Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

One Thousand Exercises in Probability

Author : Geoffrey Grimmett
Publisher : Oxford University Press
ISBN 13 : 9780198572213
Total Pages : 452 pages
Book Rating : 4.5/5 (722 download)

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Book Synopsis One Thousand Exercises in Probability by : Geoffrey Grimmett

Download or read book One Thousand Exercises in Probability written by Geoffrey Grimmett and published by Oxford University Press. This book was released on 2001-05-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This guide provides a wide-ranging selection of illuminating, informative and entertaining problems, together with their solution. Topics include modelling and many applications of probability theory.

Codes and Cryptography

Author : Dominic Welsh
Publisher : Oxford University Press
ISBN 13 : 9780198532873
Total Pages : 274 pages
Book Rating : 4.5/5 (328 download)

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Book Synopsis Codes and Cryptography by : Dominic Welsh

Download or read book Codes and Cryptography written by Dominic Welsh and published by Oxford University Press. This book was released on 1988 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook unifies the concepts of information, codes and cryptography as first considered by Shannon in his seminal papers on communication and secrecy systems. The book has been the basis of a very popular course in Communication Theory which the author has given over several years to undergraduate mathematicians and computer scientists at Oxford. The first five chapters of the book cover the fundamental ideas of information theory, compact encoding of messages, and an introduction to the theory of error-correcting codes. After a discussion of mathematical models of English, there is an introduction to the classical Shannon model of cryptography. This is followed by a brief survey of those aspects of computational complexity needed for an understanding of modern cryptography, password systems and authentication techniques. Because the aim of the text is to make this exciting branch of modern applied mathematics available to readers with a wide variety of interests and backgrounds, the mathematical prerequisites have been kept to an absolute minimum. In addition to an extensive bibliography there are many exercises (easy) and problems together with solutions.

Introduction to Metric and Topological Spaces

Author : Wilson A Sutherland
Publisher : Oxford University Press
ISBN 13 : 0191568309
Total Pages : 219 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Introduction to Metric and Topological Spaces by : Wilson A Sutherland

Download or read book Introduction to Metric and Topological Spaces written by Wilson A Sutherland and published by Oxford University Press. This book was released on 2009-06-18 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.

Applied Partial Differential Equations

Author : J. R. Ockendon
Publisher :
ISBN 13 : 9780198527718
Total Pages : 466 pages
Book Rating : 4.5/5 (277 download)

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Book Synopsis Applied Partial Differential Equations by : J. R. Ockendon

Download or read book Applied Partial Differential Equations written by J. R. Ockendon and published by . This book was released on 2003 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics.

Parallel Scientific Computation

Author : Rob H. Bisseling
Publisher :
ISBN 13 : 0198788347
Total Pages : 410 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Parallel Scientific Computation by : Rob H. Bisseling

Download or read book Parallel Scientific Computation written by Rob H. Bisseling and published by . This book was released on 2020 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel Scientific Computation presents a methodology for designing parallel algorithms and writing parallel computer programs for modern computer architectures with multiple processors.