Mathematics Books

Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources help students with learning and revision. Written for the AQA AS/A Level Mathematics specifications for first teaching from 2017, this print Student Book covers the content for AS and the first year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Includes answers to aid independent study. This book is AQA approvedTable of Contents1. Proof and mathematical communication; 2. Indices and surds; 3. Quadratic functions; 4. Polynomials; 5. Using graphs; 6. Coordinate geometry; 7. Logarithms; 8. Exponential models; 9. Binomial expansion; Focus on proof 1; Focus on problem solving 1; Focus on modelling 1; Cross-topic review exercise 1; 10. Trigonometric functions and equations; 11. Triangle geometry; 12. Differentiation; 13. Applications of differentiation; 14. Integration; Focus on proof 2; Focus on problem solving 2; Focus on modelling 2; Cross-topic review exercise 2; 15. Vectors; 16. Introduction to kinematics; 17. Motion with constant acceleration; 18. Forces and motion; 19. Objects in contact; Focus on proof 3; Focus on problem solving 3; Focus on modelling 3; Cross-topic review exercise 3; 20. Working with data; 21. Probability; 22. Statistical hypothesis testing; Focus on proof 4; Focus on problem solving 4; Focus on modelling 4; Cross-topic review exercise 4.

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources help students with learning and revision. Written for the OCR AS/A Level Mathematics specifications for first teaching from 2017, this print Student Book covers the content for AS and the first year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Includes answers to aid independent study.Table of Contents1. Proof and mathematical communication; 2. Indices and surds; 3. Quadratic functions; 4. Polynomials; 5. Using graphs; 6. Coordinate geometry; 7. Logarithms; 8. Exponential models; 9. Binomial expansion; Focus on proof 1; Focus on problem solving 1; Focus on modelling 1; Cross-topic review exercise 1; 10. Trigonometric functions and equations; 11. Triangle geometry; 12. Vectors; 13. Differentiation; 14. Applications of differentiation; 15. Integration; Focus on proof 2; Focus on problem solving 2; Focus on modelling 2; Cross-topic review exercise 2; 16. Working with data; 17. Probability; 18. Statistical hypothesis testing; Focus on proof 3; Focus on problem solving 3; Focus on modelling 3; Cross-topic review exercise 3; 19. Introduction to kinematics; 20. Motion with constant acceleration; 21. Force and motion; 22. Objects in contact; Focus on proof 4; Focus on problem solving 4; Focus on modelling 4; Cross-topic review exercise 4.

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Book SynopsisPlease note that this Floris Books edition has been revised for UK and European notation, language and metric systems.From the early peoples who marvelled at the geometry of nature -- the beehive and bird's nest -- to ancient civilisations who questioned beautiful geometric forms and asked 'why?', the story of geometry spans thousands of years. Using only three simple tools -- the string, the straight-edge and the shadow -- human beings revealed the basic principles and constructions of elementary geometry. Weaving history and legend, this fascinating book reconstructs the discoveries of mathematics's most famous figures. Through illustrations and diagrams, readers are able to follow the reasoning that lead to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, or the construction of the five regular solids.This insightful and engaging book makes geometry accessible to everyone. Readers will be fascinated with how the knowledge and wisdom of so many cultures helped shape our civilisation today.String, Straight-edge and Shadow is also a useful and inspiring book for those teaching geometry in Steiner-Waldorf classrooms.Trade Review'Shows us what we don't realise we know, what civilisations before us learnt and passed down to us. It brings an awe and magic back to our learning… Those that advanced knowledge of geometry had a grounded and practical understanding of where it came from. This book helps us to do that.'-- The Smart Happy Project'This was an enjoyable read for the everyday person of curious mind.' - Amazon.com'Fantastic, accurate, readable, teachable and Classical.' -- Amazon.com'The well constructed narrative brings these people and their excitement over these discoveries to life. I learned about the patterns in math from a new perspective and it made me wonder why math is always taught in the abstract format. These people understood it in a completely different way and I would think that some people would learn it better if it were explained this way.' -- Goodreads'This gem is about ancient Geometry that has definite application today. Knowing the stories behind many great discoveries make them so much more interesting and really helps math to come alive.' -- Goodreads'Whether you are learning geometry for the first time, teaching it to students at home or in the classroom, or are parents helping your children through their first geometry course, this is a must-read for everyone! You will be fascinated with the graphic illustrations and written depiction of how the knowledge and wisdom of so many cultures helped shape our civilization today.' -- Waldorf Books‘String, Straight-edge and Shadow (is) an interesting and informative book and its numerous diagrams and illustrations are part of its appeal. Anyone interested in learning how discoveries made thousands of years ago still underpin much of our modern day science and mathematics will find this a useful and engaging read.’-- New View

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Book SynopsisExam Board: AQALevel: GCSE Grade 9-1 HigherSubject: MathsSuitable for the 2024 examsComplete coverage of the GCSE grade 9-1 courseRevision that Sticks! Collins AQA GCSE 9-1 Maths Higher Revision Guide uses a revision method that really works: repeated practice throughout.This revision guide contains clear and concise revision notes for every topic covered in the curriculum, plus five practice opportunities to ensure the best results.Includes:quick tests to check understandingend-of-topic practice questionstopic review questions later in the bookmixed practice questions at the end of the bookfree Q&A flashcards to download onlinean ebook version of the revision guide

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Book SynopsisAn engaging, accessible introduction into how numbers work and why we shouldn't be afraid of them, frommaths expertRachel Riley.Do you know your fractions from your percentages? Your adjacent to your hypotenuse? And who really knows how to do long division, anyway?Puzzled already? Don't blame youBut fret not! You won't be At Sixes and Sevens for long. In this brilliant, well-rounded guide, Countdown''s Rachel Riley will take you back to the very basics, allow you to revisit what you learnt at school (and may have promptly forgotten, *ahem*), build your understanding of maths from the get-go and provide you with the essential toolkit to gain confidence in your numerical abilities.Discover how to divide and conquer, make your decimal debut, become a pythagoras professional and so much more with these easy-to-learn tips and tricks. Packed full of working examples, fool-proof methods, quirky trivia and brainteasers to try from puzzle-pro Dr Gareth Moore, this book is an absolute must-read for anyone and everyone who ever thought maths was above' them. Because the truth is: you can do it. What's more, it can be pretty fun too!

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Book Synopsis“In Gonick’s work, clever design and illustration make complicated ideas or insights strikingly clear.”—New York Times Book ReviewLarry Gonick, master cartoonist, former Harvard instructor, and creator of the New York Times bestselling, Harvey Award-winning Cartoon Guide series now does for calculus what he previously did for science and history: making a complex subject comprehensible, fascinating, and fun through witty text and light-hearted graphics. Gonick’s The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere.Trade Review"How do you humanize calculus and bring its equations and concepts to life? Larry Gonick's clever and delightful answer is to have characters talking, commenting, and joking-all while rigorously teaching equations and concepts and indicating calculus's utility. It's a remarkable accomplishment-and a lot of fun." -- Lisa Randall, Professor of Physics, Harvard University, and author of Knocking on Heaven's Door Gonick is to graphical expositions of advanced materials as Newton or Leibniz is to calculus. The difference is that Gonick has no rival. -- Xiao-Li Meng, Whipple V. N. Jones Professor of Statistics and Department Chair, Harvard University Larry Gonick's sparkling and inventive drawings make a vivid picture out of every one of the hundreds of formulas that underlie Calculus. Even the jokers in the back row will ace the course with this book. -- David Mumford, Professor emeritus of Applied Mathematics at Brown University and recipient of the National Medal of Science I always thought that there are no magic tricks that use calculus. Larry Gonick proves me wrong. His book is correct, clear and interesting. It is filled with magical insights into this most beautiful subject. -- Persi Diaconis, Professor of Mathematics, Stanford It has no mean derivative results about the only derivatives that matter... A spunky tool-toting heroine called Delta Wye seems the perfect role model for our next generation. -- Susan Holmes, Professor of Statistics, Stanford A creative take on an old, and for many, tough subject...Gonick's cartoons and intelligent humor make it a fun read. -- Amy Langville, Recipient of the Distinguished Researcher Award at College of Charleston and South Carolina Faculty of the Year

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Book SynopsisThe international bestseller - a whip-smart, entertaining exploration of the geometry that underlies our world, from the author of How Not to Be WrongHow should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play chess? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? The answers to all these questions can be found in geometry.If you''re like most people, geometry is a dimly-remembered exercise, handed down from the ancients, that you gladly left behind in school. It seemed to be a tortuous way of proving some fact about triangles that was obvious to you in the first place. That''s not geometry. OK, it is geometry, but only a tiny part, that has as much to do with the modern, fast-moving discipline as conjugating a verb has to do with a great novel.In Shape, SundTrade ReviewThis mind-bending book will change how you see the world (Five stars) -- Simon Ings * Telegraph *Shape is a triumph of mathematical exposition, exposing profound truths - from the nature of distance to the predictability of randomness - as well as profound mistakes - from historical misattributions to Supreme Court justice hardheadedness - with eloquence and hilarious wit. Ellenberg's evident affection for both his subject and his reader makes us feel like the lucky ones who get to hear him hold forth in an intimate setting about his favorite subject, mathematics -- Cathy O'NeilEllenberg's skill as a storyteller, combined with a natural ability to spot otherwise obscure connections, enables him to capitalize on geometry as math's gateway drug... A deeply enjoyable and insightful book -- Matt Parker * New York Times *Ellenberg, in both his arguments and his enthusiasm, is persuasive -- Michael Prodger * New Statesman *Serious mathematics at its intriguing, transporting best . . . [A] humorous, anecdotally rich dive into numerous mathematical theories * Kirkus *Unreasonably entertaining... reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning -- Parul Sehgal * New York Times *Droopy cheese and the curve of the Earth, the everyday and the cosmic, are beautifully interwoven in the mathematician Jordan Ellenberg's new book Shape -- Derek Thompson * Atlantic *Almost anyone is likely to enjoy Ellenberg's prose, and mind * Harvard Magazine *

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Book SynopsisFeaturing a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: applications and interpretation HL syllabus, for first teaching in September 2019. Each Enhanced Online Course Book Pack is made up of one full-colour, print textbook and one online textbook - packed full of investigations, exercises, worksheets, worked solutions and answers, plus assessment preparation support.

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Book SynopsisFeaturing a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: analysis and approaches HL syllabus, for first teaching in September 2019. Each Enhanced Online Course Book Pack is made up of one full-colour, print textbook and one online textbook - packed full of investigations, exercises, worksheets, worked solutions and answers, plus assessment preparation support.

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Book SynopsisGottfried Wilhelm Leibniz (1646-1716) was a man of extraordinary intellectual creativity who lived an exceptionally rich and varied intellectual life in troubled times. More than anything else, he was a man who wanted to improve the life of his fellow human beings through the advancement of all the sciences and the establishment of a stable and just political order. In this Very Short Introduction Maria Rosa Antognazza outlines the central features of Leibniz''s philosophy in the context of his overarching intellectual vision and aspirations. Against the backdrop of Leibniz''s encompassing scientific ambitions, she introduces the fundamental principles of Leibniz''s thought, as well as his theory of truth and theory of knowledge. Exploring Leibniz''s contributions to logic, mathematics, physics, and metaphysics, she considers how his theories sat alongside his concerns with politics, diplomacy, and a broad range of practical reforms: juridical, economic, administrative, technological, medical, and ecclesiastical. Discussing Leinbniz''s theories of possible worlds, she concludes by looking at what is ultimately real in this actual world that we experience, the good and evil there is in it, and Leibniz''s response to the problem of evil through his theodicy. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsCONCLUSION; REFERENCES; FURTHER READING; INDEX

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Book SynopsisVery Short Introductions: Brilliant, sharp, inspiringThe 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn''t until the 18th and 19th centuries that mathematicians--especially Bolzano, Cauchy, and Weierstrass--began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis.This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsAcknowledgements 1: Taming Infinity 2: All change... 3: Should I believe my computer? 4: Dimensions aplenty 5: I'll name that tune in... 6: Putting the i in analysis 7: But there's more... Appendix Historical timeline References Further Reading Index

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Book SynopsisThis book introduces physics to a first year undergraduate in the language of mathematics. As such it aims to give a mathematical foundation to the physics taught pre-university, as well as extending it to the skills and disciplines approached during a first degree course in physical science or engineering. It bridges two gaps in modern education - between the level of difficulty in pre-university study and undergraduate study, and between mathematics and physics. Many of the concepts are revised or introduced in the course of ''workshop'' questions which are an integral part of the text. Fully explained solutions to these workshops are given as a substantial appendix to the book. The student will be enabled to study classical mechanics in terms of vector calculus, fields in terms of line and surface integrals, oscillations and waves in terms of complex exponentials and so on. As far as we are aware, this book is unique in its aim, its content, and its approach.Trade ReviewThis book is highly recommended for first-year undergraduate students. * Contemporary Physics *The gap in knowledge and understanding between A-level exit and University entrance in Physics and Engineering has long been a concern to both school teachers and University tutors. 'The Language of Physics' is thus warmly to be welcomed, filling as it does the growing divide between general A-level texts and specialised undergraduate books. 6th formers wanting to prepare for University entrance in the applied mathematical and physical sciences should read 'The Language of Physics' to open their eyes to the sheer beauty of their subject, presented here in a straightforward and elegant manner. Confused first year science undergraduates will also find it invaluable in piecing together a wide range of seemingly disparate topics in a stylish and concise way. * Stephen Payne, University of Oxford *This is an excellently written textbook that explains very clearly how to describe physical processes in terms of mathematics. This is an essential skill that undergraduates need to acquire and there are many illuminating problems given on mechanics, fields, rotation, oscillations and waves, circuits, and thermal physics. While it is principally aimed at first year undergraduates in physics or engineering, it would also be a very useful preparatory textbook for students about to start at university. It is highly recommended. * Nick Jelley, University of Oxford *Table of Contents1. Linear Mechanics ; 2. Fields ; 3. Rotation ; 4. Oscillations & Waves ; 5. Circuits ; 6. Thermal Physics ; 7. Miscellany ; 8. Summary of Equations ; Workshop Solutions

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Book SynopsisDo high-speed, complicated arithmetic in your head using the Trachtenberg Speed System.Ever find yourself struggling to check a bill or a payslip? With The Trachtenberg Speed System you can. Described as the 'shorthand of mathematics', the Trachtenberg system only requires the ability to count from one to eleven. Using a series of simplified keys it allows anyone to master calculations, giving greater speed, ease in handling numbers and increased accuracy.Jakow Trachtenberg believed that everyone is born with phenomenal abilities to calculate. He devised a set of rules that allows every child to make multiplication, division, addition, subtraction and square-root calculations with unerring accuracy and at remarkable speed. It is the perfect way to gain confidence with numbers.Trade ReviewTeachers should read this book ... which could well revolutionise the teaching of mathematics in the future. * Teachers' World *Even in the age of the calculator this new ... edition is well worth reading and the challenge of teaching the method to children who find arithmetic difficult is one which an adventurous teacher might well find rewarding. -- John Dunford * The Mathematical Gazette *

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Book SynopsisUse TRIZ to unlock creative problem solving Are you new to TRIZ and looking for an easy-to-follow guide on how you can use it to enhance your company's creativity, innovation and problem-solving abilities? Look no further! Written in plain English and packed with tons of accessible and easy-to-follow instruction, TRIZ For Dummies shows you how to use this powerful toolkit to discover all the ways of solving a problem, uncover new concepts and identify previously unseen routes for new product development. An international science that relies on the study of patterns in problems and solutions, TRIZ offers a powerful problem-solving and creativity-generating solution for companies looking to promote innovation, especially in the face of having to do more with less. Inside, you'll find out how to successfully apply this problem-solving toolkit to benefit from the experience of the whole worldnot just the spontaneous and occasional creativity of individuals or groups of engineers with an orTrade ReviewThe book is entertaining and engaging, and reading it may be the first step to changing the way you approach problems forever (Professional Engineering, May 2016)Table of ContentsIntroduction 1 About This Book 2 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part I: Getting Started with TRIZ 5 Chapter 1: Going from Zero to TRIZ 7 Getting to Know TRIZ 8 Increasing Ideality 8 Uncovering patterns in human creativity 10 Learning to think in the abstract 11 Connecting conceptual thinking with your knowledge and experience 13 Going beyond your own experience 14 Thinking functionally 15 Starting Your TRIZ Journey 16 Getting a handle on the TRIZ tools 16 Reapplying proven knowledge to deliver innovative new solutions 17 Modelling problems conceptually 19 Supercharging your thinking 20 Mastering TRIZ 22 Putting the tools together in the TRIZ problem‐solving process 22 Innovating with others by sharing solutions 24 Cultivating the motivation for innovation 24 Being humble and looking like a genius 26 Chapter 2: Understanding the Fundamental TRIZ Philosophy 27 Thinking TRIZ 28 Picturing TRIZ’s beginnings 28 Standing on the shoulders of giants – or reinventing the wheel? 29 Understanding the TRIZ Philosophy 30 Learning to think conceptually 30 Reapplying proven knowledge to solve problems 32 Getting everything you want without changing anything 34 Developing confidence 35 Being Systematic and Creative 36 Using TRIZ processes for understanding and solving problems 36 Thinking freely 37 Challenging assumptions 37 Part II: Opening Your TRIZ Toolbox 39 Chapter 3: Solving Contradictions with the 40 Inventive Principles 41 Uncovering and Understanding Unresolved Conflicts 41 Spotting contradictions and seeing how they’re resolved 42 Understanding the two types of contradiction 44 Reapplying other people’s genius solutions 44 Solving Technical Contradictions 46 Improving imperfect solutions with a little help from your friends 48 Using the Contradiction Matrix 48 Getting to Grips with Physical Contradictions 53 Resolving Physical Contradictions 54 Clever Tricks to Outsmart Contradictions: Using the 40 Inventive Principles 56 Applying the 40 Inventive Principles to real problems 56 Digging for buried treasure in the right places 58 Chapter 4: Applying the Trends of Technical Evolution 61 Looking More Closely at the Trends 62 Discovering the 8 Trends 65 Charting future product directions 69 Achieving a system’s ultimate destiny 73 Applying the Trends 74 Listening to the voice of the product 75 Using the Trends to develop a next‐generation system 76 Moving systems forward and knowing when to go back 78 Applying the Trends More Generally 79 Increasing Ideality 79 Transition to the Super‐System 79 Increasing System Coordination 79 S‐Curves 80 Using the Trends to Create Strong Patents 80 Strengthening and ring‐fencing your own patents 80 Leapfrogging competitors’ technology 81 Chapter 5: Improving Ideality by Using Resources 83 Understanding the Ideality Equation: How TRIZ Defines Value 84 Defining benefits 84 Defining costs 86 Defining downsides 86 Putting the Ideality Equation together 87 Understanding the Links Between Benefits, Functions and Solutions 89 Thinking Resourcefully 90 Understanding resources and where to find them 91 Learning how to hunt for resources 92 Getting what you want using what you have 95 Embedding resource thinking into everyday life 96 Chapter 6: Using the TRIZ Effects Database 99 Thinking Innovatively with the Prism of TRIZ 100 Taking out unnecessary detail 100 Reapplying clever solutions in new and exciting ways 102 Making new connections between existing technologies 104 Using the Database of Scientific Effects 105 Learning to look for what you want 105 Applying the Effects Database to solve problems 106 Strategies for analogous searching 109 Inventing with TRIZ 110 Matching needs and systems 110 Uncovering unmet needs 113 Applying existing technologies to create novel inventions 114 Part III: Thinking Like a Genius 117 Chapter 7: Breaking Psychological Inertia with the TRIZ Creativity Tools 119 Recognising Psychological Inertia 120 Appreciating the Benefits of Psychological Inertia 122 Beating Psychological Inertia 124 Why bad solutions are a good idea 124 Using the 13 TRIZ tools for creative thinking 125 Understanding and Solving Problems Using Smart Little People 127 Modelling problems and solutions conceptually 128 Breaking out of practical thinking 129 Bringing wacky ideas back to reality 130 Stretching Your Thinking with Size–Time–Cost 132 Restructuring your view of what’s possible 133 Finding inventive solutions 134 Chapter 8: Thinking in Time and Scale 137 Stretching Your Thinking in Time and Scale 137 Remembering to stretch yourself 140 Considering whether 9 boxes are really enough 141 Thinking big and thinking small 142 Looking at your situation with new eyes 143 Understanding Problems in Time and Scale 144 Recognising the importance of the big picture 145 Mapping causes of problems and hazards 145 Thinking strategically: Predicting future opportunities and threats 145 Finding Novel Solutions in Time and Scale 148 Locating inventive times and places to solve a problem 148 Covering the waterfront by finding all possible solutions 149 Learning to Think in Time and Scale 151 Chapter 9: Living in Utopia (then Coming Back to Reality) 153 Defining the Ideal Outcome 153 Locating your North Star: Setting your problem‐solving direction 154 Outlining benefits as a team 154 Striving for perfection with the Ideal Outcome, Prime Benefit and Ultimate Goal 156 Setting your constraints 158 Considering stakeholders: Don’t be afraid to ask your customers 159 Taking a Step Towards Reality with Ideal Systems 160 Thinking of what you want and then getting it 160 Using 9 Boxes to define your Ideal System 161 Using divergent thinking with Ideal Functions 162 Making Sensible Decisions by Considering All Benefits, Costs and Harms 163 From perfection to reality: Defining the Ideality you want 164 Learning to compare apples and pears 165 Thinking about the unthinkable: Managing risk 166 Chapter 10: Problem Solving and Being Creative with Others 167 Going for What You Really Want 167 Thinking in Extremes 170 Challenging constraints: Real or imagined? 170 Restructuring problems and solutions 173 Thinking crazily (while being practical) 173 Being Persistent in the Face of Failure 175 Improving imperfect solutions 175 Fixing things when something’s gone wrong 177 Knowing when to stop 178 Sharing and Developing Ideas with Other People 178 Recognising why bad solutions are a good idea 179 Seeing the flaws in your own solutions 180 Learning to love other people’s solutions 181 Capturing, sharing and combining solutions 181 Creating a climate for innovation 182 Part IV: Understanding, Defining and Solving Difficult Problems with TRIZ 185 Chapter 11: Applying the TRIZ Problem‐Solving Process 187 Logically and Systematically Solving Problems 187 Trusting the process (and yourself) 188 Making big leaps by taking small steps 189 Developing your own problem‐solving map 189 Climbing the Problem‐Solving Steps 191 Understanding the overall process 191 Sharpening the axe 193 Knowing your needs and scoping the situation 195 Defining your problem correctly 195 Generating Solutions 196 Expecting the unexpected 196 Applying the TRIZ solution tools 197 Ranking and Developing Solutions 198 Developing solutions further 198 Ranking solutions by Ideality 199 Converging by concept 200 Solving Difficult Problems Effectively in a Team 201 Gaining team understanding and consensus 201 Converging and diverging 201 Thinking fast and thinking slow 202 Putting solutions into practice 203 Chapter 12: Getting to Grips with Your Problems with Function Analysis 205 Making Complex Problems Simple 205 Understanding the building blocks of Function Analysis 207 Defining interactions: The good, the bad and the ugly 208 Charting all parts of your system and beyond 210 Building a Function Analysis Diagram 212 Completing a Function Analysis 212 Listing your components and their interactions 212 Drawing a Function Map 213 Listing, prioritising and solving problems 213 Uncovering Conflicts: Putting Contradictions in Context 214 Understanding How Everything Fits Together 215 Using Function Analysis 216 Modelling difficult problems 217 Gaining the confidence required to change things 218 Achieving clarity in complex situations 220 Communicating effectively 220 Chapter 13: Solving Problems using the TRIZ Standard Solutions 223 Defining a Subject–action–Object 223 Categorising Problems 225 Dealing with Harmful Actions 226 Improving Insufficient Actions 228 Measuring and Detecting 228 Applying the Standard Solutions 231 Developing a well‐formulated problem 231 Solving problems outlined in a Function Analysis 232 Generating innovative solutions 233 Tackling a real problem 235 Improving a solution 237 Chapter 14: Trimming for Elegant, Low‐Cost Solutions 241 Making Things Better and Cheaper 241 Improving systems by removing stuff 242 Clever cost‐cutting: Doing more with less 245 Using resources wisely 247 Creating Elegant Solutions 248 Applying the Trimming Rules 248 Following the process and going off‐piste 252 Trimming to Infinity and Beyond 252 Trimming to Create Strong Intellectual Property 254 Getting round someone else’s patent 254 Developing your own patent further 255 Part V: The Part of Tens 257 Chapter 15: Ten Pitfalls to Avoid 259 Thinking TRIZ Doesn’t Apply to You 259 Waiting for the ‘Right’ Problem 260 Starting Too Big 260 Tackling Problems for Which You Can’t Implement Solutions 261 Tackling Problems without Involving the Problem Owner 261 Trying to Solve Problems When You Don’t Understand the Issue or the Technology 262 Trying to Solve Problems When You Lack Crucial Knowledge 262 Working on a Problem That’s Already Been Solved 263 Undertaking TRIZ by Stealth 263 Giving Up Too Soon 264 Chapter 16: Ten Tips for Getting Started with TRIZ 265 Learn It 265 Use It 266 Start Small 266 Attend a Workshop 266 Think and Talk TRIZ 267 Find a Friend 267 Fail Safely 268 Be Bold 268 Fail Better 269 Reflect 269 Part VI: Appendixes 271 Appendix A: The 40 Inventive Principles 273 Inventive Principle 1: Segmentation 273 Inventive Principle 2: Taking Out 274 Inventive Principle 3: Local Quality 274 Inventive Principle 4: Asymmetry 275 Inventive Principle 5: Merging 275 Inventive Principle 6: Multi‐Function 275 Inventive Principle 7: Nested Doll 276 Inventive Principle 8: Counterweight 276 Inventive Principle 9: Prior Counteraction 276 Inventive Principle 10: Prior Action 277 Inventive Principle 11: Cushion in Advance 277 Inventive Principle 12: Equal Potential 277 Inventive Principle 13: The Other Way Round 278 Inventive Principle 14: Spheres and Curves 278 Inventive Principle 15: Dynamism 279 Inventive Principle 16: Partial or Excessive Action 279 Inventive Principle 17: Another Dimension 279 Inventive Principle 18: Mechanical Vibration 280 Inventive Principle 19: Periodic Action 280 Inventive Principle 20: Continuous Useful Action 281 Inventive Principle 21: Rushing Through 281 Inventive Principle 22: Blessing in Disguise 281 Inventive Principle 23: Feedback 282 Inventive Principle 24: Intermediary 282 Inventive Principle 25: Self‐service 283 Inventive Principle 26: Copying 283 Inventive Principle 27: Cheap, Short‐Living Objects 284 Inventive Principle 28: Replace Mechanical System 284 Inventive Principle 29: Pneumatics and Hydraulics 285 Inventive Principle 30: Flexible Membranes and Thin Films 285 Inventive Principle 31: Porous Materials 285 Inventive Principle 32: Colour Change 286 Inventive Principle 33: Uniform Material 286 Inventive Principle 34: Discarding and Recovering 287 Inventive Principle 35: Parameter Change 287 Inventive Principle 36: Phase Changes 288 Inventive Principle 37: Thermal Expansion 289 Inventive Principle 38: Boosted Interactions 289 Inventive Principle 39: Inert Atmosphere 290 Inventive Principle 40: Composite Structures 290 Appendix B: The Contradiction Matrix 291 Appendix C: The 39 Parameters of the Contradiction Matrix 293 Appendix D: The Separation Principles 299 Appendix E: The Oxford TRIZ Standard Solutions 301 Solutions for Dealing with Harms 302 H1 Trim out the harm 302 H2 Block the harm 303 H3 Turn the harm into good 304 H4 Correct the harm 304 Solutions for Improving Insufficiency 305 i1 Add something to the subject or object 305 i2 Evolve the subject and object 306 i.a Improve the action 307 Solutions for Detection and Measurement 308 M1 Indirect methods 309 M2 Add something 309 M3 Enhance measurement with fields 309 M4 Use additives with fields 310 M5 Evolve the measurement system 310 Index 311

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Book SynopsisStudy smarter and stay on top of your calculus course with the bestselling Schaumâs Outlineânow with the NEW Schaumâs app and website! Schaumâs Outline of Calculus, Seventh Edition is the go-to study guide for hundreds of thousands of high school and college students enrolled in calculus coursesâincluding Calculus, Calculus II, Calculus III, AP Calculus and Precalculus. With an outline format that facilitates quick and easy review, Schaumâs Outline of Calculus, Seventh Edition helps you understand basic concepts and get the extra practice you need to excel in these courses. Chapters include Linear Coordinate Systems, Functions, Limits, Rules for Differentiating Functions, Law of the Mean, Inverse Trigonometric Functions, The Definite Integral, Space Vectors, Directional Derivatives, and much, much more.Features: NEW to this edition: the new Schaumâs app and website! 1,105 problems solved step by step<Table of ContentsPrefaceChapter 1 Linear Coordinate Systems. Absolute Value. Inequalities. Linear Coordinate System Finite Intervals Infinite Intervals Inequalities Solved Problems Supplementary ProblemsChapter 2 Rectangular Coordinate Systems Coordinate Axes Coordinates Quadrants The Distance Formula The Midpoint Formulas Proofs of Geometric Theorems Solved Problems Supplementary ProblemsChapter 3 Lines The Steepness of a Line The Sign of the Slope Slope and Steepness Equations of Lines A Point–Slope Equation Slope–Intercept Equation Parallel Lines Perpendicular Lines Solved Problems Supplementary ProblemsChapter 4 Circles Equations of Circles The Standard Equation of a Circle Solved Problems Supplementary ProblemsChapter 5 Equations and Their Graphs The Graph of an Equation Parabolas Ellipses Hyperbolas Conic Sections Solved Problems Supplementary ProblemsChapter 6 Functions Solved Problems Supplementary ProblemsChapter 7 Limits Limit of a Function Right and Left Limits Theorems on Limits Infinity Solved Problems Supplementary ProblemsChapter 8 Continuity Continuous Function Solved Problems Supplementary ProblemsChapter 9 The Derivative Delta Notation The Derivative Notation for Derivatives Differentiability Solved Problems Supplementary ProblemsChapter 10 Rules for Differentiating Functions Differentiation Composite Functions. The Chain Rule. Chain Rule Alternative Formulation of the Chain Rule Inverse Functions Higher Derivatives Solved Problems Supplementary ProblemsChapter 11 Implicit Differentiation Implicit Functions Derivatives of Higher Order Solved Problems Supplementary ProblemsChapter 12 Tangent and Normal Lines The Angles of Intersection Solved Problems Supplementary ProblemsChapter 13 Law of the Mean. Increasing and Decreasing Functions. Relative Maximum and Minimum Increasing and Decreasing Functions Solved Problems Supplementary ProblemsChapter 14 Maximum and Minimum Values Critical Numbers Second Derivative Test for Relative Extrema First Derivative Test Absolute Maximum and Minimum Tabular Method for Finding the Absolute Maximum and Minimum Solved Problems Supplementary ProblemsChapter 15 Curve Sketching. Concavity. Symmetry. Concavity Points of Inflection Vertical Asymptotes Horizontal Asymptotes Symmetry Inverse Functions and Symmetry Even and Odd Functions Hints for Sketching the Graph G of y = f (x) Solved Problems Supplementary ProblemsChapter 16 Review of Trigonometry Angle Measure Directed Angles Sine and Cosine Functions Solved Problems Supplementary ProblemsChapter 17 Differentiation of Trigonometric Functions Continuity of cos x and sin x Graph of sin x Graph of cos x Other Trigonometric Functions Derivatives Other Relationships Graph of y = tan x Graph of y = sec x Angles Between Curves Solved Problems Supplementary ProblemsChapter 18 Inverse Trigonometric Functions The Derivative of sin−1 x The Inverse Cosine Function The Inverse Tangent Function Solved Problems Supplementary ProblemsChapter 19 Rectilinear and Circular Motion Rectilinear Motion Motion Under the Influence of Gravity Circular Motion Solved Problems Supplementary ProblemsChapter 20 Related Rates Solved Problems Supplementary ProblemsChapter 21 Differentials. Newton’s Method. The Differential Definition Newton’s Method Solved Problems Supplementary ProblemsChapter 22 Antiderivatives Laws for Antiderivatives Solved Problems Supplementary ProblemsChapter 23 The Definite Integral. Area Under a Curve. Sigma Notation Area Under a Curve Properties of the Definite Integral Solved Problems Supplementary ProblemsChapter 24 The Fundamental Theorem of Calculus Mean Value Theorem for Integrals Average Value of a Function on a Closed Interval Fundamental Theorem of Calculus Change of Variable in a Definite Integral Solved Problems Supplementary ProblemsChapter 25 The Natural Logarithm The Natural Logarithm Definition Properties of the Natural Logarithm Solved Problems Supplementary ProblemsChapter 26 Exponential and Logarithmic Functions Definition Properties of ex The General Exponential Function General Logarithmic Functions Solved Problems Supplementary ProblemsChapter 27 L’Hôpital’s Rule L’Hôpital’s Rule Indeterminate Type 0 · ∞ Indeterminate Type ∞ − ∞ Indeterminate Types 00, ∞0, and 1∞ Solved Problems Supplementary ProblemsChapter 28 Exponential Growth and Decay Half-Life Solved Problems Supplementary ProblemsChapter 29 Applications of Integration I: Area and Arc Length Area Between a Curve and the Y-Axis Areas Between Curves Arc Length Solved Problems Supplementary ProblemsChapter 30 Applications of Integration II: Volume Disk Formula Washer Method Cylindrical Shell Method Difference of Shells Formula Cross-Section Formula (Slicing Formula) Solved Problems Supplementary ProblemsChapter 31 Techniques of Integration I: Integration by Parts Solved Problems Supplementary ProblemsChapter 32 Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions Trigonometric Integrands Trigonometric Substitutions Solved Problems Supplementary ProblemsChapter 33 Techniques of Integration III: Integration by Partial Fractions Method of Partial Fractions Solved Problems Supplementary ProblemsChapter 34 Techniques of Integration IV: Miscellaneous Substitutions Solved Problems Supplementary ProblemsChapter 35 Improper Integrals Infinite Limits of Integration Discontinuities of the Integrand Solved Problems Supplementary ProblemsChapter 36 Applications of Integration III: Area of a Surface of Revolution Solved Problems Supplementary ProblemsChapter 37 Parametric Representation of Curves Parametric Equations Arc Length for a Parametric Curve Solved Problems Supplementary ProblemsChapter 38 Curvature Derivative of Arc Length Curvature The Radius of Curvature The Circle of Curvature The Center of Curvature The Evolute Solved Problems Supplementary ProblemsChapter 39 Plane Vectors Scalars and Vectors Sum and Difference of Two Vectors Components of a Vector Scalar Product (or Dot Product) Scalar and Vector Projections Differentiation of Vector Functions Solved Problems Supplementary ProblemsChapter 40 Curvilinear Motion Velocity in Curvilinear Motion Acceleration in Curvilinear Motion Tangential and Normal Components of Acceleration Solved Problems Supplementary ProblemsChapter 41 Polar Coordinates Polar and Rectangular Coordinates Some Typical Polar Curves Angle of Inclination Points of Intersection Angle of Intersection The Derivative of the Arc Length Curvature Solved Problems Supplementary ProblemsChapter 42 Infinite Sequences Infinite Sequences Limit of a Sequence Monotonic Sequences Solved Problems Supplementary ProblemsChapter 43 Infinite Series Geometric Series Solved Problems Supplementary ProblemsChapter 44 Series with Positive Terms. The Integral Test. Comparison Tests. Series of Positive Terms Solved Problems Supplementary ProblemsChapter 45 Alternating Series. Absolute and Conditional Convergence. The Ratio Test. Alternating Series Definition Solved Problems Supplementary ProblemsChapter 46 Power Series Power Series Uniform Convergence Solved Problems Supplementary ProblemsChapter 47 Taylor and Maclaurin Series. Taylor’s Formula with Remainder. Taylor and Maclaurin Series Applications of Taylor’s Formula with Remainder Solved Problems Supplementary ProblemsChapter 48 Partial Derivatives Functions of Several Variables Limits Continuity Partial Derivatives Partial Derivatives of Higher Order Solved Problems Supplementary ProblemsChapter 49 Total Differential. Differentiability. Chain Rules. Total Differential Differentiability Chain Rules Chain Rule (2 → 1) Chain Rule (2 → 2) Implicit Differentiation Solved Problems Supplementary ProblemsChapter 50 Space Vectors Vectors in Space Direction Cosines of a Vector Determinants Vector Perpendicular to Two Vectors Vector Product of Two Vectors Triple Scalar Product The Straight Line The Plane Solved Problems Supplem entary ProblemsChapter 51 Surfaces and Curves in Space Planes Spheres Cylindrical Surfaces Ellipsoid Elliptic Paraboloid Elliptic Cone Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Tangent Line and Normal Plane to a Space Curve Tangent Plane and Normal Line to a Surface Surface of Revolution Solved Problems Supplementary ProblemsChapter 52 Directional Derivatives. Maximum and Minimum Values. Directional Derivatives Relative Maximum and Minimum Values Absolute Maximum and Minimum Values Solved Problems Supplementary ProblemsChapter 53 Vector Differentiation and Integration Vector Differentiation Space Curves Surfaces The Operation ∇ Divergence and Curl Integration Line Integrals Solved Problems Supplementary ProblemsChapter 54 Double and Iterated Integrals The Double Integral The Iterated Integral Solved Problems Supplementary ProblemsChapter 55 Centroids and Moments of Inertia of Plane Areas Plane Area by Double Integration Centroids Moments of Inertia Solved Problems Supplementary ProblemsChapter 56 Double Integration Applied to Volume Under a Surface and the Area of a Curved Surface Solved Problems Supplementary ProblemsChapter 57 Triple Integrals Cylindrical and Spherical Coordinates The Triple Integral Evaluation of Triple Integrals Centroids and Moments of Inertia Solved Problems Supplementary ProblemsChapter 58 Masses of Variable Density Solved Problems Supplementary ProblemsChapter 59 Differential Equations of First and Second Order Separable Differential Equations Homogeneous Functions Integrating Factors Second-Order Equations Solved Problems Supplementary ProblemsAppendix A Trigonometric FormulasAppendix B Geometric FormulasIndex

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Book SynopsisEndorsed by Cambridge Assessment International Education to provide full support for Paper 4 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the Boost eBook.**To have full access to the eBook and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.com/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. This book covers the syllabus content for Mechanics, including forces and equilibrium, kinematics of motion in a straight line, momentum, Newton's laws of motion, and energy, work and power.

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Book SynopsisAchieve the best grades in 2025 or 2026 with this unbeatable course book from CGP!This in-depth CGP Student Book for AS-Level (and Year 1 of the full A-Level) Maths covers all the Pure Maths, Statistics and Mechanics content needed to tackle the first year of the AQA Maths course. It's packed with no-nonsense theory and plenty of step-by-step examples - plus helpful tips to make the trickier bits easier to handle. We've also included a wide range of practice questions with fully worked answers. And to cover everything the examiners could ask for, there are modelling and problem solving questions and examples throughout the book. If that wasn't enough, this book also comes with a free Online Edition (accessed using the unique code printed inside the front cover) that lets you read the entire book on a PC, Mac or tablet.

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Book SynopsisAchieve the best grades in 2025 and 2026 with this all-in-one book from CGP - including study notes, examples and practice questions!This superb all-in-one CGP Complete Revision & Practice guide is a perfect way to revise every topic from Year 1 & 2 of the OCR MEI A-Level Maths course. It contains essential revision notes and worked examples for every topic, plus plenty of questions to test students on what they've learned (including answers). What's more, the book comes with a free Online Edition to read on a PC, Mac or tablet. Don't miss CGP's matching A-Level Maths Exam Practice Workbook to make sure students are 100% prepared for the real exams (9781782947431).

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Book SynopsisAchieve the best grades in 2025 and 2026 with this all-in-one book from CGP - including study notes, examples and practice questions!This CGP Complete Revision & Practice book is a fantastic all-in-one guide to AS & A-Level Edexcel Further Maths. It's bursting with crystal-clear revision notes and worked examples for the Core Pure topics as well as the Further Pure 1, Further Statistics 1, Further Mechanics 1 and Decision Mathematics 1 options. There are also plenty of exam-style questions to test students on what they've learned (including step-by-step answers at the back). And to top things off, the book comes with a free Online Edition - just use the code printed inside the book to read it on a PC, Mac or tablet.

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Book SynopsisHugh Barker is a non-fiction author and editor; as the latter he has edited several successful popular maths books, including A Slice of Pi. Hugh is a keen amateur mathematician and was accepted to study maths at Cambridge University aged 16.

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Book SynopsisAt first glance, the concept of equality in maths seems unambiguous. Denoted by two parallel lines, the equals sign looks elegant, simple and entirely black and white. But between those two lines lies a grey area, a world of flexibility, creativity and innovation. And once you see this nuance, you quickly realise that sameness and difference, equality and inequality, are not nearly as immutable as they may seem. In fact, they are the opposite: a mathematical playground of choice and abstraction, leading to far greater insight than you could have dreamed. In UnEqual, Mathematician Eugenia Cheng explores the rich and rewarding world of the interplay between sameness and difference, from numbers to manifolds to category theory and beyond.

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Book SynopsisFrom Newton's Law of Gravity to the Black-Scholes model used by bankers to predict the markets, equations, are everywhere -- and they are fundamental to everyday life.Seventeen Equations that Changed the World examines seventeen ground-breaking equations that have altered the course of human history. He explores how Pythagoras's Theorem led to GPS and Satnav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrödinger's cat. Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration -- and explanation -- of life on earth.Trade ReviewHis wondrous world of worked-out maths and joined-up thinking is radical and even romantic * The Times *Interesting and authoritative * BBC Focus *

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Book SynopsisWhich famous proof did Archimedes inscribe on his tombstone? How and why do knots make perfect pentagons? Have you ever seen a proof so completely that it is just obvious? In this delicious little book, top down-under mathemagician Dr. Polster presents many of the most visually intuitive and exciting proofs from the dusty annuals of mathematical history. You can test your ability to follow the logic, leap into mathemagnosis and experience eureka-moment after eureka-moment. This is the first UK edition of this original classic from Wooden Books, highly successful in the US. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.Trade Review"The fascinating, informative Wooden Books series blends ancient wisdom and modern knowledge. The books are thin, impeccably designed, and will stimulate more thinking and subsequent 'Eureka' moments than a dozen novels laced with narrative innovation and postmodern stylings."

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Book SynopsisThe scientific research enterprise is built on a foundation of trust. Scientists trust that the results reported by others are valid. Society trusts that the results of research reflect an honest attempt by scientists to describe the world accurately and without bias. But this trust will endure only if the scientific community devotes itself to exemplifying and transmitting the values associated with ethical scientific conduct. On Being a Scientist was designed to supplement the informal lessons in ethics provided by research supervisors and mentors. The book describes the ethical foundations of scientific practices and some of the personal and professional issues that researchers encounter in their work. It applies to all forms of researchwhether in academic, industrial, or governmental settings-and to all scientific disciplines. This third edition of On Being a Scientist reflects developments since the publication of the original edition in 1989 and a second edition in 1995. A contTable of Contents1 Front Matter; 2 Introduction to the Responsible Conduct of Research; 3 Advising and Mentoring; 4 The Treatment of Data; 5 Mistakes and Negligence; 6 Research Misconduct; 7 Responding to Suspected Violations of Professional Standards; 8 Human Participants and Animal Subjects in Research; 9 Laboratory Safety in Research; 10 Sharing of Research Results; 11 Authorship and the Allocation of Credit; 12 Intellectual Property; 13 Competing Interests, Commitments, and Values; 14 The Researcher in Society; 15 Appendix: Discussion of Case Studies; 16 Additional Resources

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Book SynopsisAcross the Islamic world, illuminating Korans from Morocco to Malaysia, and adorning mosques, mausoleums and palaces, are hidden some of the most exquisite geometrical devices ever conceived by man. In this excellent little book, geometer Daud Sutton unravels the mystery of Islamic patterns, explaining where they come from, how to draw them, and hinting at the Divine messages they encode. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

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Book SynopsisPrimary Maths for Scotland Textbook 1C is the third of 3 first level textbooks. These engaging and pedagogically rigorous books are the first maths textbooks for Scotland completely aligned to the benchmarks and written specifically to support Scottish children in mastering mathematics at their own pace.Primary Maths for Scotland Textbook 1C is the third of 3 first level textbooks. The books are clear and simple with a focus on developing conceptual understanding alongside procedural fluency. They cover the entire first level mathematics Curriculum for Excellence in an easy-to-use set of textbooks which can fit in with teacher's existing planning, resources and scheme of work.- Packed with problem-solving, investigations and challenging problems- Diagnostic check lists at the start of each unit ensure that pupils possess the required pre-requisite knowledge to engage on the unit of work- Worked examples and non-examples help pupils fully understand mathematical concepts- Includes intel

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Book SynopsisThis new book from the author of ''The Music of the Primes'' combines a personal insight into the mind of a working mathematician with the story of one of the biggest adventures in mathematics: the search for symmetry.This is the story of how humankind has come to its understanding of the bizarre world of symmetry a subject of fundamental significance to the way we interpret the world around us.Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, the pyramid to the pentagon. Symmetry indicates a dynamic relationship or connection between objects, and it is all-pervasive: in chemistry and physics the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; symmetry and the breaking of symmetry are central to ideas in art, architecture and music; the mathematics of symmetry is even exploited in industry, for example to find efficiTrade Review'If you don't experience a thrill of foreboding as du Sautoy ventures into this twilit territory, nothing in maths will be for you. Even if the thought of sitting down to a quintic equation makes you want to cry, it would still be hard to resist Moonshine's cocktail of anecdote, swashbuckling potted history and haphazard self-revelation. The moments of autobiographical intimacy bring the book to life…a joy.' Daily Telegraph 'Mesmerising…articulate, fluent, funny and personable, [du Sautoy] is also absolutely passionate about mathematics, with a burning desire to make the rest of us as excited as he is about its problems, its patterns and its beauty. He captures for us with brilliant vividness the excitement of the pursuit of a solution to a difficult problem.' Lisa Jardine, Sunday Times 'A fascinating and absorbing read.' Financial Times 'A marvellous account…these exasperating people with unkempt beards, untidy clothes, impossible manners and extraordinary obsessions, become, in this narrative, ultimately enviable.' Guardian

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Book SynopsisTHE CLASSIC GUIDE, NOW FULLY REVISED AND UPDATEDWhy do we need Statistics?What do terms like ''dispersion'', ''correlation'', ''normal distribution'' and ''significance'' actually mean?How can I learn how to think statistically?This bestselling introduction is for anyone who wants to know how statistics works and the powerful ideas behind it. Teaching through words and diagrams instead of requiring you to do complex calculations, it assumes no expert knowledge and makes the subject accessible even to readers who consider themselves non-mathematical. This clear and informative ''tutorial in print'' includes questions for you to respond to in the light of what you have read so far, ensuring your developing ability to think statistically.

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Book SynopsisWhen Kurt Gödel published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, it had a profound impact on mathematical ideas and philosophical thought. Adrian Moore places the theorem in its intellectual and historical context, explaining the key concepts and misunderstandings.

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Book SynopsisThis is an advanced textbook on the subject of turbulence, and is suitable for engineers, physical scientists and applied mathematicians. The aim of the book is to bridge the gap between the elementary accounts of turbulence found in undergraduate texts, and the more rigorous monographs on the subject. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. Chapters 1 to 5 may be appropriate as background material for an advanced undergraduate or introductory postgraduate course on turbulence, while chapters 6 to 10 may be suitable as background material for an advanced postgraduate course on turbulence, or act as a reference source for professional researchers.This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the EarthTable of ContentsTHE CLASSICAL PICTURE OF TURBULENCE; FREELY-DECAYING, HOMOGENEOUS TURBULENCE; SPECIAL TOPICS

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Book SynopsisAn introduction to the Bayesian approach to statistical inference that demonstrates its superiority to orthodox frequentist statistical analysis.This book offers an introduction to the Bayesian approach to statistical inference, with a focus on nonparametric and distribution-free methods. It covers not only well-developed methods for doing Bayesian statistics but also novel tools that enable Bayesian statistical analyses for cases that previously did not have a full Bayesian solution. The book's premise is that there are fundamental problems with orthodox frequentist statistical analyses that distort the scientific process. Side-by-side comparisons of Bayesian and frequentist methods illustrate the mismatch between the needs of experimental scientists in making inferences from data and the properties of the standard tools of classical statistics.The book first covers elementary probability theory, the binomial model, the multinomial model, and methods for comparing dif

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Book SynopsisThis classic by one of the 20th century''s most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.

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Book SynopsisMental Arithmetic provides rich and varied practice to develop pupils' essential maths skills at Key Stage 2. Questions in Mental Arithmetic 6 extend beyond the primary curriculum, consolidating key topic areas, whilst also introducing more advanced concepts such as profit and loss, using spreadsheets and conducting mathematical investigations.

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Book SynopsisThis 2007 book discusses the design of reliable numerical methods to retrieve missing information in models of complex systems.Table of ContentsPreface; 1. Introduction; 2. Linear algebra; 3. Discrete-time signals and systems; 4. Random variables and signals; 5. Kalman filtering; 6. Estimation of spectra and frequency response functions; 7. Output-error parametric model estimation; 8. Prediction-error parametric model estimation; 9. Subspace model identification; 10. The system identification cycle; Notation and symbols; List of abbreviations; References; Index.

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Book SynopsisHit the geometry wall? Get up and running with this no-nonsense guide! Does the thought of geometry make you jittery? You''re not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you''ll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time. Geometry is a subject full of mathematical richness and beauty. But it''s a subject that bewilders many students because it''s so unlike the math they''ve done beforeit requires the use of deductive logic in formal proofs. If you''re having a hard time wrapping your mind around what that even means, you''ve come to the right place! Inside, you''ll find out how a proof''s chain of logic works and even discover some secrets for getting past rough spots along the way. You don''t have to beTable of ContentsIntroduction 1 Part 1: Getting Started with Geometry Basics 5 Chapter 1: Introducing Geometry 7 Chapter 2: Building Your Geometric Foundation 17 Chapter 3: Sizing Up Segments and Analyzing Angles 31 Part 2: Introducing Proofs 43 Chapter 4: Prelude to Proofs 45 Chapter 5: Your Starter Kit of Easy Theorems and Short Proofs 55 Chapter 6: The Ultimate Guide to Tackling a Longer Proof 75 Part 3: Triangles: Polygons of the Three-Sided Variety 87 Chapter 7: Grasping Triangle Fundamentals 89 Chapter 8: Regarding Right Triangles 107 Chapter 9: Completing Congruent Triangle Proofs 125 Part 4: Polygons of the Four-or-More-Sided Variety 153 Chapter 10: The Seven Wonders of the Quadrilateral World 155 Chapter 11: Proving That You Have a Particular Quadrilateral 177 Chapter 12: Polygon Formulas: Area, Angles, and Diagonals 193 Chapter 13: Similarity: Same Shape, Different Size 211 Part 5: Working with Not-So-Vicious Circles 235 Chapter 14: Coming Around to Circle Basics 237 Chapter 15: Circle Formulas and Theorems 255 Part 6: Going Deep with 3-D Geometry 277 Chapter 16: 3-D Space: Proofs in a Higher Plane of Existence 279 Chapter 17: Getting a Grip on Solid Geometry 287 Part 7: Placement, Points, and Pictures: Alternative Geometry Topics 303 Chapter 18: Coordinate Geometry 305 Chapter 19: Changing the Scene with Geometric Transformations 323 Chapter 20: Locating Loci and Constructing Constructions 343 Part 8: The Part of Tens 361 Chapter 21: Ten Things to Use as Reasons in Geometry Proofs 363 Chapter 22: Ten Cool Geometry Problems 369 Index 377

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Book SynopsisTable of ContentsBasic Math and Pre-Algebra For Dummies, 2nd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: Playing the Numbers Game 7 CHAPTER 2: It’s All in the Fingers: Numbers and Digits 23 CHAPTER 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29 Part 2: Getting a Handle on Whole Numbers 47 CHAPTER 4: Putting the Big Four Operations to Work 49 CHAPTER 5: A Question of Values: Evaluating Arithmetic Expressions 63 CHAPTER 6: Say What? Turning Words into Numbers 75 CHAPTER 7: Divisibility 87 CHAPTER 8: Fabulous Factors and Marvelous Multiples 95 Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109 CHAPTER 9: Fooling with Fractions 111 CHAPTER 10: Parting Ways: Fractions and the Big Four Operations 125 CHAPTER 11: Dallying with Decimals 149 CHAPTER 12: Playing with Percents 171 CHAPTER 13: Word Problems with Fractions, Decimals, and Percents 183 Part 4: Picturing and Measuring — Graphs, Measures, Stats, and Sets 195 CHAPTER 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197 CHAPTER 15: How Much Have You Got? Weights and Measures 205 CHAPTER 16: Picture This: Basic Geometry 217 CHAPTER 17: Seeing Is Believing: Graphing as a Visual Tool 239 CHAPTER 18: Solving Geometry and Measurement Word Problems 247 CHAPTER 19: Figuring Your Chances: Statistics and Probability 259 CHAPTER 20: Setting Things Up with Basic Set Theory 271 Part 5: The X-Files: Introduction to Algebra 279 CHAPTER 21: Enter Mr X: Algebra and Algebraic Expressions 281 CHAPTER 22: Unmasking Mr X: Algebraic Equations 299 CHAPTER 23: Putting Mr X to Work: Algebra Word Problems 311 Part 6: The Part of Tens 321 CHAPTER 24: Ten Little Math Demons That Trip People Up 323 CHAPTER 25: Ten Important Number Sets to Know 329 Index 337 Basic Math and Pre-Algebra Workbook For Dummies, 3rd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: We've Got Your Numbers 7 CHAPTER 2: Smooth Operators: Working with the Big Four Operations 23 CHAPTER 3: Getting Down with Negative Numbers 37 CHAPTER 4: It's Just an Expression 49 CHAPTER 5: Dividing Attention: Divisibility, Factors, and Multiples 69 Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89 CHAPTER 6: Fractions Are a Piece of Cake 91 CHAPTER 7: Fractions and the Big Four 109 CHAPTER 8: Getting to the Point with Decimals 143 CHAPTER 9: Playing the Percentages 165 Part 3: A Giant Step Forward: Intermediate Topics 177 CHAPTER 10: Seeking a Higher Power through Scientific Notation 179 CHAPTER 11: Weighty Questions on Weights and Measures 189 CHAPTER 12: Shaping Up with Geometry 203 CHAPTER 13: Getting Graphic: Xy-Graphs 223 Part 4: The X Factor: Introducing Algebra 235 CHAPTER 14: Expressing Yourself with Algebraic Expressions 237 CHAPTER 15: Finding the Right Balance: Solving Algebraic Equations 259 Part 5: The Part of Tens 277 CHAPTER 16: Ten Alternative Numeral and Number Systems 279 CHAPTER 17: Ten Curious Types of Numbers 287 Index 293

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Book SynopsisMACHINE LEARNING FOR BUSINESS ANALYTICS An up-to-date introduction to a market-leading platform for data analysis and machine learning Machine Learning for Business Analytics: Concepts, Techniques, and Applications with JMP Pro, 2nd ed. offers an accessible and engaging introduction to machine learning. It provides concrete examples and case studies to educate new users and deepen existing users' understanding of their data and their business. Fully updated to incorporate new topics and instructional material, this remains the only comprehensive introduction to this crucial set of analytical tools specifically tailored to the needs of businesses. Machine Learning for Business Analytics: Concepts, Techniques, and Applications with JMP Pro, 2nd ed. readers will also find: Updated material which improves the book's usefulness as a reference for professionals beyond the classroom Four new chapTable of ContentsForeword xix Preface xx Acknowledgments xxiii Part I Preliminaries 1 Introduction 3 1.1 What Is Business Analytics? 3 1.2 What Is Machine Learning? 5 1.3 Machine Learning, AI, and Related Terms 5 Statistical Modeling vs. Machine Learning 6 1.4 Big Data 6 1.5 Data Science 7 1.6 Why Are There So Many Different Methods? 8 1.7 Terminology and Notation 8 1.8 Road Maps to This Book 10 Order of Topics 12 2 Overview of the Machine Learning Process 17 2.1 Introduction 17 2.2 Core Ideas in Machine Learning 18 Classification 18 Prediction 18 Association Rules and Recommendation Systems 18 Predictive Analytics 19 Data Reduction and Dimension Reduction 19 Data Exploration and Visualization 19 Supervised and Unsupervised Learning 19 2.3 The Steps in A Machine Learning Project 21 2.4 Preliminary Steps 22 Organization of Data 22 Sampling from a Database 22 Oversampling Rare Events in Classification Tasks 23 Preprocessing and Cleaning the Data 23 2.5 Predictive Power and Overfitting 29 Overfitting 29 Creation and Use of Data Partitions 31 2.6 Building a Predictive Model with JMP Pro 34 Predicting Home Values in a Boston Neighborhood 34 Modeling Process 36 2.7 Using JMP Pro for Machine Learning 42 2.8 Automating Machine Learning Solutions 43 Predicting Power Generator Failure 44 Uber’s Michelangelo 45 2.9 Ethical Practice in Machine Learning 47 Machine Learning Software: The State of the Market by Herb Edelstein 47 Problems 52 Part II Data Exploration and Dimension Reduction 3 Data Visualization 59 3.1 Introduction 59 3.2 Data Examples 61 Example 1: Boston Housing Data 61 Example 2: Ridership on Amtrak Trains 62 3.3 Basic Charts: Bar Charts, Line Graphs, and Scatter Plots 62 Distribution Plots: Boxplots and Histograms 64 Heatmaps 67 3.4 Multidimensional Visualization 70 Adding Variables: Color, Hue, Size, Shape, Multiple Panels, Animation 70 Manipulations: Rescaling, Aggregation and Hierarchies, Zooming, Filtering 73 Reference: Trend Line and Labels 77 Scaling Up: Large Datasets 79 Multivariate Plot: Parallel Coordinates Plot 80 Interactive Visualization 80 3.5 Specialized Visualizations 82 Visualizing Networked Data 82 Visualizing Hierarchical Data: More on Treemaps 83 Visualizing Geographical Data: Maps 84 3.6 Summary: Major Visualizations and Operations, According to Machine Learning Goal 87 Prediction 87 Classification 87 Time Series Forecasting 87 Unsupervised Learning 88 Problems 89 4 Dimension Reduction 91 4.1 Introduction 91 4.2 Curse of Dimensionality 92 4.3 Practical Considerations 92 Problems 112 Part III Performance Evaluation 5 Evaluating Predictive Performance 117 5.1 Introduction 118 5.2 Evaluating Predictive Performance 118 Problems 142 Part IV Prediction and Classification Methods 6 Multiple Linear Regression 147 6.1 Introduction 147 6.2 Explanatory vs. Predictive Modeling 148 6.3 Estimating the Regression Equation and Prediction 149 Example: Predicting the Price of Used Toyota Corolla Automobiles 150 6.4 Variable Selection in Linear Regression 155 Reducing the Number of Predictors 155 How to Reduce the Number of Predictors 156 Manual Variable Selection 156 Automated Variable Selection 157 Regularization (Shriknage Models) 164 Problems 170 7 k-Nearest Neighbors (k-NN) 175 7.1 The 𝑘-NN Classifier (Categorical Outcome) 175 Problems 186 8 The Naive Bayes Classifier 189 8.1 Introduction 189 Threshold Probability Method 190 Conditional Probability 190 Problems 203 9 Classification and Regression Trees 205 9.1 Introduction 206 Tree Structure 206 Decision Rules 207 Classifying a New Record 207 9.2 Classification Trees 207 Recursive Partitioning 207 Example 1: Riding Mowers 208 Categorical Predictors 210 Standardization 210 9.3 Growing a Tree for Riding Mowers Example 210 Choice of First Split 211 Choice of Second Split 212 Final Tree 212 Using a Tree to Classify New Records 213 9.4 Evaluating the Performance of a Classification Tree 215 Example 2: Acceptance of Personal Loan 215 9.5 Avoiding Overfitting 219 Stopping Tree Growth: CHAID 220 Growing a Full Tree and Pruning It Back 220 How JMP Pro Limits Tree Size 221 9.6 Classification Rules from Trees 222 9.7 Classification Trees for More Than Two Classes 224 9.8 Regression Trees 224 Prediction 224 Evaluating Performance 225 9.9 Advantages and Weaknesses of a Single Tree 227 9.10 Improving Prediction: Random Forests and Boosted Trees 229 Random Forests 229 Boosted Trees 230 Problems 233 10 Logistic Regression 237 10.1 Introduction 237 10.2 The Logistic Regression Model 239 10.3 Example: Acceptance of Personal Loan 240 Model with a Single Predictor 241 Estimating the Logistic Model from Data: Multiple Predictors 243 Interpreting Results in Terms of Odds (for a Profiling Goal) 246 10.4 Evaluating Classification Performance 247 10.5 Variable Selection 249 10.6 Logistic Regression for Multi-class Classification 250 Logistic Regression for Nominal Classes 250 Logistic Regression for Ordinal Classes 251 Example: Accident Data 252 10.7 Example of Complete Analysis: Predicting Delayed Flights 253 Data Preprocessing 255 Model Fitting, Estimation, and Interpretation---A Simple Model 256 Model Fitting, Estimation and Interpretation---The Full Model 257 Model Performance 257 Problems 264 11 Neural Nets 267 11.1 Introduction 267 11.2 Concept and Structure of a Neural Network 268 11.3 Fitting a Network to Data 269 Example 1: Tiny Dataset 269 Computing Output of Nodes 269 Preprocessing the Data 272 Training the Model 273 Using the Output for Prediction and Classification 279 Example 2: Classifying Accident Severity 279 Avoiding Overfitting 281 11.4 User Input in JMP Pro 282 11.5 Exploring the Relationship Between Predictors and Outcome 284 11.6 Deep Learning 285 Convolutional Neural Networks (CNNs) 285 Local Feature Map 287 A Hierarchy of Features 287 The Learning Process 287 Unsupervised Learning 288 Conclusion 289 11.7 Advantages and Weaknesses of Neural Networks 289 Problems 290 12 Discriminant Analysis 293 12.1 Introduction 293 Example 1: Riding Mowers 294 Example 2: Personal Loan Acceptance 294 12.2 Distance of an Observation from a Class 295 12.3 From Distances to Propensities and Classifications 297 12.4 Classification Performance of Discriminant Analysis 300 12.5 Prior Probabilities 301 12.6 Classifying More Than Two Classes 303 Example 3: Medical Dispatch to Accident Scenes 303 12.7 Advantages and Weaknesses 306 Problems 307 13 Generating, Comparing, and Combining Multiple Models 311 13.1 Ensembles 311 Why Ensembles Can Improve Predictive Power 312 Simple Averaging or Voting 313 Bagging 314 Boosting 315 Stacking 316 Advantages and Weaknesses of Ensembles 317 13.2 Automated Machine Learning (AutoML) 317 AutoML: Explore and Clean Data 317 AutoML: Determine Machine Learning Task 318 AutoML: Choose Features and Machine Learning Methods 318 AutoML: Evaluate Model Performance 320 AutoML: Model Deployment 321 Advantages and Weaknesses of Automated Machine Learning 322 13.3 Summary 322 Problems 323 Part V Intervention and User Feedback 14 Interventions: Experiments, Uplift Models, and Reinforcement Learning 327 14.1 Introduction 327 14.2 A/B Testing 328 Example: Testing a New Feature in a Photo Sharing App 329 The Statistical Test for Comparing Two Groups (𝑇 -Test) 329 Multiple Treatment Groups: A/B/n Tests 333 Multiple A/B Tests and the Danger of Multiple Testing 333 14.3 Uplift (Persuasion) Modeling 333 Getting the Data 334 A Simple Model 336 Modeling Individual Uplift 336 Creating Uplift Models in JMP Pro 337 Using the Results of an Uplift Model 338 14.4 Reinforcement Learning 340 Explore-Exploit: Multi-armed Bandits 340 Markov Decision Process (MDP) 341 14.5 Summary 344 Problems 345 Part VI Mining Relationships Among Records 15 Association Rules and Collaborative Filtering 349 15.1 Association Rules 349 Discovering Association Rules in Transaction Databases 350 Example 1: Synthetic Data on Purchases of Phone Faceplates 350 Data Format 350 Generating Candidate Rules 352 The Apriori Algorithm 353 Selecting Strong Rules 353 The Process of Rule Selection 356 Interpreting the Results 358 Rules and Chance 359 Example 2: Rules for Similar Book Purchases 361 15.2 Collaborative Filtering 362 Data Type and Format 363 Example 3: Netflix Prize Contest 363 User-Based Collaborative Filtering: “People Like You” 365 Item-Based Collaborative Filtering 366 Evaluating Performance 367 Advantages and Weaknesses of Collaborative Filtering 368 Collaborative Filtering vs. Association Rules 369 15.3 Summary 370 Problems 372 16 Cluster Analysis 375 16.1 Introduction 375 Example: Public Utilities 377 16.2 Measuring Distance Between Two Records 378 Euclidean Distance 379 Standardizing Numerical Measurements 379 Other Distance Measures for Numerical Data 379 Distance Measures for Categorical Data 382 Distance Measures for Mixed Data 382 16.3 Measuring Distance Between Two Clusters 383 Minimum Distance 383 Maximum Distance 383 Average Distance 383 Centroid Distance 383 16.4 Hierarchical (Agglomerative) Clustering 385 Single Linkage 385 Complete Linkage 386 Average Linkage 386 Centroid Linkage 386 Ward’s Method 387 Dendrograms: Displaying Clustering Process and Results 387 Validating Clusters 391 Two-Way Clustering 393 Limitations of Hierarchical Clustering 393 16.5 Nonhierarchical Clustering: The 𝐾-Means Algorithm 394 Choosing the Number of Clusters (𝑘) 396 Problems 403 Part VII Forecasting Time Series 17 Handling Time Series 409 17.1 Introduction 409 17.2 Descriptive vs. Predictive Modeling 410 17.3 Popular Forecasting Methods in Business 411 Combining Methods 411 17.4 Time Series Components 411 Example: Ridership on Amtrak Trains 412 17.5 Data Partitioning and Performance Evaluation 415 Benchmark Performance: Naive Forecasts 417 Generating Future Forecasts 417 Problems 419 18 Regression-Based Forecasting 423 18.1 A Model with Trend 424 Linear Trend 424 Exponential Trend 427 Polynomial Trend 429 18.2 A Model with Seasonality 430 Additive vs. Multiplicative Seasonality 432 18.3 A Model with Trend and Seasonality 433 18.4 Autocorrelation and ARIMA Models 433 Computing Autocorrelation 433 Improving Forecasts by Integrating Autocorrelation Information 437 Fitting AR Models to Residuals 439 Evaluating Predictability 441 Problems 444 19 Smoothing and Deep Learning Methods for Forecasting 455 19.1 Introduction 455 19.2 Moving Average 456 Centered Moving Average for Visualization 456 Trailing Moving Average for Forecasting 457 Choosing Window Width (𝑤) 460 19.3 Simple Exponential Smoothing 461 Choosing Smoothing Parameter 𝛼 462 Relation Between Moving Average and Simple Exponential Smoothing 465 19.4 Advanced Exponential Smoothing 465 Series With a Trend 465 Series With a Trend and Seasonality 466 19.5 Deep Learning for Forecasting 470 Problems 472 Part VIII Data Analytics 20 Text Mining 483 20.1 Introduction 483 20.2 The Tabular Representation of Text: Document–Term Matrix and “Bag-of-Words” 484 20.3 Bag-of-Words vs. Meaning Extraction at Document Level 486 20.4 Preprocessing the Text 486 Tokenization 487 Text Reduction 488 Presence/Absence vs. Frequency (Occurrences) 489 Term Frequency-Inverse Document Frequency (TF-IDF) 489 From Terms to Topics: Latent Semantic Analysis and Topic Analysis 490 Extracting Meaning 491 From Terms to High Dimensional Word Vectors: Word2Vec 491 20.5 Implementing Machine Learning Methods 492 20.6 Example: Online Discussions on Autos and Electronics 492 Importing the Records 493 Text Preprocessing in JMP 494 Using Latent Semantic Analysis and Topic Analysis 496 Fitting a Predictive Model 499 Prediction 499 20.7 Example: Sentiment Analysis of Movie Reviews 500 Data Preparation 500 Latent Semantic Analysis and Fitting a Predictive Model 500 20.8 Summary 502 Problems 503 21 Responsible Data Science 505 21.1 Introduction 505 Example: Predicting Recidivism 506 21.2 Unintentional Harm 506 21.3 Legal Considerations 508 The General Data Protection Regulation (GDPR) 508 Protected Groups 508 21.4 Principles of Responsible Data Science 508 Non-maleficence 509 Fairness 509 Transparency 510 Accountability 511 Data Privacy and Security 511 21.5 A Responsible Data Science Framework 511 Justification 511 Assembly 512 Data Preparation 513 Modeling 513 Auditing 513 21.6 Documentation Tools 514 Impact Statements 514 Model Cards 515 Datasheets 516 Audit Reports 516 21.7 Example: Applying the RDS Framework to the COMPAS Example 517 Unanticipated Uses 518 Ethical Concerns 518 Protected Groups 518 Data Issues 518 Fitting the Model 519 Auditing the Model 520 Bias Mitigation 526 21.8 Summary 526 Problems 528 Part IX Cases 22 Cases 533 22.1 Charles Book Club 533 The Book Industry 533 Database Marketing at Charles 534 Machine Learning Techniques 535 Assignment 537 22.2 German Credit 541 Background 541 Data 541 Assignment 544 22.3 Tayko Software Cataloger 545 Background 545 The Mailing Experiment 545 Data 545 Assignment 546 22.4 Political Persuasion 548 Background 548 Predictive Analytics Arrives in US Politics 548 Political Targeting 548 Uplift 549 Data 549 Assignment 550 22.5 Taxi Cancellations 552 Business Situation 552 Assignment 552 22.6 Segmenting Consumers of Bath Soap 554 Business Situation 554 Key Problems 554 Data 555 Measuring Brand Loyalty 556 Assignment 556 22.7 Catalog Cross-Selling 557 Background 557 Assignment 557 22.8 Direct-Mail Fundraising 559 Background 559 Data 559 Assignment 559 22.9 Time Series Case: Forecasting Public Transportation Demand 562 Background 562 Problem Description 562 Available Data 562 Assignment Goal 562 Assignment 563 Tips and Suggested Steps 563 22.10 Loan Approval 564 Background 564 Regulatory Requirements 564 Getting Started 564 Assignment 564 References 567 Data Files Used in the Book 571 Index 573

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Book SynopsisMaths Progress (Second Edition) develops reasoning, fluency and problem-solving to boost students’ confidence at Key Stage 3 and give them the best preparation for progressing to GCSE study.

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Book SynopsisTable of Contents1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 2. Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 3. Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 4. Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L'Hôpital's Rule 4.6 Applied Optimization 4.7 Newton's Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 5. Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work and Fluid Forces 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 7. Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions 7.4 Relative Rates of Growth Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 8. Techniques of Integration 8.1 Using Basic Integration Formulas 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitutions 8.5 Integration of Rational Functions by Partial Fractions 8.6 Integral Tables and Computer Algebra Systems 8.7 Numerical Integration 8.8 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 9. Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 10. Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates 10.6 Conic Sections 10.7 Conics in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 12. Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 13.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 13. Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multipliers 13.9 Taylor's Formula for Two Variables 13.10 Partial Derivatives with Constrained Variables Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 14. Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 15. Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green's Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes' Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 16. First-Order Differential Equations 16.1 Solutions, Slope Fields, and Euler's Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Questions to Guide Your Review Practice Exercises Technology Application Projects 17. Second-Order Differential Equations 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Technology Application Projects 18. Complex Functions (online) 18.1 Complex Numbers 18.2 Limits and Continuity 18.3 Complex Derivatives 18.4 The Cauchy-Riemann Equations 18.5 Complex Series 18.6 Conformal Maps 19. Fourier Series and Wavelets (online) 19.1 Periodic Functions 19.2 Summing Sines and Cosines 19.3 Vectors and Approximation in Three and More Dimensions 19.4 Approximation of Functions 19.5 Advanced Topic: The Haar System and Wavelets Appendix A A.1 Real Numbers and the Real Line A.2 Graphing with Software A.3 Mathematical Induction A.4 Lines, Circles, and Parabolas A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 The Distributive Law for Vector Cross Products A.9 Probability A.10 The Mixed Derivative Theorem and the Increment Theorem Appendix B B.1 Determinants B.2 Extreme Values and Saddle Points for Functions of More than Two Variables B.3 The Method of Gradient Descent Answers to Odd-Numbered Exercises Applications Index Subject Index A Brief Table of Integrals Credits

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book provides your child with a whole year of ready to go activitiesand support on key Mathematics topics which will be beingtaught in school from 2014. *Workbooks for home learning or classroompractice *Linked website with additional activities, answersand support for parents. *Developed by teachers.

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Book SynopsisJudith Gersting''s text has long been acclaimed for its clear presentation of essential concepts and it''s exceptional range of applications relevant to computer science majors. The seventh edition contains over 200 new examples and exercises, updated to demonstrate the role that mathematics and computer science plays in a wide range of disciplines.

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Book SynopsisThe human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it.In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain''s processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of MoTrade ReviewGrace Lindsay provides a masterful tour of this important frontier, tackling intimidating topics with verve and wit. * Sean Carroll *This is a remarkable book … an excellent introduction to an area that few of us probably know anything about, and all the more fascinating because of that. * Popular Science *Models of the Mind is a grand tour through the history of computational neuroscience, from its humble beginnings in information theory and neuron structure up to its modern manifestations harnessing supercomputers to run large scale convolutional neural networks that model important brain systems. * Women You Should Know *The book is not only wide-ranging in its choice of topics but is also a lively journey through the history of these efforts and traces the lives of the eccentric and fascinating scientists who were instrumental in figuring out the brain’s working by using tools ranging from information theory and graph theory to Bayesian modeling and neural networks. * 3 Quarks Daily * ‘Enthralling, erudite and accessible … an engrossing history of science and an enlightening guide to neuroscience’s current frontiers.’ * Liam Drew, Neurobiologist and author of I, Mammal: The Story of What Makes Us Mammals *‘This book is an anthology of the scientific poetry that has illuminated our studies and conceptions of the brain.’ * Professor Larry Abbott, Center for Theoretical Neuroscience, Columbia University *Table of Contents1: Spherical Cows 2: How Neurons Get Their Spike 3: Learning to Compute 4: Making and Maintaining Memories 5: Excitation and Inhibition 6: Stages of Sight 7: Cracking the Neural Code 8: Movement in Low Dimensions 9: From Structure to Function 10: Making Rational Decisions 11: How Rewards Guide Actions 12: Grand Unified Theories of the Brain Mathematical Appendix Acknowledgements Bibliography Index

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Basic Mathematics teaches you all the maths you need for everyday situations. If you are terrified by maths, this is the book for you.Do you shy away from using numbers? Basic Mathematics can help. An easy-to-follow guide, it will ensure you gain the confidence you need to tackle maths and overcome your fears. It offers simple explanations of all the key areas, including decimals, percentages, measurements and graphs, and applies them to everyday situations, games and puzzles to help you understand mathematics quickly and enjoyably.Everything you need is here in this one book. Each chapter includes clear explanations, worked examples and test questions. At the end of the book there are challenges and games to give you new and interesting ways to practise your new skills.

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Book SynopsisA ''difficult'' subject so simply taught - brilliant book'' - Amazon 5 star review ⭐⭐⭐⭐⭐''This is a great refresher book! Lots of worked out examples, great explanations [and] hundreds of practice problems and solutions'' - Amazon 5 star review ⭐⭐⭐⭐⭐''This book has been very helpful for my calculus class, I recommend it to anyone that needs extra help, or just feel like learning something new.'' - Amazon 5 star review ⭐⭐⭐⭐⭐Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. 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 areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithm

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