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.

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.

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.

There is no surprise that arithmetic properties of integral ('whole') numbers are controlled by analytic functions of complex variable. At the same time, the values of analytic functions themselves happen to be interesting numbers, for which we often seek explicit expressions in terms of other 'better known' numbers or try to prove that no such exist. This natural symbiosis of number theory and analysis is centuries old but keeps enjoying new results, ideas and methods.The present book takes a semi-systematic review of analytic achievements in number theory ranging from classical themes about primes, continued fractions, transcendence of π and resolution of Hilbert's seventh problem to some recent developments on the irrationality of the values of Riemann's zeta function, sizes of non-cyclotomic algebraic integers and applications of hypergeometric functions to integer congruences.Our principal goal is to present a variety of different analytic techniques that are used in number theory, at a reasonably accessible — almost popular — level, so that the materials from this book can suit for teaching a graduate course on the topic or for a self-study. Exercises included are of varying difficulty and of varying distribution within the book (some chapters get more than other); they not only help the reader to consolidate their understanding of the material but also suggest directions for further study and investigation. Furthermore, the end of each chapter features brief notes about relevant developments of the themes discussed.

This book was created to help teachers as they instruct students through the Master’s Class Chemistry course by Master Books. The teacher is one who guides students through the subject matter, helps each student stay on schedule and be organized, and is their source of accountability along the way. With that in mind, this guide provides additional help through the laboratory exercises, as well as lessons, quizzes, and examinations that are provided along with the answers. The lessons in this study emphasize working through procedures and problem solving by learning patterns. The vocabulary is kept at the essential level. Practice exercises are given with their answers so that the patterns can be used in problem solving. These lessons and laboratory exercises are the result of over 30 years of teaching home school high school students and then working with them as they proceed through college. Guided labs are provided to enhance instruction of weekly lessons. There are many principles and truths given to us in Scripture by the God that created the universe and all of the laws by which it functions. It is important to see the hand of God and His principles and wisdom as it plays out in chemistry. This course integrates what God has told us in the context of this study. Features: Each suggested weekly schedule has five easy-to-manage lessons that combine reading and worksheets. Worksheets, quizzes, and tests are perforated and three-hole punched — materials are easy to tear out, hand out, grade, and store. Adjust the schedule and materials needed to best work within your educational program. Space is given for assignments dates. There is flexibility in scheduling. Adapt the days to your school schedule. Workflow: Students will read the pages in their book and then complete each section of the teacher guide. They should be encouraged to complete as many of the activities and projects as possible as well. Tests are given at regular intervals with space to record each grade. About the Author: DR. DENNIS ENGLIN earned his bachelor’s from Westmont College, his master of science from California State University, and his EdD from the University of Southern California. He enjoys teaching animal biology, vertebrate biology, wildlife biology, organismic biology, and astronomy at The Master’s University. His professional memberships include the Creation Research Society, the American Fisheries Association, Southern California Academy of Sciences, Yellowstone Association, and Au Sable Institute of Environmental Studies.

Every child's potential is regularly determined by a standardized measurement: their quotient (Q). Score high enough, and attend a top tier school with a golden future. Score too low, and it's off to a federal boarding school with limited prospects afterwards. The purpose? An improved society where education costs drop, teachers focus on the more promising students, and parents are happy.Elena Fairchild is a teacher at one of the state's elite schools. When her nine-year-old daughter bombs a monthly test and her Q score drops to a disastrously low level, she is immediately forced to leave her top school for a federal institution hundreds of miles away. As a teacher, Elena thought she understood the tiered educational system, but as a mother whose child is now gone, Elena's perspective is changed forever. She just wants her daughter back.And she will do the unthinkable to make it happen. (4e de couverture)

Alex Rogo is a harried plant manager working ever more desperately to try and improve performance. His factory is rapidly heading for disaster. So is his marriage. He has ninety days to save his plant - or it will be closed by corporate HQ, with hundreds of job losses. It takes a chance meeting with a colleague from student days - Jonah - to help him break out of conventional ways of thinking to see what needs to be done. Described by Fortune as a 'guru to industry' and by Businessweek as a 'genius', Eliyahu M. Goldratt was an internationally recognized leader in the development of new business management concepts and systems. This 20th anniversary edition includes a series of detailed case study interviews by David Whitford, Editor at Large, Fortune Small Business, which explore how organizations around the world have been transformed by Eli Goldratt's ideas. The story of Alex's fight to save his plant contains a serious message for all managers in industry and explains the ideas which underline the Theory of Constraints (TOC) developed by Eli Goldratt. Written in a fast-paced thriller style, The Goal is the gripping novel which is transforming management thinking throughout the Western world. It is a book to recommend to your friends in industry - even to your bosses - but not to your competitors!