Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.
Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
If any of these questions took you more than a few seconds to solve, you need this book. Short-Cut Math is a concise, remarkably clear compendium of about 150 math short-cuts — timesaving tricks that provide faster, easier ways to add, subtract, multiply, and divide.
By using the simple foolproof methods in this volume, you can double or triple your calculation speed — even if you always hated math in school. Here's a sampling of the amazingly effective techniques you will learn in minutes: Adding by 10 Groups; No-Carry Addition; Subtraction Without Borrowing; Multiplying by Aliquot Parts; Test for Divisibility by Odd and Even Numbers; Simplifying Dividends and Divisors; Fastest Way to Add or Subtract Any Pair of Fractions; Multiplying and Dividing with Mixed Numbers, and more.
The short-cuts in this book require no special math ability. If you can do ordinary arithmetic, you will have no trouble with these methods. There are no complicated formulas or unfamiliar jargon — no long drills or exercises. For each problem, the author provides an explanation of the method and a step-by-step solution. Then the short-cut is applied, with a proof and an explanation of why it works.
Students, teachers, businesspeople, accountants, bank tellers, check-out clerks — anyone who uses numbers and wishes to increase his or her speed and arithmetical agility, can benefit from the clear, easy-to-follow techniques given here.
The author can awaken for you a faculty which is surprisingly dormant in accountants, engineers, scientists, businesspeople, and others who work with figures. This is "number sense" — or the ability to recognize relations between numbers considered as whole quantities. Lack of this number sense makes it entirely possible for a scientist to be proficient in higher mathematics, but to bog down in the arithmetic of everyday life.
This book teaches the necessary mathematical techniques that schools neglect to teach: Horizontal addition, left to right multiplication and division, etc. You will learn a method of multiplication so rapid that you'll be able to do products in not much more time than it would take to write the problem down on paper.
This is not a collection of tricks that work in only a very few special cases, but a serious, capably planned course of basic mathematics for self-instruction. It contains over 9,000 short problems and their solutions for you to work during spare moments. Five or ten minutes spent daily on this book will, within ten weeks, give you a number sense that will double or triple your calculation speed.
This handy book is designed to streamline your methods and resharpen your calculation skills for a variety of situations. Starting with the most elementary operations, the book goes on to cover all basic topics and processes of arithmetic: addition, subtraction, multiplication, division, fractions, percentage, interest, ratio and proportion, denominate numbers, averages, etc. The text continues into other useful matters, such as powers and roots, logarithms, positive and negative numbers, harmonic progression, and introductory concepts of algebra.
Entirely practical in approach and using an easy-to-follow question and answer style, this book covers a wide range of common knotty areas: filling and emptying receptacles, scales for models and maps, business and financial calculations (partial payment problems, compound interest, bank and sales discount, profit and loss problems, etc.), angle measurement, mixtures and solutions, graph and chart problems, and the like.
The discussion contains numerous alternate and short-cut methods, such as quick ways to figure compound interest; to square a number from 1 to 100; to divide by 5, 25, 125, 99, etc.; to multiply two 2-digit numbers having the same figure in the tens place; and many more. These valuable tips, together with the huge fund of exercise problems (a total of 809, half of them answered in an appendix), help you to increase your computational proficiency and speed, and make this an extremely useful volume to have on your shelf at home or at work. Anyone who has to do any figuring at all — housewife, merchant, student — will profit from this refresher. Parents will find it an excellent source of material for helping children in school work.
The book contains 33 different styles for writing the term frequency task. The styles are grouped into nine categories: historical, basic, function composition, objects and object interactions, reflection and metaprogramming, adversity, data-centric, concurrency, and interactivity. The author verbalizes the constraints in each style and explains the example programs. Each chapter first presents the constraints of the style, next shows an example program, and then gives a detailed explanation of the code. Most chapters also have sections focusing on the use of the style in systems design as well as sections describing the historical context in which the programming style emerged.
In his latest foray into mathematics, David Berlinski takes on the simplest questions that can be asked: What is a number? How do addition, subtraction, multiplication, and division actually work? What are geometry and logic? As he delves into these subjects, he discovers and lucidly describes the beauty and complexity behind their seemingly simple exteriors, making clear how and why these mercurial, often slippery concepts are essential to who we are.
Filled with illuminating historical anecdotes and asides on some of the most fascinating mathematicians through the ages, One, Two, Three is a captivating exploration of the foundation of mathematics: how it originated, who thought of it, and why it matters.
From the Hardcover edition.
In the twenty-first century, computers have become indispensable in music making, distribution, performance, and consumption. Making Music with Computers: Creative Programming in Python introduces important concepts and skills necessary to generate music with computers. It interweaves computing pedagogy with musical concepts and creative activities, showing students how to integrate the creativity and design of the arts with the mathematical rigor and formality of computer science.
The book provides an introduction to creative software development in the Python programming language. It uses innovative music-creation activities to illustrate introductory computer programming concepts, including data types, algorithms, operators, iteration, lists, functions, and classes. The authors also cover GUIs, event-driven programming, big data, sonification, MIDI programming, client–server programming, recursion, fractals, and complex system dynamics.
Requiring minimal musical or programming experience, the text is designed for courses in introductory computer science and computing in the arts. It helps students learn computer programming in a creative context and understand how to build computer music applications. Also suitable for self-study, the book shows musicians and digital music enthusiasts how to write music software and create algorithmic music compositions.
A supplementary website (http://jythonMusic.org) provides a music library and other software resources used in the text. The music library is an extension of the jMusic library and incorporates other cross-platform programming tools. The website also offers example course and associated media resources.
New to the Third Edition
New chapter on special topics, including discrete Cauchy–Euler equations; gamma, beta, and digamma functions; Lambert W-function; Euler polynomials; functional equations; and exact discretizations of differential equations New chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences Additional problems in all chapters Expanded bibliography to include recently published texts related to the subject of difference equations
Suitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.
Ordinary Differential Equations: An Introduction to the Fundamentals also includes access to an author-maintained website featuring detailed solutions and a wealth of bonus material. Use of a math software package that can do symbolic calculations, graphing, and so forth, such as MapleTM or Mathematica®, is highly recommended, but not required.
Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization and examines advanced foundational topics, such as multivariable poles and zeros and LQG/LQR.
The textbook presents only the most essential mathematical derivations and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review.
Easy-to-use textbook in unique lecture-style formatSidebars explain topics in further detailAnnotated proofs and discussions of MATLAB commandsBalanced chapters can each be taught in two hours of course lectureNew practice exercises with solutions included
"The well-written, comprehensive book...[is] aiming to become a de facto reference for the language and its features and capabilities. The pace is appropriate for beginners; programming concepts are introduced progressively through a range of examples and then used as tools for building applications in various domains, including sophisticated data structures and algorithms...Highly recommended. Students of all levels, faculty, and professionals/practitioners.
—D. Papamichail, University of Miami in CHOICE Magazine
Mark Lewis’ Introduction to the Art of Programming Using Scala was the first textbook to use Scala for introductory CS courses. Fully revised and expanded, the new edition of this popular text has been divided into two books. Object-Orientation, Abstraction, and Data Structures Using Scala, Second Edition is intended to be used as a textbook for a second or third semester course in Computer Science.
The Scala programming language provides powerful constructs for expressing both object orientation and abstraction. This book provides students with these tools of object orientation to help them structure solutions to larger, more complex problems, and to expand on their knowledge of abstraction so that they can make their code more powerful and flexible. The book also illustrates key concepts through the creation of data structures, showing how data structures can be written, and the strengths and weaknesses of each one. Libraries that provide the functionality needed to do real programming are also explored in the text, including GUIs, multithreading, and networking.
The book is filled with end-of-chapter projects and exercises, and the authors have also posted a number of different supplements on the book website. Video lectures for each chapter in the book are also available on YouTube. The videos show construction of code from the ground up and this type of "live coding" is invaluable for learning to program, as it allows students into the mind of a more experienced programmer, where they can see the thought processes associated with the development of the code.
About the Authors
Mark Lewis is an Associate Professor at Trinity University. He teaches a number of different courses, spanning from first semester introductory courses to advanced seminars. His research interests included simulations and modeling, programming languages, and numerical modeling of rings around planets with nearby moons.
Lisa Lacher is an Assistant Professor at the University of Houston, Clear Lake with over 25 years of professional software development experience. She teaches a number of different courses spanning from first semester introductory courses to graduate level courses. Her research interests include Computer Science Education, Agile Software Development, Human Computer Interaction and Usability Engineering, as well as Measurement and Empirical Software Engineering.
In an inspiring introduction, science writer Edward Stoddard offers important suggestions for mastering an entirely new system of figuring. Without having to discard acquired information about mathematical computation, students build on the knowledge they already have, "streamline" these techniques for rapid use and then combine them with classic shortcuts.
Initially, readers learn to master a basic technique known as the Japanese "automatic" figuring method — the principle behind the abacus. This method enables users to multiply without carrying, divide with half the written work of long division, and mentally solve mathematical problems that usually require pencil and paper or a calculator. Additional chapters explain how to build speed in addition and subtraction, how to check for accuracy, master fractions, work quickly with decimals, handle percentages, and much more.
A valuable asset for people in business who work with numbers on a variety of levels, this outstanding book will also appeal to students, teachers, and anyone looking for a reliable way to improve skill and speed in doing basic arithmetic.
Ajawad I. Haijais a professor of physics at Indiana University of Pennsylvania.
M. Z. Numanis professor and chair of the department of physics at Indiana University of Pennsylvania.
W. Larry Freemanis Emeritus Professor of Physics at Indiana University of Pennsylvania.
These key stages are identified as: Stage 1a: Fair Sharing Stage 1b: Part-Whole Stage 2a: Disembedding and IteratingStage 2b: Measuring with Unit Fractions Stage 2c: Reversing Fractions Stage 3a: Fractions as Numbers Stage 3b: Operating with Fractions As the newest addition to the bestselling Maths Recovery Series, this book will be a useful guide for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors.
The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible.
The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
Updated and expanded with new topics, The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition presents the essential core of mathematical principles needed by scientists and engineers. Starting from the basic concepts of trigonometry, the book covers calculus, differential equations, and vector calculus. A new chapter on applications discusses how we see objects "mathematically" with the eye, how quantum mechanics works, and more.
A Convenient, Student-Friendly Format Rich with Diagrams and Clear Explanations
The book presents essential mathematics ideas from basic to advanced level in a way that is useful to both students and practicing professionals. It offers a unique and educational approach that is the signature style of the author’s companion books. The author explains mathematical concepts clearly, concisely, and visually, illustrating how scientists use the language of mathematics to describe and communicate physical principles.
Be sure to check out the author’s other companion books:
The Materials Physics Companion, 2nd Edition
The Physics Companion, 2nd Edition
The Electronics Companion: Devices and Circuits for Physicists and Engineers, 2nd Edition
The Chemistry Companion
Swarm Intelligence: Principles, Advances, and Applications presents a comprehensive treatment of modern swarm intelligence optimization methods, complete with illustrative examples and an extendable MATLAB® package for feature selection in wrapper mode applied on different data sets with benchmarking using different evaluation criteria. The book provides beginners with a solid foundation of swarm intelligence fundamentals, and offers experts valuable insight into new directions and hybridizations.
Introduction to Recursive Programmingprovides a detailed and comprehensive introduction to recursion. This text will serve as a useful guide for anyone who wants to learn how to think and program recursively, by analyzing a wide variety of computational problems of diverse difficulty.
It contains specific chapters on the most common types of recursion (linear, tail, and multiple), as well as on algorithm design paradigms in which recursion is prevalent (divide and conquer, and backtracking). Therefore, it can be used in introductory programming courses, and in more advanced classes on algorithm design. The book also covers lower-level topics related to iteration and program execution, and includes a rich chapter on the theoretical analysis of the computational cost of recursive programs, offering readers the possibility to learn some basic mathematics along the way.
It also incorporates several elements aimed at helping students master the material. First, it contains a larger collection of simple problems in order to provide a solid foundation of the core concepts, before diving into more complex material. In addition, one of the book's main assets is the use of a step-by-step methodology, together with specially designed diagrams, for guiding and illustrating the process of developing recursive algorithms. Furthermore, the book covers combinatorial problems and mutual recursion. These topics can broaden students' understanding of recursion by forcing them to apply the learned concepts differently, or in a more sophisticated manner.
The code examples have been written in Python 3, but should be straightforward to understand for students with experience in other programming languages. Finally, worked out solutions to over 120 end-of-chapter exercises are available for instructors.
In the first section of the text, the authors cover two classical theoretical models of parallel computation (PRAMs and sorting networks), describe network models for topology and performance, and define several classical communication primitives. The next part deals with parallel algorithms on ring and grid logical topologies as well as the issue of load balancing on heterogeneous computing platforms. The final section presents basic results and approaches for common scheduling problems that arise when developing parallel algorithms. It also discusses advanced scheduling topics, such as divisible load scheduling and steady-state scheduling.
With numerous examples and exercises in each chapter, this text encompasses both the theoretical foundations of parallel algorithms and practical parallel algorithm design.
Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you’ll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.
Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation—the precursor to our modern system—and compares ancient Egyptian mathematics to today’s math, letting you decide for yourself which is better.
Julian Havil explores Napier’s original development of logarithms, the motivations for his approach, and the reasons behind certain adjustments to them. Napier’s inventive mathematical ideas also include formulas for solving spherical triangles, "Napier’s Bones" (a more basic but extremely popular alternative device for calculation), and the use of decimal notation for fractions and binary arithmetic. Havil also considers Napier’s study of the Book of Revelation, which led to his prediction of the Apocalypse in his first book, A Plaine Discovery of the Whole Revelation of St. John—the work for which Napier believed he would be most remembered.
John Napier assesses one man’s life and the lasting influence of his advancements on the mathematical sciences and beyond.