Download or read book Practice Arithmetic and Number Theory written by Cleo Borac and published by . This book was released on 2013-12-21 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: About "Competitive Mathematics for Gifted Students" This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as AMC-8, AMC-10, Math Kangaroo in USA, Math Leagues, USAMTS, or AIME? This series will open the doors to consistent performance. About Level 3 This level of the series is designed for students who can solve linear equations, are fluent with fractions, and can factor into primes. The problem sets are designed to strengthen specific areas where we know students have difficulty on AMC-8 and AMC-10. The level 2 books are a strong preparation for AMC-8 and a partial preparation for AMC-10 and AIME. Level 2 consists of: Word Problems (volume 9), Arithmetic and Number Theory (volume 10), Operations and Algebra (volume 11), Geometry (volume 12), and Combinatorics (volume 13). On the contest list for this level: MATHCOUNTS, Math Kangaroo levels 5-6 and 7-8, MOEMS-M, Purple Comet, AMC-8, AMC-10. The computational complexity makes these problem sets useful for preparing the AIME in the long run. About Volume 10 - Arithmetic and Number Theory The problem sets reflect the use of the most elementary facts of number theory in challenging ways. Instead of imitating contest problems, we have focused on presenting questions that explore the nuts and bolts used to create problems. This volume is particularly suitable for young students who aim to do well on AIME in later years and have the patience to explore the elementary facts of number theory in depth. We continue in level 4 with more advanced number theory. Fluency with order of operations and the ability to handle simple algebraic expressions are pre-requisites.
Download or read book Number Theory Modular Arithmetic written by Xing Zhou and published by Createspace Independent Publishing Platform. This book was released on 2017-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Remainder does not seem to be a big topic in school math. However, in competition math, it is. Almost every contest at middle school and high school level has remainder related problems. For example, in 2017 AMC 10B, out of total 25 problems, at least 3 are related to this topic: the 14th, 23rd, and 25th. Modular arithmetic is a branch in mathematics which studies remainders and tackles related problems. However, this important subject is not taught in schools. Consequently, many students rely on their intuition when attempting to solve such problems. This is clearly not the best situation. This book aims to provide a complete coverage of this topic at the level which is suitable for middle school and high school students. Contents will include both theoretical knowledge and practical techniques. Therefore, upon completion, students will have a solid skill base to solve related problems in math competitions. More information, including table of contents, pre-assessment etc, can be found at http: //www.mathallstar.org/
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 Number Theory Through Exercises written by Nairi Sedrakyan and published by . This book was released on 2019-03-18 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a teacher's manual of Number Theory and a self-study handbook for high-school or college students, and mathematical competitors. The book teaches new and classical proof techniques of Number Theory through practical and challenging problems. It is arranged by topics and difficulty level.It mainly consists of new problems created by authors with author-prepared-solutions, some of these problems were proposed in different national and international Mathematical Olympiads from 1984 to 2018.The book gives a broad view of Number Theory and goes beyond the typical elementary mathematics by providing deeper treatment of the topics.This book consists of two parts. Part 1 is a separate book consisting of Chapter 1, Chapter 2 and Chapter 3.Part 2 is a separate book consisting of Chapter 4, Chapter 5 and Chapter 6.
Download or read book Introduction to Number Theory written by Anthony Vazzana and published by CRC Press. This book was released on 2007-10-30 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
Download or read book Number Theory and Geometry An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2019-03-21 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Download or read book Exercises in Number Theory written by D.P. Parent and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy of its distinguished past. More 'and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and talent. In so doing, their work enriches the whole of mathematics with new and fertile methods. To be in a position to tackle these problems, it is neces sary to be familiar with many specific aspects of number theory. These are very different from those encountered in analysis or geometry. The necessary know-how can only be acquired by study ing and solving numerous problems. Now it is very easy to form ulate problems whose solutions, while sometimes obvious, more often go beyond current methods. Moreover, there is no doubt that, even more than in other disciplines, in mathematics one must have exercises available whose solutions are accessible. This is the objective realised by this work. It is the collab orative work of several successful young number theorists. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.
Download or read book Practice Arithmetic written by Cleo Borac and published by . This book was released on 2014-06-24 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2nd Edition - 2014 About "Competitive Mathematics for Gifted Students" This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as MOEMS, Math Kangaroo in USA, or Noetic Math? This series will open the doors to consistent performance. About Level 2 This level of the series is designed for students who know the multiplication tables, integer division with remainder and basic operations with decimals. Our level 1 books explain concepts that may need review before attempting level 2. Level 2 books are suitable for preparing Math Kangaroo 3-4 and MOEMS-E. Many of the concepts presented, however, reach much farther into the AMC-8 level. Level 2 consists of: Word Problems (volume 5), Operations (volume 6), Arithmetic (volume 7), and Combinatorics (volume 8). About Volume 7 - Arithmetic This volume provides material for the practicing problems with combinations of digits, cryptarithms, repdigits, palindromes, digit sum and digit product, sequences, sums of consecutive numbers, divisibility rules and remainders. Divisibility rules are not proven at this level, only applied (proofs in level 3 books). For some students, it may be necessary to work on our level 1 books before attempting level 2.
Download or read book Practice by Subject written by Xing Zhou and published by Createspace Independent Publishing Platform. This book was released on 2018-12-03 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practice makes perfect. This book contains over 150 MOD related problems with complete solutions aiming to polish students' competition skills. It also contains a review chapter which highlights all the important concepts, theorems and techniques.It is recommended that reader should use this book together with the book Number Theory (MOD) which is also part of the Math All Star series. Additional information can be found online at https: //www.mathallstar.org
Download or read book 250 Problems in Elementary Number Theory written by Wacław Sierpiński and published by Elsevier Publishing Company. This book was released on 1970 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Shape Symmetry written by Diane L. Herrmann and published by CRC Press. This book was released on 2012-10-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
Download or read book A Conversational Introduction to Algebraic Number Theory Arithmetic Beyond Z written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2017-08-01 with total page 312 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 Approximation Theory and Approximation Practice Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
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 The Theory of Numbers written by Andrew Adler and published by Jones & Bartlett Publishers. This book was released on 1995 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Problems in Algebraic Number Theory written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2005-09-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
Download or read book The Practice of Mathematics written by Yvette Solomon and published by Routledge. This book was released on 2013-08-21 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The psychological description and explanation of how children learn to work with numbers is dominated by the theories of Piaget. Yvette Solomon suggests an alternative approach to the child's conception of number.
