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:
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.
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:
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.
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.
Download or read book Combinatorics written by Mykola Perestyuk and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of our book is to provide easy access to the basic principles and methods that combinatorial calculations are based upon. The rule of product, the identity principle, recurrence relations and inclusion-exclusion principle are the most important of the above. Significant parts of the book are devoted to classical combinatorial structures, such as: ordering (permutations), tuples, and subsets (combinations). A great deal of attention is paid to the properties of binomial coefficients, and in particular, to model proofs of combinatorial identities. Problems concerning some exact combinatorial configurations such as paths in a square, polygonal chains constructed with chords of a circle, trees (undirected graphs with no cycles) etc. are included too. All chapters contain a considerable number of exercises of various complexity, from easy training tasks to complex problems which require decent persistence and skill from the one who dares to solve them. If one aims to passively familiarise oneself with the subject, methods and the most necessary facts of combinatorics, then it may suffice to limit one's study to the main text omitting the exercise part of the book. However, for those who want to immerse themselves in combinatorial problems and to gain skills of active research in that field, the exercise section is rather important. The authors hope that the book will be helpful for several categories of readers. University teachers and professors of mathematics may find somewhat unusual coverage of certain matters and exercises which can be readily applied in their professional work. We believe that certain series of problems may serve as a base for serious creative works and essays. This especially refers to students at pedagogical universities and colleges who need to prepare themselves to the teaching of the basics of combinatorics, mainly building on arithmetic and geometry. Most of the exercises of the book are of this very origin.
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
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.
Download or read book Number Theory written by George E. Andrews and published by Courier Corporation. This book was released on 2012-04-30 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Download or read book Mathematics the First Step written by Ramesh Chandra and published by Notion Press. This book was released on 2017-04-19 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book intended exclusively for the usage of students, teachers and persons who are related to competitive exams. The book is based on our experience over the past 8 years and design on the basis of current competitive level of Engineering like IIT JEE mains/ Advanced, MHT-CET, BITSAT + NTSE, KVPY, Olympiad, IIT Foundation + CAT and other state engineering exams in India, where 1194938 i.e. around 12 Lakh of students (Year 2016) write a single engineering exam. As an educator, I understand the student’s need of these topics and the difficulties faces by students in transition from standard 10th to 11th class. As students enter their 11th standard, they find a substantial change in the course content and level of difficulty. They find some totally new concepts of Mathematics, widely used in Physics and Chemistry. They may be completely unfamiliar with concepts of absolute value, Interval Methods, Set Notation, inequalities etc. The book has been prepared for them to learn the concepts of algebra from basic to advanced level of thinking. The book is prepared to serve as a bridge for 10th to 11th standards, CAT aspirants etc. Software engineers can also be in benefit in writing the code due to concepts clarity. The book contains the following Learning Methodology. (i) Basic concepts and easy learning. (ii) Necessary examples and experiments for beginners level to expert. (iii) Psychology of student’s brain and their thinking. (iv) Pictorial view of problems and solutions. (v) Challenging problems (Ultimate Finish – for Top All India Rankers between 1 - 500). (vi) Exercises and Assignments to test the understanding and growing knowledge. (vii) Sample Test Paper to have experience before actual exam. (viii) Puzzles and interactive learning to keep interest. (ix) How to make notes to up-to-date and add your thinking inside the book. (x) Archive of IIT-JEE Mains/Advanced. (xi) All types of questions (Single and Multi-correct, Integer Type, Comprehension, Assertion-reason, Matrix-Match) i.e Subjective and Objective both.
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
Download or read book The Joy of X written by Steven Henry Strogatz and published by Houghton Mifflin Harcourt. This book was released on 2012 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."
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.
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 331 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!
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.
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).
Download or read book First Steps in Music Theory Grades 1 to 5 written by Eric Robert Taylor and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "An introduction to the necessary elements of music, this title is suitable for students preparing for examinations, as well as a resource for those learning to read music. It also features a step-by-step presentation of the basic facts of music theory; a grade-by-grade format; numerous music examples; and more." -- Provided by publisher.
