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Humans are pattern-matching creatures, and astrology is the universe's grandest pattern-matching game. In this refreshing work of history and analysis, data scientist Alexander Boxer examines classical texts on astrology to expose its underlying scientific and mathematical framework. Astrology, he argues, was the ancient world's most ambitious applied mathematics problem, a monumental data-analysis enterprise sustained by some of history's most brilliant minds, from Ptolemy to al-Kindi to Kepler. Thousands of years ago, astrologers became the first to stumble upon the powerful storytelling possibilities inherent in numerical data. To correlate the configurations of the cosmos with our day-to-day lives, astrologers relied upon a "scheme of heaven," or horoscope, showing the precise configuration of the planets at a particular instant in time as viewed from a particular place on Earth. Although recognized as pseudoscience today, horoscopes were once considered a cutting-edge scientific tool. Boxer teaches us how to read these esoteric charts-and appreciate the complex astronomical calculations needed to generate them-by diagramming how the heavens appeared at important moments in astrology's history, from the assassination of Julius Caesar as viewed from Rome to the Apollo 11 lunar landing as seen from the surface of the Moon. He then puts these horoscopes to the test using modern data sets and statistical science, arguing that today's data scientists do work similar to astrologers of yore. By looking back at the algorithms of ancient astrology, he suggests, we can better recognize the patterns that are timeless characteristics of our own pattern-matching tendencies. At once critical, rigorous, and far ranging, A Scheme of Heaven recontextualizes astrology as a vast, technological project-spanning continents and centuries-that foreshadowed our data-driven world today.
Mental Arithmetic provides rich and varied practice to develop pupils' essential maths skills and prepare them for all aspects of the Key Stage 2 national tests. It may also be used as preparation for the 11+, and with older students for consolidation and recovery. Tailored to meet the requirements of the National Curriculum for primary mathematics, each book contains 36 one-page tests. Each test is presented in a unique three-part format comprising: questions where use of language is kept to a minimum; questions using number vocabulary; questions focusing on one- and two-step word problems. Structured according to ability rather than age, the series allows children to work at their own pace, building confidence and fluency. Two Entry Tests are available in the Mental Arithmetic Teacher's Guide and on the Schofield & Sims website, enabling teachers, parents and tutors to select the appropriate book for each child. All the books can be used flexibly for individual, paired, group or whole-class maths practice, as well as for homework and one-to-one intervention.Mental Arithmetic 4 Answers contains answers to all the questions included in the Mental Arithmetic 4 pupil book, as well as guidance on how to use the series and measure progress. Answers are clearly laid out in the format of a correctly completed pupil book making marking quick and easy, while a card cover ensures durability.
Challenge yourself with the GCHQ team's long-awaited second puzzle book - full of both harder and easier brain teasers. 'This is the perfect gift to fuel his ludicrous presumption that he could have definitely been a spy - even better if he's already dog-eared the first version' - Huffington Post, (10 Christmas Gifts for him under GBP15) 'Fiendishly tricky' - Daily Mail With their first bestselling book, The GCHQ Puzzle Book, the UK's intelligence and security experts tested us with puzzles, codes and real-life entrance tests from their archives. Now, they are back with a NEW collection of head-scratching, mind-boggling and brain-bending puzzles that will leave you pondering for hours. For those who often found themselves stumped with the first book, there will be even more starter puzzles to get those brains warmed up. Puzzle aficionados needn't worry though, as there will also be an 'Even Harder' section to test everyone to their limits. Not only that, but in celebration of GCHQ's centenary, the puzzles in this new book will sit alongside stories, facts and photos from the organisation's first 100 years at the heart of the nation's security. From the Government Code & Cipher School, to Bletchley Park, through to protecting against cyberattacks, the security of our country is in the hands of GCHQ. With this book, you'll get exclusive snapshots into the organisation that keeps us all safe. if you haven't yet tested yourself with the first instalment of The GCHQ Puzzle Book, check it out now!
The successful 30-Second series tackles numbers, with experts on maths and data demystifying the essential numerical topics. We know that we use numbers pretty often, some of us confidently, others reluctantly. But are we aware of just how essential they are to almost every decision we make? Counting and measuring when we're shopping, travelling, studying or playing are just the beginning; the applications of numbers are endless, from assessing variables and analysing data to the calculations and predictions of advanced artificial intelligence. 30-Second Numbers explores number categories, the science of measuring, how guesstimates work, and the visualisation of numbers, taking you behind the digits into the world of statistics, probability, risk and ratios. Numbers are our way of imposing order on the world, and each of the 50 topics here uses just 300 words and one picture to give you a sense of control, helping you to understand trends in statistical data, how algorithms are used and the methods involved in machine learning. With this book, numbers need never be daunting again.
A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Readers can create their own patterns and illustrations to color. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.
This informative survey chronicles the process of abstraction that
ultimately led to the axiomatic formulation of the abstract notion
of group. Hans Wussing, former Director of the Karl Sudhoff
Institute for the History of Medicine and Science at Leipzig
University, contradicts the conventional thinking that the roots of
the abstract notion of group lie strictly in the theory of
algebraic equations. Wussing declares their presence in the
geometry and number theory of the late eighteenth and early
Written by a noted expert on logic and set theory, this study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Geared toward undergraduate and beginning graduate students, it requires minimal mathematical training. Several helpful appendixes supplement the text. The author is Professor of Mathematics at Queens College in New York.
Fully revised to match the more traditional sequence of course materials, this full-color second edition presents the basic principles and methods of thermodynamics using a clear and engaging style and a wealth of end-of-chapter problems. It includes five new chapters on topics such as mixtures, psychrometry, chemical equilibrium, and combustion, and discussion of the Second Law of Thermodynamics has been expanded and divided into two chapters, allowing instructors to introduce the topic using either the cycle analysis in Chapter 6 or the definition of entropy in Chapter 7. Online ancillaries including a password-protected solutions manual, figures in electronic format, prepared PowerPoint lecture slides, and instructional videos are available.
Highlighted by numerous examples, this book explores methods of the
projective geometry of the plane. It derives the projective
properties of the conic and discusses representation by the general
equation of the 2nd degree, concluding with a study of the
relationship between Euclidean and projective geometry. 1960
This concise text introduces students to the elements of analytical geometry, covering basic ideas and methods. Topics include transformation of axes, the line at infinity, conics and pencils of conics, homographic correspondence, line-coordinates, and generalized homogeneous coordinates. An appendix discusses solutions to many of the examples. 1957 edition.
The most effective way to study any branch of mathematics is to tackle its problems. This wide-ranging anthology offers a straightforward approach, with 431 challenging problems in all phases of group theory, from elementary to the most advanced. The problems are arranged in eleven chapters: subgroups, permutation groups, automorphisms and finitely generated Abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, the group ring and monomial representations, Frattini subgroup, factorization, linear groups, and representations and characters. Each chapter features a preface of pertinent definitions and theorems, and full solutions appear in a separate section. Most of these problems are derived from research papers published since 1950 (a listing of 102 references is supplied). This compilation makes them readily accessible as a supplement to courses in group theory. The presentation places equal emphasis on techniques and results, encouraging the development of both skill and comprehension.
All of the sciences have a need for quantitative measurement. This
influential series established the formal foundations for
measurement, justifying the assignment of numbers to objects in
terms of their structural correspondence. 1990 edition.
This text develops the theory of systems of stochastic differential
equations and presents applications in probability, partial
differential equations, and stochastic control problems. Originally
published in 2 volumes, it combines a book of basic theory with a
book of applications. Familiarity with elementary probability is
the sole prerequisite. 1975 edition.
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Metric Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!
A sequence of 2,400 propositions and problems features only hints.
Suitable for advanced undergraduates and graduate students, this
unique approach encourages students to work out their own proofs.
A compact, sophomore-to-senior-level guide, Dr. Seeley's text
introduces Fourier series in the way that Joseph Fourier himself
used them: as solutions of the heat equation in a disk. Emphasizing
the relationship between physics and mathematics, Dr. Seeley begins
with a physical problem and applies the results to different
situations. 1966 edition.
Mann's Introductory Statistics is written for a one- or two-semester first course in applied statistics. This book is intended for students who do not have a strong background in mathematics. The only prerequisite for this text is knowledge of elementary algebra. The goal of Introductory Statistics has been to make the subject of statistics interesting and accessible to a wide and varied audience. Three major elements of this text support this goal: * Realistic content of its examples and exercises, drawing from a comprehensive range of applications from all facets of life * Clarity and brevity of presentation * Soundness of pedagogical approach Table of Contents * Introduction * Organizing and Graphing Data * Numerical Descriptive Measures * Probability * Discrete Random Variables and Their Probability Distribution * Continuous Random Variables and the Normal Distribution * Sampling Distributions * Estimation of the Mean and Proportion * Hypothesis Tests About the Mean and Proportion * Estimation and Hypothesis Testing: Two Populations * Chi-Square Tests * Analysis of Variance * Simple Linear Regression * Multiple Regression (online only) * Nonparametric Methods (online only) * Appendix A: Explanation of Data Sets * Appendix B: Statistical Tables New To This Edition * WileyPLUS with ORION: WileyPLUS is equipped with an adaptive learning modulecalled ORION. Based on cognitive science, WileyPLUS with ORION provides students with a personal, adaptive learning experience to build their proficiency on topics and use their study time more effectively. It helps students learn by learning about them. * ORION Refresher Module: An adaptive practice to master algebra skills providesstudents with a personalized study plan to master concepts prior to the course, allowing for instructors to focus class time on Introductory Statistics. * New Video Program: Videos reviewing key concepts will be available for each text section. * New Exercises: A large number of the examples and exercises are new or revised,providing contemporary and varied ways for students to practice statistical concepts, including updated Uses and Misuses sections as well as Decide for Yourself sections. * Case Studies: All case studies are new or revised, drawing on current uses of statistics in areas of student interest. * Updated Technology Instruction sections: These sections have been updated tosupport the use of the latest versions of TI-94/85+, Minitab, and Excel. The Technology Assignments are all either new or have been updated. The Wiley Advantage * WileyPLUS is a research-based online environment for effective teaching andlearning. Interactive study tools and resources including the complete online textbook give students more value for their money. * Industry-leading support from WileyPLUS with ORION:Resources and personal support are available from the first day of class onward through technical support; WileyPLUS account managers; WileyPLUS with QuickStart; and WileyPLUS Student Partner Program. * Thorough Examples: A wealth of examples that cover a wide variety of relevanttopics, based on real data taken from government and private data sources and reports, newspapers, magazines, and professional journals. * Enlightening Pedagogy: Effective markers and aids for students including: marginnotes for examples; diagrams
This introductory text presents detailed accounts of the different
forms of the theory developed by Stroock and Bismut, discussions of
the relationship between these two approaches, and a variety of
applications. 1987 edition.
Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Subjects include simple roots and the Cartan matrix, the classical and exceptional Lie algebras, the Weyl group, and more. 1984 edition.
Derived from a course in fluid mechanics, this text for advanced
undergraduates and beginning graduate students employs symmetry
arguments to demonstrate the principles of dimensional analysis.
The examples provided illustrate the effectiveness of symmetry
arguments in obtaining the mathematical form of the functions
yielded by dimensional analysis. Students will find these methods
applicable to a wide field of interests.
Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.
This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.
An examination of approaches to easy-to-understand but
difficult-to-solve mathematical problems, this classic text begins
with a discussion of Dirichlet's principle and the boundary value
problem of potential theory, then proceeds to examinations of
conformal mapping on parallel-slit domains and Plateau's problem.
Also explores minimal surfaces with free boundaries and unstable
minimal surfaces. 1950 edition.
Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Here is a complete self-teaching guide for anyoneneeding knowledge of math as it applies toengineering and technical fields.
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