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 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 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!
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 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 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 The First Steps in Number written by George Albert Wentworth and published by . This book was released on 1891 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 First Steps in Modal Logic written by Sally Popkorn and published by Cambridge University Press. This book was released on 1994-12-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory.
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.
Download or read book The First Steps in Algebra written by George Albert Wentworth and published by . This book was released on 1894 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Elementary Number Theory Primes Congruences and Secrets written by William Stein and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
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"--
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
