In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    The fifth edition of this classic reference work has been updated to give a reasonably accurate account of the present state of knowledge.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

    Contains complete worked solutions to all regular exercises and computer exercises in the text; additional test questions and their solutions; an online laboratory manual for the computer algebra system GAP, with exercises tied to the book and an instructor answer key; and links on the author's website to true/false questions, flash cards, essays, software downloads, and other abstract algebra-related materials.

    Introduction to Modern Cryptography provides a rigorous yet accessible treatment of modern cryptography, with a focus on formal definitions, precise assumptions, and rigorous proofs.The authors introduce the core principles of modern cryptography, including the modern, computational approach to security that overcomes the limitations of perfect secrecy. An extensive treatment of private-key encryption and message authentication follows. The authors also illustrate design principles for block ciphers, such as the Data Encryption Standard (DES) and the Advanced Encryption Standard (AES), and present provably secure constructions of block ciphers from lower-level primitives. The second half of the book focuses on public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, El Gamal, and other cryptosystems. After exploring public-key encryption and digital signatures, the book concludes with a discussion of the random oracle model and its applications.Serving as a textbook, a reference, or for self-study, Introduction to Modern Cryptography presents the necessary tools to fully understand this fascinating subject.

    Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.

    Whether it is a visualization of the Catalan numbers or an explanation of how the Fibonacci numbers occur in nature, there is something in here to delight everyone. The diagrams and pictures, many of which are in color, make this book particularly appealing and fun. A few of the discussions may be confusing to those who are not adept mathematicians; those who are may be irked that certain facts are mentioned without an accompanying proof. Nonetheless, The Book of Numbers will succeed in infecting any reader with an enthusiasm for numbers.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    New co-authors--Irl Bivens and Stephen Davis--from Davidson College; both distinguished educators and writers.* More emphasis on graphing calculators in exercises and examples, including CAS capabilities of graphing calculators.* More problems using tabular data and more emphasis on mathematical modeling.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    There is one worksheet for each type of math problem including different digits with operations of addition, subtraction, multiplication and division. These varying level of mathematical ability activities help in improving adding, subtracting, multiplying and dividing operation skills of the student by frequent practicing of the worksheets provided.There is nothing more effective than a pencil and paper for practicing some math skills. These math worksheets are ideal for teachers, parents, students, and home schoolers. The companion ebook allows you to take print outs of these worksheets instantly or you can save them for later use. The learner can significantly improve math knowledge by developing a simple habit to daily practice the math drills.Tutors and homeschoolers use the maths worksheets to test and measure the child's mastery of basic math skills. These math drill sheets can save you precious planning time when homeschooling as you can use these work sheets to give extra practice of essential math skills. Parents use these mathematics worksheets for their kids homework practice too.Designed for after school study and self study, it is used by homeschooler, special needs and gifted kids to add to the learning experience in positive ways. You can also use the worksheets during the summer to get your children ready for the upcoming school term. It helps your child excel in school as well as in building good study habits. If a workbook or mathematic textbook is not allowing for much basic practise, these sheets give you the flexibility to follow the practice that your student needs for an education curriculum.These worksheets are not designed to be grade specific for students, rather depend on how much practice they've had at the skill in the past and how the curriculum in your school is organized. Kids work at their own level and their own pace through these activities. The learner can practice one worksheet a day, two worksheets a day, one every alternate day, one per week, two per week or can follow any consistent pattern. Make best use of your judgement.

    

    The nature of football continually changes, which means its analysis must also keep pace. This book is for students, thinkers, and theorists of the game.'Ted Hopkins - Carlton premiership player, author, and co-founder of Champion Data. Australian Rules football has been described as the most data-rich sport on Earth. Every time and everywhere an AFL side takes to the field, it is shadowed by an army of statisticians and number crunchers. The information they gather has become the sport's new language and currency. ABC journalist James Coventry, author of the acclaimed Time and Space, has joined forces with a group of razor-sharp analysts to decipher the data, and to use it to question some of football's long-held truisms. Do umpires really favour the home side? Has goal kicking accuracy deteriorated? Is Geelong the true master of the draft? Are blonds unfairly favoured in Brownlow medal voting? And are Victorians the most passionate fans? Through a blend of entertaining storytelling and expert analysis, this book will answer more questions about footy than you ever thought to ask. Praise for Time and Space:'Brilliant, masterful' - The Guardian'Arguably one of the most important books yet written on Australian Rules football.' - Inside History'Should find its way into the hands of every coach.' - AFL Record