UPDATED EDITION: The new edition includes these updates:The updated edition numbers the questions and answers. This helps to easily find the correct answers in the back of the book.100% of the answers to the updated edition have been independently verified both by computer and by an international math whiz.AUTHOR: Chris McMullen earned his Ph.D. in physics from Oklahoma State University and currently teaches physics at Northwestern State University of Louisiana. He developed the Improve Your Math Fluency series of workbooks to help students become more fluent in basic math skills.CONTENTS: This Algebra Essentials Practice Workbook with Answers provides ample practice for developing fluency in very fundamental algebra skills - in particular, how to solve standard equations for one or more unknowns. These algebra 1 practice exercises are relevant for students of all levels - from grade 7 thru college algebra. This workbook is conveniently divided up into seven chapters so that students can focus on one algebraic method at a time. Skills include solving linear equations with a single unknown (with a separate chapter dedicated toward fractional coefficients), factoring quadratic equations, using the quadratic formula, cross multiplying, and solving systems of linear equations. Not intended to serve as a comprehensive review of algebra, this workbook is instead geared toward the most essential algebra skills. An introduction describes how parents and teachers can help students make the most of this workbook. Students are encouraged to time and score each page. In this way, they can try to have fun improving on their records, which can help lend them confidence in their math skills.PRACTICE: With no pictures, this workbook is geared strictly toward learning the material and developing fluency through practice.EXAMPLES: Each section begins with a few pages of instructions for how to solve the equations followed by a few examples. These examples should serve as a useful guide until students are able to solve the problems independently.ANSWERS: Answers to 100% of the exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes. All answers from the updated edition have been verified both by computer and independently by an international math whiz.PHOTOCOPIES: The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient if you have multiple children/students or if a child/student needs additional practice.NOTE: The answer key uses standard form. Fractions are expressed as reduced fractions, denominators are rationalized, and perfect squares are factored out of square roots. For example, if you receive an answer of 1 over root 8, the answer key will instead show root 2 over 4; both answers are the same, but the answer key uses standard form. Read more

The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this comprehensive workbook (with full solutions to every problem) to share his strategies for mastering calculus. This workbook covers a variety of essential calculus skills, including:derivatives of polynomials, trig functions, exponentials, and logarithmsthe chain rule, product rule, and quotient rulesecond derivativeshow to find the extreme values of a functionlimits, including l’Hopital’s ruleantiderivatives of polynomials, trig functions, exponentials, and logarithmsdefinite and indefinite integralstechniques of integration, including substitution, trig sub, and integration by partsmultiple integralsThe goal of this workbook isn’t to cover every possible topic from calculus, but to focus on the most essential skills needed to apply calculus to other subjects, such as physics or engineering. Read more

For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers:partial derivativesextreme values with multiple variables (including saddle points)vectors, vector analysis (such as the dot and cross products), and vector calculusthe gradient, divergence, and curlthe main coordinate systems: Cartesian, 2D polar, spherical, and cylindricalpath integrals, surface integrals, and volume integralsflux integrals, center of mass, and moment of inertiatangent and normal vectorsand moreThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors. Read more

'An invaluable companion for anyone who wants a deep understanding of what’s under the hood of often inscrutable machines' Melanie Mitchell A rich, narrative explanation of the mathematics that has brought us machine learning and the ongoing explosion of artificial intelligenceMachine-learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumour is cancerous, or deciding whether someone gets bail. They now influence discoveries in chemistry, biology and physics - the study of genomes, extra-solar planets, even the intricacies of quantum systems.We are living through a revolution in artificial intelligence that is not slowing down. This major shift is based on simple mathematics, some of which goes back centuries: linear algebra and calculus, the stuff of eighteenth-century mathematics. Indeed by the mid-1850s, a lot of the groundwork was all done. It took the development of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see all around us today. In this enlightening book, Anil Ananthaswamy explains the fundamental maths behind AI, which suggests that the basics of natural and artificial intelligence might follow the same mathematical rules.As Ananthaswamy resonantly concludes, to make the most of our most wondrous technologies we need to understand their profound limitations - the clues lie in the maths that makes AI possible. Read more

A marvelous compendium of mathematical symbols and their fascinating historiesGalileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one.In dozens of lively and informative entries, Raúl Rojas shows how today’s mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, René Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time.An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning. Read more

Algebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra.Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences.Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.Chapter 1: The meaning of algebraChapter 2: Elementary operations in algebraChapter 3: Brackets and operations with themChapter 4: Positive and negative numbersChapter 5: Equations and expressionsChapter 6: Linear equationsChapter 7: FormulaeChapter 8: Simultaneous equationsChapter 9: Linear inequalitiesChapter 10: Straight-line graphs; coordinatesChapter 11: Using inequalities to define regionsChapter 12: Multiplying algebraical expressions Chapter 13: FactorsChapter 14: FractionsChapter 15: Graphs of quadratic functionsChapter 16: Quadratic equationsChapter 17: IndicesChapter 18: LogarithmsChapter 19: Ratio and proportionChapter 20: VariationChapter 21: The determination of lawsChapter 22: Rational and irrational numbers and surdsChapter 23: Arithmetical and geometric sequences Read more

This math workbook, authored by Chris McMullen, Ph.D., is focused on essential prealgebra skills. It includes examples, plenty of practice problems, answers, and full solutions to most problems. Topics include:order of operations; PEMDASfractions, decimals, and percentsexponents and square rootsa beginning introduction to working with variablesratios and ratesnegative numbersother prealgebra skillsThe author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for applying arithmetic and prealgebra skills. Read more

Shortlisted for the Royal Society Science Book Prize 2019 A magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians. This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence. Filled with idiosyncratic characters from Pythagoras to Fourier, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides. Read more

’Be warned: cracking puzzles releases a very addictive drug.’ – Marcus du SautoyHave you ever wanted to be a puzzle pro or logical luminary? Well, look no further!The perfect way to liven up your day, The Ultimate Mathematical Challenge has over 365 puzzles to test your wits and excite your mind. From starter puzzles to perplexing Olympiad problems designed to stretch even the strongest mathematicians, this book is the ideal forum to get your brain into gear and feed it with the challenges it craves.Specially curated from the UK Mathematics Trust’s catalogue of puzzles, most of these problems can be tackled using no more than a little numerical knowledge, logical thinking and native wit. Including interludes of crossnumber conundrums and shuttle challenges, space for your working out and a handy glossary for those obscure mathematical terms, this book has everything you need to solve captivating problems all year round.Do you have what it takes to conquer The Ultimate Mathematical Challenge? Read more

Property Investment for BeginnersOverviewOver the past 20 years, property investment has provided an excellent opportunity for ambitious, free-thinking investors to grow their wealth and reclaim their financial independence.These investors have achieved their success in spite of the great financial crisis, a global pandemic, and the first serious outburst of inflation we’ve seen for forty years. And so can you.Property Investment for Beginners is a step-by-step guide that will take you from property beginner to putting down an offer on your first buy-to-let in just four-weeks. You’ll learn how to:- set your investment goals and build a team around you- value residential property and model your likely returns- finance deals and use leverage to build wealth faster- choose where to invest and find good property deals- carry out property viewings and succeed in negotiationsYou don’t need an MBA or a masters degree in finance. Anyone can pursue a passion for property and learn how to build a portfolio, generate a second income and enjoy greater financial security.Whether you’re looking at property as a way to plan for retirement or replace the income from your day job, this book will give you the knowledge you need to get started in property today.List of ChaptersWeek One : Learning the basicsChapter 1 - Why invest in property?Chapter 2 - Rental yield calculationsChapter 3 - Capital growthChapter 4 - Using leverage to enhance returnsChapter 5 - The effect of compoundingWeek Two : Getting yourself set upChapter 6 - Setting your property goalsChapter 7 - Pick the right tax structureChapter 8 - Introduction to deal financingChapter 9 - Build a team around youChapter 10 - Gathering your resourcesWeek Three : Finding property dealsChapter 11 - Choosing where to investChapter 12 - Narrowing it down furtherChapter 13 - How to value a propertyChapter 14 - Modelling potential returnsChapter 15 - Using a property sourcerWeek Four : Viewings and negotiationsChapter 16 - How to arrange viewingsChapter 17 - What to do during viewingsChapter 18 - Refining your modellingChapter 19 - Offers and negotiationsChapter 20 - The conveyancing processAbout the AuthorRobert Heaton is a property investor, writer and qualified actuary.He blogs about property investment and property investing at his website. Read more

Unlock the Power of Numbers and Master Essential Skills for Success!Are you ready to build rock-solid mathematical foundations and confidently tackle algebra? Whether you're a student striving for academic excellence, a parent aiming to boost your child's math confidence, or a self-learner sharpening vital skills, this comprehensive guide is precisely the resource you've been searching for.Step by step, chapter by chapter, this easy-to-follow guide uncovers all the essentials—from integers, fractions, decimals, and percents to ratios, equations, inequalities, exponents, and beyond. Each clearly explained concept is crafted to make complex topics easy and engaging, ensuring steady progress and lasting understanding.What Sets This Guide Apart?✓ Clear and Engaging Content – Designed specifically for learners at all levels, turning confusion into clarity.✓ Logical Step-by-Step Structure – Build upon your skills incrementally, developing deep understanding and confidence.✓ Comprehensive Coverage – Master everything from basic arithmetic to algebraic expressions, equations, and problem-solving techniques—without the stress.✓ Valuable Problem-Solving Strategies – Real-life scenarios and carefully constructed challenges help you apply your knowledge practically and effectively.✓ Ideal for Independent Study and Classroom Use – Perfect as a personal study guide, homeschool resource, or classroom companion.Empower yourself or someone you care about with the math skills that open doors to advanced concepts, academic achievement, and lifelong confidence. Explore your path to math mastery today—your journey ahead has never been clearer. Read more

'Startling in scope and bravado' The New York TimesIn his now-classic and hugely influential exploration of the evolving union of human and machine, world-renowned inventor and futurist Ray Kurzweil foresees the dawning of a new civilisation where humans will transcend our biological limitations and amplify our creativity by combining our aptitudes with the vastly greater capacity, speed and knowledge-sharing abilities of Artificial Intelligence. This melding of human and machine is what he terms 'the singularity'.On the eve of publication of his latest book, The Singularity is Nearer, this new edition of the first instalment of his ground breaking vision offers a fascinating and thought-provoking perspective on decades of innovation - and what still lies ahead.*** PRAISE FOR THE SINGULARITY IS NEAR *** 'Artfully envisions a breathtakingly better world' Los Angeles Times'Elaborate, smart and persuasive' The Boston Globe'A pleasure to read' The Wall Street JournalAn Amazon Best Science Book of 2005A CBS News Best Autumn Books of 2005A St Louis Post-Dispatch Best Nonfiction Book of 2005 Read more

An Observer Book of the YearA Times Science Book of the YearA New Statesman Book of the YearA Financial Times Science Book of the Year'Astonishingly bold' Daily Mail'It is hard to imagine a more timely book ... much of the modern world will make more sense having read it.' The TimesWe live in a world that's more interconnected than ever before. Our lives are shaped by outbreaks - of disease, of misinformation, even of violence - that appear, spread and fade away with bewildering speed. To understand them, we need to learn the hidden laws that govern them. From 'superspreaders' who might spark a pandemic or bring down a financial system to the social dynamics that make loneliness catch on, The Rules of Contagion offers compelling insights into human behaviour and explains how we can get better at predicting what happens next.Along the way, Adam Kucharski explores how innovations spread through friendship networks, what links computer viruses with folk stories - and why the most useful predictions aren't necessarily the ones that come true.Now revised and updated with content on Covid-19. Read more

Think of a number between one and ten. No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context. Read more

Calculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader. Read more

Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic. In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. 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. Read more

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings.  It is a revolutionary work, astounding in its foresight and contemporaneity.  The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.     Read more

Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back­ ground or maturity from the reader, and which can be read and understood with no extra assistance. Our first three chapters are based almost entirely on A-level mathematics, while the next five require little else beyond some el­ ementary group theory. It is only in the last three chapters, where we treat more advanced topics, including recent developments, that we require greater mathematical background; here we use some basic ideas which students would expect to meet in the first year or so of a typical undergraduate course in math­ ematics. Throughout the book, we have attempted to explain our arguments as fully and as clearly as possible, with plenty of worked examples and with outline solutions for all the exercises. There are several good reasons for choosing number theory as a subject. It has a long and interesting history, ranging from the earliest recorded times to the present day (see Chapter 11, for instance, on Fermat's Last Theorem), and its problems have attracted many of the greatest mathematicians; consequently the study of number theory is an excellent introduction to the development and achievements of mathematics (and, indeed, some of its failures). In particular, the explicit nature of many of its problems, concerning basic properties of inte­ gers, makes number theory a particularly suitable subject in which to present modern mathematics in elementary terms. Read more

In this book we introduce ordinary differential equations and discuss basic methods for solving them. Many examples are given throughout to aid in the understanding and execution of the methods discussed. The goal of this book is to teach students a practical way of recognizing, classifying, and solving differential equations. This book is suitable for students with a basic knowledge of calculus. We strongly believe in teaching by examples, and that repetition is the best way to internalize new ideas. Each example intends to guide the student through the thinking process without skipping steps and touches on all of the new material presented. Read more

This book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on.The first part of the book gives a full treatise of the W function from theoretical point of view.The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient.The third part presents a large number of applications from physics, biology, game theory, bacterial cell growth models, and so on.The second part presents the generalized Lambert functions based on the tools we had developed in the first part. In the third part familiarity with Newtonian physics will be useful. The text is written to be accessible for everyone with only basic knowledge on calculus and complex numbers. Additional features include the Further Notes sections offering interesting research problems and information for further studies. Mathematica codes are included.The Lambert function is arguably the simplest non-elementary transcendental function out of the standard set of sin, cos, log, etc., therefore students who would like to deepen their understanding of real and complex analysis can see a new “almost elementary” function on which they can practice their knowledge. Read more