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Author : S. Shirali
Publisher : Universities Press
ISBN 13 : 9788173713682
Total Pages : 176 pages
Book Rating : 4.7/5 (136 download)
Download or read book First Steps in Number Theory written by S. Shirali and published by Universities Press. This book was released on 2001-07 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Douglas Faires
Publisher : MAA
ISBN 13 : 9780883858240
Total Pages : 344 pages
Book Rating : 4.8/5 (582 download)
Download or read book First Steps for Math Olympians written by J. Douglas Faires and published by MAA. This book was released on 2006-12-21 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Western Australia. Department of Education and Training
Publisher : Don Mills, Ont. : Pearson Professional Learning
ISBN 13 : 9780132018869
Total Pages : 322 pages
Book Rating : 4.0/5 (188 download)
Download or read book First Steps in Mathematics written by Western Australia. Department of Education and Training and published by Don Mills, Ont. : Pearson Professional Learning. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul Pollack
Publisher : Springer Nature
ISBN 13 : 3030650774
Total Pages : 191 pages
Book Rating : 4.0/5 (36 download)
Download or read book Steps into Analytic Number Theory written by Paul Pollack and published by Springer Nature. This book was released on 2021-02-08 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
Author : Andrew McInerney
Publisher : Springer Science & Business Media
ISBN 13 : 1461477328
Total Pages : 420 pages
Book Rating : 4.4/5 (614 download)
Download or read book First Steps in Differential Geometry written by Andrew McInerney and published by Springer Science & Business Media. This book was released on 2013-07-09 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Author : Paul Pollack
Publisher : American Mathematical Soc.
ISBN 13 : 1470436531
Total Pages : 329 pages
Book Rating : 4.4/5 (74 download)
Download or read book A Conversational Introduction to Algebraic Number Theory written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2017-08-01 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Author : Sue Willis
Publisher : First Steps
ISBN 13 : 9780975998687
Total Pages : pages
Book Rating : 4.9/5 (986 download)
Download or read book First Steps in Mathematics written by Sue Willis and published by First Steps. This book was released on 2005-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides teachers with a range of practical tools to improve the mathematical learning for all students
Author : J. Douglas Faires
Publisher : American Mathematical Soc.
ISBN 13 : 1470451263
Total Pages : 307 pages
Book Rating : 4.4/5 (74 download)
Download or read book First Steps for Math Olympians: Using the American Mathematics Competitions written by J. Douglas Faires and published by American Mathematical Soc.. This book was released on 2020-10-26 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! 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. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!
Author : C. Greenidge
Publisher :
ISBN 13 : 9781545501269
Total Pages : 134 pages
Book Rating : 4.5/5 (12 download)
Download or read book FIRST STEPS to Mathematics written by C. Greenidge and published by . This book was released on 2017-04-27 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Steps to Mathematics for Infants is a three-part book which introduces the young learner to Mathematics. The concepts are presented in an easy and interesting manner with a variety of activities for reinforcement. The first part introduces concepts like left right and middle, same and different, bigger and smaller, patterns, light and heavy, tall, short and long, and holds more and holds less. The second part focuses on numbers zero to ten. The activities include tracing and writing the numbers, drawing objects for the numbers, circling and completing sets, and counting and matching to the number.The third part presents concepts like shapes, one to one correspondence, equals, more than and less than, bigger and smaller number, missing numbers in series 0-10, number names zero to ten, ordinals, whole and fractions, pictographs, classifying, and adding and taking away. Although designed for the 4-6 age group, it may be helpful to older children who have not mastered the concepts.
Author : Leo Moser
Publisher : The Trillia Group
ISBN 13 : 1931705011
Total Pages : 95 pages
Book Rating : 4.9/5 (317 download)
Download or read book An Introduction to the Theory of Numbers written by Leo Moser and published by The Trillia Group. This book was released on 2004 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description
Author : Wolfram Pohlers
Publisher : Springer Science & Business Media
ISBN 13 : 354069319X
Total Pages : 380 pages
Book Rating : 4.5/5 (46 download)
Download or read book Proof Theory written by Wolfram Pohlers and published by Springer Science & Business Media. This book was released on 2008-10-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ̈ Wilhelms–Universitat ̈ in Munster ̈ . It was planned as a successor of Springer Lecture Notes in Mathematics 1407. H- ever, when preparing it, I decided to also include material which has not been treated in SLN 1407. Since the appearance of SLN 1407 many innovations in the area of - dinal analysis have taken place. Just to mention those of them which are addressed in this book: Buchholz simpli?ed local predicativity by the invention of operator controlled derivations (cf. Chapter 9, Chapter 11); Weiermann detected applications of methods of impredicative proof theory to the characterization of the provable recursive functions of predicative theories (cf. Chapter 10); Beckmann improved Gentzen’s boundedness theorem (which appears as Stage Theorem (Theorem 6. 6. 1) in this book) to Theorem 6. 6. 9, a theorem which is very satisfying in itself - though its real importance lies in the ordinal analysis of systems, weaker than those treated here. Besides these innovations I also decided to include the analysis of the theory (? –REF) as an example of a subtheory of set theory whose ordinal analysis only 2 0 requires a ?rst step into impredicativity. The ordinal analysis of(? –FXP) of non- 0 1 0 monotone? –de?nable inductive de?nitions in Chapter 13 is an application of the 1 analysis of(? –REF).
Author : Sheldon Axler
Publisher : Springer Science & Business Media
ISBN 13 : 9780387982595
Total Pages : 276 pages
Book Rating : 4.9/5 (825 download)
Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author : Derek Allan Holton
Publisher : World Scientific Publishing Company
ISBN 13 : 9814365254
Total Pages : 292 pages
Book Rating : 4.8/5 (143 download)
Download or read book A First Step To Mathematical Olympiad Problems written by Derek Allan Holton and published by World Scientific Publishing Company. This book was released on 2009-07-30 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Alexander Zawaira
Publisher : OUP Oxford
ISBN 13 : 0191561703
Total Pages : 368 pages
Book Rating : 4.1/5 (915 download)
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.
Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.4/5 (471 download)
Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Author : Avner Ash
Publisher : Princeton University Press
ISBN 13 : 0691178518
Total Pages : 248 pages
Book Rating : 4.6/5 (911 download)
Download or read book Summing It Up written by Avner Ash and published by Princeton University Press. This book was released on 2018-01-30 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The power and properties of numbers, from basic addition and sums of squares to cutting-edge theory We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
