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Author: Andrew Granville Publisher: American Mathematical Society ISBN: 1470463709 Category : Mathematics Languages : en Pages : 587
Book Description
Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.
Author: Andrew Granville Publisher: American Mathematical Society ISBN: 1470463709 Category : Mathematics Languages : en Pages : 587
Book Description
Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.
Author: Andrew Granville Publisher: American Mathematical Soc. ISBN: 1470441578 Category : Education Languages : en Pages : 264
Book Description
Number Theory Revealed: An Introduction acquaints undergraduates with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an “elective appendix” with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests.
Author: Martin H. Weissman Publisher: American Mathematical Soc. ISBN: 1470463717 Category : Education Languages : en Pages : 341
Book Description
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
Author: Jean-Marie De Koninck Publisher: American Mathematical Soc. ISBN: 1470464896 Category : Education Languages : en Pages : 329
Book Description
This book is about the life of primes. Indeed, once they are defined, primes take on a life of their own and the mysteries surrounding them begin multiplying, just like living cells reproduce themselves, and there seems to be no end to it. This monograph takes the reader on a journey through time, providing an accessible overview of the numerous prime number theory problems that mathematicians have been working on since Euclid. Topics are presented in chronological order as episodes. These include results on the distribution of primes, from the most elementary to the proof of the famous prime number theorem. The book also covers various primality tests and factorisation algorithms. It is then shown how our inability to factor large integers has allowed mathematicians to create today's most secure encryption method. Computer science buffs may be tempted to tackle some of the many open problems appearing in the episodes. Throughout the presentation, the human side of mathematics is displayed through short biographies that give a glimpse of the lives of the people who contributed to the life of primes. Each of the 37 episodes concludes with a series of problems (many with solutions) that will assist the reader in gaining a better understanding of the theory.
Author: Dennis Englin Publisher: New Leaf Publishing Group ISBN: 1683440730 Category : Science Languages : en Pages : 35
Book Description
What is chemistry? It is the study of the composition, structure, and properties of matter. It is through an understanding of chemistry that the products that have benefited society were discovered and technologies to sustain the environment were put in place. Knowledge taught in this course of how matter changes will give us an insight into the origin of life, so we can realize that life could only have been formed by a supernatural act of creation, not by a process of change over time. High school science course with lab curriculumLab experiments are included with step-by-step images for guidanceBased on the principle that those who can understand and apply information do much better than those who simply memorize material This course has been taught by Dr. Englin for many years, with students going on to medical and graduate school. He wanted to develop a series of courses that would give students the tools to help them succeed in higher education. The comprehensive material has God the Creator as its foundation. A teacher guide is available for Chemistry, providing this full-year science course with a detailed schedule, worksheets, and tests.
Author: Eric Lehman Publisher: ISBN: 9789888407064 Category : Business & Economics Languages : en Pages : 988
Book Description
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Author: William J. LeVeque Publisher: Courier Corporation ISBN: 0486141500 Category : Mathematics Languages : en Pages : 292
Book Description
This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect. The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few. Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.
Author: Corey Rosenbloom Publisher: John Wiley & Sons ISBN: 0470594594 Category : Business & Economics Languages : en Pages : 324
Book Description
A practical guide covering everything the serious trader needs to know While a variety of approaches can be used to analyze financial market behavior and identify potential trading/investing opportunities, no approach is completely accurate. The challenge for traders is to find a method that they feel comfortable with and are able to implement consistently, through the normal ups and downs of trading. The Trading Course provides you with a detailed description of the methods used to analyze markets, spot profitable trading opportunities, and properly execute trades. Page by page, this book references different trading methodologies, but focuses specifically on applying them when attempting to identify good trades. Discusses the principles of price behavior, trends, trade set ups, trade execution, and intermarket relationships Details different trading tools and techniques, including Japanese Candlesticks, Elliott Wave, Dow Theory, momentum indicators, and much more If you want to become a successful trader, you have to be prepared. This book will show you what it takes to make it in this field and how you can excel without getting overwhelmed.
Author: George E. Andrews Publisher: Courier Corporation ISBN: 0486135101 Category : Mathematics Languages : en Pages : 292
Book Description
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.
Author: David A. Phillips, Ph.D. Publisher: Hay House, Inc ISBN: 1401930255 Category : Body, Mind & Spirit Languages : en Pages : 285
Book Description
Discover the science of self-discovery To the conventional scientist, numbers are merely symbols of comparative quantities, but in the broader, metaphysical sense, they assume a deeper, more profound significance. The Complete Book of Numerology reveals the underlying meaning behind the numbers in your life and enables you to understand the connection between your numerological patterns and your degree of abundance, health, and general well-being. Overall, delving into the world of numbers will provide you with a simple and accurate way to decipher your experiences in the same manner that a road map helps you navigate a route that you haven’t previously traveled.
Author: Andrew Granville
Author: Andrew Granville
Author: Andrew Granville
Author: Martin H. Weissman
Author: Jean-Marie De Koninck
Author: Dennis Englin
Author: Eric Lehman
Author: William J. LeVeque
Author: Corey Rosenbloom
Author: George E. Andrews
Author: David A. Phillips, Ph.D.