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Vedic Mathematics For All Ages, A Beginner’s Guide Vandana Singhal 2007. 298p. 16 Sutras for mental calculations easily explained formulae with practical exercises. This book is original in that it integrates these core vedic math principles with polygonal calculations in geometric forms, a unique application, along with a very clear and fun presentation of the core techniques of rapid math calculation techniques. CONTENTS: Complement; Subtraction’ Multiplication by Specific Numbers; Base Multiplication; Working with Multiplication; Algebra; Digital Roots; Divisibility; Division 1 & 2; Squares; Straight Squaring; Cubes’; Square roots of exact squares; Cube roots of exact cubes; Straight Division; Sutras. CAT#152 $25.00 Paperback, Motilal Banarsidass 

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Vedic Mathematics, or 'Sixteen Simple Mathematical Formulae From the Vedas' Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja, Shankaracharya of Govardhana Hatha, Puri. 1994, revised. (Original 1965) 367 P. This original work on Vedic Mathematics (Vedic Maths) begins with various introductions prefaces etc., illustrative specimen samples and a list of the Sutras and their corollaries. The book covers a considerable range of topics and is intended as an introduction to Vedic Mathematics. Contents: 1 Actual Applications Of The Vedic Sutras. 2 Arithmetical Computations. 3 Multiplication. Practical Application In "Compound Multiplication" Practice And Proportion In "Compound Multiplication". 4 Division By The Nikhilam Method. 5 Division By The Paravartya Method. 6 Argumental Division Linking Note (Recapitulation And Conclusion). 7 Factorisation (Of Simple Quadratics). 8 Factorisation (Of Harder Quadratics). 9 Factorisation Of Cubics Etc. 10 Highest Common Factor. 11 Simple Equations (First Principles). 12 Simple Equations (By Sunyam Etc.)13 Merger Type Of Simple Easy Equations. 14 Complex Mergers. 15 Simultaneous Simple Equations. 16 Miscellaneous (Simple) Equations. 17 Quadratic Equations. 18 Cubic Equations. 19 BiQuadratic Equations. 20 Multiple Simultaneous Equations. 21 Simultaneous Quadratic Equations. 22 Factorisation And Differential Calculus. 23 Partial Fractions. 24 Integration By Partial Fractions. 25 The Vedic Numerical Code. 26 Recurring Decimals. 27 Straight Division. 28 Auxiliary Fractions. 29 Divisibility And Simple Osculators. 30 Divisibility And Complex Multiplex Osculators. 31 Sum And Difference Of Squares. 32 Elementary Squaring, Cubing Etc. 33 Straight Squaring. 34 Vargamula (Square Root). 35 Cube Roots Of Exact Cubes. 36 Cube Roots (General). 37 Pythagoras' Theorem Etc. 38 Apollonius' Theorem. 39 Analytical Conics. 40 Miscellaneous Matters. Recapitulation And Conclusion. CAT#368 $30.00. Hardcover Motilal Banarsidass India 

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The Circle Revelation. Andrew P. Nicholas 1999. 221p. This fascinating book is the most popular, simple and direct introduction to rapid geometry techniques and calculations developed from Vedic Maths, a popularized version of "Geometry For an Oral Tradition", listed below. It is a delightful read which will completely reorientate one's vision and understanding of Geometry within as little as a few hours. The approach is ideally suited to the twentyfirst century, when audiovisual forms of communication are likely to be dominant. Contents: Angles, Triangles & Quadrilaterals; Properties of a Circle; Multiplication & Area; Parallels & Parallelograms; Similar Triangle' Equality & Equations; Number Arithemetic, Geometry & Algebra; Equal Areas & Similar Triangles; Further Properties of Circles; Pythagoras' Theorem; Proportion. CAT#370 $25.00 OUT OF STOCK 

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Geometry For An Oral Tradition. Andrew P. Nicholas 1999. 130 Large pages. Inspired by Vedic Maths and Euclid, this book presents direct, immediate and easily understood geometric proofs. These proofs are based on only one assumption (that magnitudes are unchanged by motion) and three additional provisions (a means of drawing figures, the language used and the ability to recognize valid reasoning). Starting from these first principles it leads to theorems on elementary properties of circles.. It includes discussion on the relevant philosophy of mathematics and is written both for mathematicians and for a wider audience. Contents: Introduction; Preliminaries; Provisions; Definitions; PROPOSITIONS; Part A: Congruence, Magnitudes and Lines; Part B: Angles, Parallels, Triangles And Quadrilaterals; Part C: Concerning ;Area Equalities And Similar Triangles Part D: Elementary Properties Of A Circle; COMMENTARY: Part I: Some Basics; Part II: Language And Reason; Part III: Comparisons With Euclid's Elements; Par IV: Movement In Geometry; Part V: The Valid Use Of Figures; Summary And Conclusions; References; APPENDICES: Appendix 1: Application Of The Sixteen Sutras To The Present System Of Geometry; Appendix 2: Alternative Proofs And Sequences In Part D; Appendix 3: Further Definitions. CAT#371 $35.00 OUT OF STOCK 

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Discover Vedic Mathematics: A Practical System Based on Sixteen Simple Formulae. Kenneth R. Williams 2004. 210 Large P. This book shows how the Vedic Maths system applies in a large number of areas of elementary mathematics, covering arithmetic, algebra, geometry, calculus etc. Each chapter concentrates on one Vedic Sutra or Subsutra and shows many applications. This gives a real feel for the Vedic Sutras each of which has its own unique character. It covers much of the content of Bharati Krishna's book above but in more detail and with more applications and explanations. It also contains Vedic solutions to GCSE and 'A' level examination questions. Preface; Illustrative Examples; 1 All From Nine And The Last From Ten; 2 Vertically And Crosswise; 3 Proportionately; 4 By Addition And By Subtraction; 5 By Alternate Elimination And Retention; 6 By Mere Observation; 7 Using The Average; 8 Transpose And Apply; 9 One In Ratio The Other One Zero; 10 When The Samuccaya Is The Same It Is Zero; 11 The First By The First And The Last By The Last; 12 By The Completion Or NonCompletion; 13 By One More Than The One Before; 14 The Product Of The Sum Is The Sum Of The Products; 15 Only The Last Terms; 16 Calculus; 'O' And 'A' Level Examination ;Papers; List Of The Vedic Sutras; Index Of The Vedic Formulae; Answers To Exercises; Index. CAT#372 $25.00 OUT OF STOCK 

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The Natural Calculator: Using The Natural Processes Of The Mind For Mental Calculations. Kenneth R. Williams 2004. 102 Pages. In this book the emphasis is on mental calculation, mainly mental multiplication, but addition, subtraction and division are also covered. Each chapter focuses on one Vedic formula and shows various ways in which it can be used. There is a detailed introduction outlining the benefits of mental mathematics(Vedic Maths). Introduction; 1 On The Flag Calculating From Left To Right; 2 Proportionately Multiplication Devices Involving Doubling And Halving; 3 By One More Than The One Before Squaring Numbers That End In 5; A Special Type Of Multiplication; 4 The First By The First And The Last By The Last Calculating Checks; A Special Type Of Multiplication; 5 All From 9 And The Last From 10 Numbers Near A Base; Subtraction; Numbers Near Different Bases; Multiplying Three Numbers Simultaneously; Squaring Numbers Near A Base; Multiplication By 9's; Addition And Subtraction; 6 Vertically And Crosswise General Multiplication: Multiplying 2Figure Numbers, 3Figure Numbers, Moving Multiplier Method, 3 And 4Figure Multiplication; General Squaring; Division Divisor Near A Base; General Division; 7 Using The Average Products Using An Average; 8 By Addition And By Subtraction Squares From Squares; Products From Products; 9 By Mere Observation Use Of Special Numbers; Proofs; References; Answers. CAT#373 $25.00 Motilal Banarsidass India 

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Vertically And Crosswise. A. P. Nicholas, K. Williams, J. Pickles 2004. 200P. This is an advanced book of sixteen chapters on one Vedic Maths Sutra, “Vertically & Crosswise”, ranging from elementary multiplication, etc. to the solution of nonlinear partial differential equations. It deals with (i) calculation of common functions and their series expansions, and (ii) the solution of equations, starting with simultaneous equations and moving on to algebraic, transcendental and differential equations. The text contains exercises and answers. Contents: 1 Introduction To The Vertically And Crosswise Sutra; 2 Combined Operations Of Elementary Arithmetic; 3 Evaluation Of Determinants; 4 The Solution Of Simultaneous Linear Equations; 5 Inversion Of Matrices; 6 CurveFitting; 7 Evaluation Of Logarithms And Exponentials; 8 Change Of Roots Of Equations; 9 Sine, Cosine And Inverse Tangent; 10 Inverse Sine And Cosine And Tangent; 11 Transcendental Equations; 12 Solution Of Cubic And Higher Order Equations; 13 Functions Of Polynomials; 14 Functions Of Bipolynomials; 15 The Solution Of Linear And NonLinear Differential, Integral And IntegroDifferential Equations; 16 The Solution Of Linear And NonLinear Partial Differential Equations. CAT#374 $25.00 Motilal Banarsidass India 

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Triples: Applications Of Pythagorean Triples. Kenneth R. Williams 2004. 168P. This book shows an original and highly effective way of unifying many branches of mathematics using Pythagorean triples and Vedic Maths. A simple, elegant method for combining these triples gives unexpected and powerful general methods for solving a wide range of mathematical problems. There are applications in trigonometry (you do not need any of those complicated formulae), coordinate geometry (2 and 3 dimensions), transformations (2 and 3 dimensions), simple harmonic motion, astronomy etc. Contents: 1 TRIPLES: The Triple Theorem; Some Historical Background; Notation for Triples; Equal, Prime and Complementary; Triples; Some Perfect Triples;2 TRIPLE ARITHMETIC; Addition of Triples; Double Angle; Triple Subtraction; Quadrant Angles; Triple Geometry; Angles of 30°, 60°, 45° etc.; Half Angle; Simplifying Calculations; Summary. 3 TRIPLE TRIGONOMETRY: Introduction; Inverse Functions; The General Triple; Solution of Trigonometrical Equations; Further Trigonometrical Equations A; Further Trigonometrical Equations B; Further Trigonometrical Equations C. 4 TRANSFORMATIONS IN A PLANE: Transposition of the Origin; Rotations; Spirals; Integration of cosx etc.; Rotation of Lines and Curves; Reflections. 5 COORDINATE GEOMETRY: Length of Perpendicular; Foot of Perpendicular; Angle between Two Lines; Equation of a Line; Further Examples. 6 CODE NUMBERS: Grouping Triples; Code Numbers; Geometrical Significance of the Code Numbers; Code Number Pairs; Code Numbers as Triples; Algebraic Formulation; Converting Code Numbers to Triples; Converting Triples to Code Numbers; Addition and Subtraction of Code Numbers; Code Numbers of Code Numbers; Code Numbers of Complementary Triples; Code Numbers of Supplementary Triples; Code Numbers for 0°, 90°, 180°, 270°; Relation between Code Numbers and Angles; Further Examples; Summary. 7 SOLUTION OF TRIANGLES: Angle Deficiency Formula; The Sine Formula; The Code Number Formula.8 FURTHER APPLICATIONS OF TRIPLES: Solution of Equations; Complex Numbers; Conics; Difference and Sum of Squares; Incircles and Circumcircles; The Golden Triple; 9 ANGLES IN PERFECT TRIPLES: Revision; Triples and Their Angles; Finding the Angle in a Given Triple; Further Applications of Code Numbers; Finding a Triple with a Given Angle; A Refinement.10 SINE, COSINE, TANGENT & INVERSES: Sine, Cosine and Tangent; Inverse Cosine and Inverse Sine; Inverse Tangent.11 HYPERBOLIC FUNCTIONS: Addition and Subtraction; Double Angle; Equations. 12 APPLIED MATHS APPLICATIONS: Simple Harmonic Motion; Projectiles; Forces in Equilibrium; Work Done by a Force and Moment of a Force. 13 THE TRIPLE METHOD: Range of Application; Deriving the Conventional Formulae; Two Comparisons of the Conventional and Triple Methods. 14 QUADRUPLES: Introduction; Quadruple Generators; Obtaining the Code Numbers of a Perfect Quadruple; The Coordinate Axes; Quadruple Subtraction; Comparative Densities of Perfect Triples and Quadruples. 15 APPLICATIONS OF QUADRUPLES: Coordinate Geometry; Work and Moment; Rotation about Coordinate axis; 3Dimensional Rotation of Curves; Rotation Conicoids. 16 QUADRUPLES IN ASTRONOMY: Addition of Perpendicular Triples. Change of Coordinate System; Quadruples and Orbits; Quadruple for given i, A; Inclination of Orbit; Quadruple Subtraction;. Quadruple Addition; Doubling and Halving a Quadruple; Code Number Addition and Subtraction; Angle in a Quadruple; Angular Advance; Relationship between d, A; To Obtain a Quadruple with a Given Inclination. PROOFS. ANSWERS TO EXERCISES. REFERENCES. INDEX OF VEDIC FORMULAE. INDEX. CAT#375 $25.00 Motilal Banarsidass 

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The Cosmic Computer Course, Book 1. Kenneth R. Williams & Mark Gaskell 1998. 250+ Large P. Each of the three books has 27 chapters each of which is prefaced by an inspiring quote from a famous mathematician, philosopher etc. Also in each book there are historical notes which relate to the authors of the quotes, a list of Sutras and three other short but interesting sections (e.g. Pascal's Triangle,Vedic Maths, Fractals). Written for 1114 year old pupils (some of the material in Books 1 and 2 is suitable for children from the age of about eight) this course covers the National Curriculum for England and Wales, but is also the perfect course for anyone who wants to develop a thorough understanding of Vedic Mathematics. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 1 deals mainly with basic arithmetic, proportion, decimals, basic algebra and geometry, polygons, area, volume etc. For detailed contents see the Expedient Learning Portal. CAT#376 Deluxe Quarto Hardcover Facsimile Edition. Maroon Suede w/Guilt Lettering. $45.00 

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The Cosmic Computer Course, Book 2. Kenneth R. Williams & Mark Gaskell 1998. 250+ Large P. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 2 extends this, covering fractions, probability, sequences, negative numbers, percentages, equations, graphs, charts, transformations, bearings, Vedic Maths, etc. For detailed contents see the Expedient Learning Portal. CAT#377 Deluxe Quarto Hardcover Facsimile Edition. Maroon Suede w/Guilt Lettering. $45.00 

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The Cosmic Computer Course, Book 3. Kenneth R. Williams & Mark Gaskell 1998. 250+ Large P. This full course consists of the Textbook, the Teacher's Guide and the Answer Book. Book 3 develops this further into recurring decimals, square and cube roots, division, divisibility, the musical scale, formulae, simultaneous equations, quadratic equations, proof, similar triangles, area of a circle, nets, conic sections, loci, motion, vectors, Pythagoras' theorem, triples, coordinate geometry, Vedic Maths, etc. For detailed contents see the Expedient Learning Portal. CAT#378 Deluxe Quarto Hardcover Facsimile Edition. Maroon Suede w/Guilt Lettering. $45.00 

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And Suddenly the Inventor Appeared: TRIZ, the Theory of Inventive Problem Solving. G. Altshuller (H. Altov) Translated by Lev Shulyak. 1990. 171P. This legendary book was first published in English in 1990. It is Altshuller's most popular book in Russia on how to become an inventor and how to solve technical problems. Originally written for high school students, it engages readers of all ages by inviting them to learn by doing. The translator, Lev Shulyak, is himself an accomplished inventor, engineer and TRIZ expert. About the Author: Genrich Altshuller received his first Soviet patent at the age of 14. While in his early 20s, he began developing TRIZ, the Theory of Inventive Problem Solving. Stalin rewarded him with 25 years imprisonment in Siberia. Released after Stalin’s death, he led the underground TRIZ revolution, a fundamental shift in the technical creativity paradigm. Altshuller spent the remainder of his life working to advance what has become the science of TRIZ. He died in 1998. The similarity between many of these techniques and Vedic Mathematics is striking, particularly considering that both authors developed their systems around the same time period. Technical Innovation Center. Paperback. CAT#383 $60.00 OUT OF STOCK 

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Astronomical Applications of Vedic Mathematics. Kenneth Williams 2004 139p. Contents: Introduction to Vedic Mathematics. Prediction of Eclipses: Prediction of the Times Of Contact of the Moon’s Penumbral and Umbral Shadows With the Earth. Partial Phase. Total Phase. Approximate Position of the Eclipse Path. Time of Total Eclipse For an Observer on Earth. Bessel’s Method, Early Eclipse Prediction, Solution of Eclipse Equation. Kepler’s Equation: A Transcendental Equation, Solution of Kepler’s Equation. Introduction to Triples: Notation & Combination, Triple Addition, Quadrant Triples, Rotations, Subtraction, HalfAngle Triple. Triple Code Numbers, Angles in Perfect Triples. Prediction of Planetary Positions: Heliocentric Position, Mean Anomaly, Geocentric Position, Geocentric Longitude, Geocentric Correction, Planet Finder. Spherical Triangles Using Triples: Triple Notation & Formulae for Spherical Trigonometry, Cosine Rule to Find an Angle, Sine Rule to Find Angle, Cotangent Rule to Find Angle, Polar Cosine Rule. Right Angled Spherical Triangles. Spherical Triangles Using Code Numbers. Determinants. Quadruples. Addition of Perpendicular Triples, Rotation About A Coordinate Axis. Quadruples & Orbits, Inclination of Orbit, Angle Between Two Directions. Inclination of Planetary Orbits. Calculation of Radius Vector. CAT#394 $25.00 Motilal Banarsidass India 

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The Cosmic Calculator. Kenneth Williams & Mark Gaskell 3 Volumes, Teachers Guide, & Answer Book. This is cheaper paper edition of the Cosmic Computer published by Motilal Banarsidass & imported from India. Best suited for teacher’s use in a classroom setting with guide & answers in separate volume. Written for 1114 year old pupils (some of the material in Books 1 and 2 is suitable for children from the age of about eight) this course covers the National Curriculum for England and Wales. The full course consists of three Textbooks, one Teacher's Guide and one Answer Book for all 3 volumes. THE TEXT BOOKS Each of the three books has 27 chapters each of which is prefaced by an inspiring quote from a famous mathematician, philosopher etc. Also in each book there are historical notes which relate to the authors of the quotes, a list of Sutras and three other short but interesting sections (e.g. Pascal's Triangle, Fractals). Book 1 deals mainly with basic arithmetic, proportion, decimals, basic algebra and geometry, polygons, area, volume etc. Book 2 extends this, covering fractions, probability, sequences, negative numbers, percentages, equations, graphs, charts, transformations, bearings etc. Book 3 develops this further into recurring decimals, square and cube roots, division, divisibility, the musical scale, formulae, simultaneous equations, quadratic equations, proof, similar triangles, area of a circle, nets, conic sections, loci, motion, vectors, Pythagoras' theorem, triples, coordinate geometry etc. THE TEACHER'S GUIDE Contains A Summary of the book. A copy of the Unified Field Chart for that book. Notes on the content of the chapters advice, suggestions etc. Mental Tests (correlated with the books) and answers which allow earlier work to be regularly revised, give stimulating ideas relevant to the current lesson and which develop themes from earlier tests which may ultimately become the subject of a lesson. Extension Material and answers (about 16 per book) these consist of a 1 or 2sided sheet given to children who work fast and get ahead of the rest of the class. Many of these are also very suitable for work with a whole class. Revision Tests and Answers There is a revision test every 4 or 5 chapters. This includes a mental test of 10 questions. Games, Worksheets etc. THE ANSWER BOOK This contains answers to all exercises and other numbered questions in the text and should be available for pupils during lessons. Motilal Banarsidass India CAT#460 $75.00 

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Vedic Math Teachers Manual, Volume 1, Elementary. Kenneth Williams 2005. Contents:PREFACE;LESSON 1 COMPLETING THE WHOLE;Introduction The Ten Point Circle; Multiples of Ten; Deficiency from Ten; Deficiency and Completion Together Mental Addition; Completing the Whole; Columns of Figures; By Addition and By Subtraction; Subtracting Numbers Near a Base; LESSON 2 DOUBLING AND HALVING: Doubling; Multiplying by 4, 8 Halving; Splitting Numbers; Dividing by 4, 8; Extending your Tables; Multiplying by 5, 50, 25 Dividing by 5, 50, 25; Dividing by 5; Dividing by 50, 25; LESSON 3 DIGIT SUMS: Adding Digits; The Nine Point; Circle; Casting out Nines; Digit Sum Puzzles; More Digit Sum Puzzles; The Digit Sum Check Multiplication Check; The Vedic square; Patterns from the Vedic Square; Number Nine; LESSON 4 LEFT TO RIGHT: Addition: Left to Right; Multiplication: Left to Right; Doubling and Halving; Subtraction: Left to Right; Checking Subtraction Sums; More Subtractions; LESSON 5 ALL FROM 9 AND THE LAST FROM 10: All From 9 and the Last from 10; Subtraction Adding Zeros; One Less; One More; One Less Again; Money LESSON 6 NUMBER SPLITTING: Addition; Subtraction; Multiplication; Division; LESSON 7 BASE MULTIPLICATION: Times Tables; Numbers just Over Ten; Multiplication Table Patterns; Recurring Decimals; Numbers Close to 100; Mentally; Numbers Over 100 Mental Maths; Russian Peasant; Multiplication; Larger Numbers; Numbers Above the Base; Proportionately; Another Application of Proportionately; Multiplying Numbers near Different Bases; Squaring Numbers near a Base; A Summary. LESSON 8 CHECKING AND DIVISIBILITY Digit Sum Check for Division The First by the First and the Last by the Last The First by the First The Last by the Last Divisibility by 4 Divisibility by 11 Remainder after Division by 11 Another Digit Sum Check LESSON 9 BAR NUMBERS Removing Bar Numbers All from 9 and the Last from 10 Subtraction Creating Bar Numbers Using Bar Numbers LESSON 10 SPECIAL MULTIPLICATION Multiplication by 11 Carries Longer Numbers By One More than the One Before Multiplication by Nines The First by the First and the Last by the Last Using the Average Special Numbers Repeating Numbers Proportionately Disguises LESSON 11 GENERAL MULTIPLICATION Revision TwoFigure Numbers Carries Moving Multiplier Extension Multiplying Binomials Multiplying 3Figure Numbers Written Calculations LESSON 12 SQUARING Squaring Numbers that end in 5 Squaring Numbers Near 50 General Squaring The Duplex Number Splitting Algebraic Squaring Digit Sums of squares Square Roots of Perfect Squares 3 and 4 Figure Numbers LESSON 13 EQUATIONS Onestep Equations Twostep Equations Threestep Equations LESSON 14 FRACTIONS Vertically and Crosswise A Simplification Comparing Fractions Unification of Operations LESSON 15 SPECIAL DIVISION Division by 9 Longer Numbers Carries A Short Cut Division by 8 etc. Division by 99, 98 etc. Divisor Below a Base Number TwoFigure answers Divisor Above a Base Number LESSON 16 THE CROWNING GEM Single Figure on the Flag Short Division Digression Longer Numbers Negative Flag Digits Decimalising the Remainder; SUTRAS AND SUBSUTRAS;9POINT CIRCLES; REFERENCES;INDEX OF THE VEDIC FORMULAE;INDEX. CAT#468 $30.00 Motilal Banarsidass 

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Vedic Math Teachers Manual, Volume 2, Intermediate. Kenneth Williams 2005. Contents:PREFACE LESSON 1 Basic Devices Introduction Digit Sums Left to Right Addition Multiplication Advantages of left to Right Calcn Writing Left to Right Sums Checking Devices Subtraction Subtraction from Left to Right Checking Subtraction Sums LESSON 2 MORE BASIC DEVICES Number Splitting Addition 14 / Subtraction Multiplication 16 / Division All from 9 and the Last from 10 Subtraction from a Base Calculations Involving Money First Extension Second Extension Combining the Extensions Bar Numbers Advantages of Bar Numbers General Subtraction LESSON 3 SPECIAL METHODS Proportionately Doubling and Halving Extending the Multiplication Tables Multiplying by 5, 50, 25 All from 9 and the Last from 10: Multiplication Numbers just below 100 Geometrical Proof Algebraic Proof Other Bases Numbers above the Base One Number ABOVE and one below the Base Proportionately Multiplying Numbers near Different Bases Squaring Numbers near a Base Mental Calculations Special methods LESSON 4 BY ONE MORE THAN THE ONE BEFORE Special Multiplications Squaring Numbers that End in 5 A Variation Multiplication Summary Recurring Decimals Denominator Ending in 9 Proof A Short Cut Proportionately Longer Numerators LESSON 5 AUXILIARY FRACTIONS Auxiliary Fractions: First Type Denominators Ending in 8, 7, 6 Auxiliary Fractions: Second Type Denominators Ending in 1 Alternative Method Denominators Ending in 2, 3, 4 Working 2, 3 etc. Figures at a Time LESSON 6 VERTICALLY AND CROSSWISE Fractions Adding & Subtracting Fractions Proof A Simplification Comparing Fractions Multiplication and Division General Multiplication Revision Multiplying 2Figure Numbers Explanation Explanation of earlier special method The Digit Sum Check Multiplying 3Figure Numbers Moving Multiplier Algebraic Multiplications The Digit Sum Check ThreeFigure Numbers FourFigure Numbers Writing Left to Right Sums From Right to Left setting the sums out Using Bar Numbers LESSON 7 SQUARES AND SQUARE ROOTS General Squaring TwoFigure Numbers Number Splitting Algebraic Squaring Squaring Longer Numbers Written Calculations – Left to Right Written Calculations – Right to Left Square Roots of Perfect Squares LESSON 8 SPECIAL MULTIPLICATION METHODS Special Numbers Repeating Numbers Proportionately Disguises Using the Average PROOF Multiplication by Nines Multiplication by 11 Percentages Increasing Reducing LESSON 9 TRIPLES Definitions Triples for 45°, 30° and 60° Triple Addition Double Angle Variations of 3,4,5 Quadrant Angles Rotations LESSON 10 SPECIAL DIVISION Division by Nine Adding Digits A Short Cut Dividing by 8 Algebraic Division Dividing by 11, 12 etc. Larger Divisors Divisor just Below a Base A Simplification Divisor just Above a Base Proportionately LESSON 11 STRAIGHT DIVISION Single Figure on the Flag Short Division Digression Longer Numbers Multiplication Reversed Decimalising the Remainder Negative Flag Digits Larger Divisors ALGEBRAIC DIVISION LESSON 12 EQUATIONS Linear One x Term Two x Terms Quadratic Equations Simultaneous Equations By Addition and By Subtraction A Special Type General Method Another Special Type LESSON 13 APPLICATIONS OF TRIPLES Triple Subtraction Triple Geometry Angle Between Two Lines Half Angle Coordinate Geometry Gradients Circle Problems Length of Perpendicular LESSON 14 SQUARE ROOTS Squaring Square Root of a Perfect square Preamble TwoFigure Answer Reversing Squaring ThreeFigure Answer Reversing Squaring General Square Roots Changing the Divisor Heuristic Proof LESSON 15 DIVISIBILITY Elementary Parts The Ekadhika Osculation Explanation Testing Longer Numbers Other Divisors The Negative Osculator LESSON 16 COMBINED CALCULATIONS Algebraic Arithmetic Pythagoras Theorem SUTRAS AND SUBSUTRAS 9POINT CIRCLES REFERENCES INDEX OF THE VEDIC FORMULAE INDEX . CAT#469 $30.00 Motilal Banarsidass 

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Vedic Math Teachers Manual, Volume 3, Advanced. Kenneth Williams 2005. Contents:PREFACE LESSON 1 LEFT TO RIGHT CALCULATIONS 1.1 INTRODUCTION 1.2 ADDITION 1.3 MULTIPLICATION Advantages OF LEFT TO RIGHT CALCULATION 1.4 WRITING LEFT TO RIGHT SUMS 1.5 SUBTRACTION 1.6 DIGIT SUMS 1.7 CHECKING DEVICES CHECKING SUBTRACTION SUMS 1.8 ALL FROM 9 AND THE LAST FROM 10 1.8a SUBTRACTION FROM A BASE 1.8b BAR NUMBERS ADVANTAGES OF BAR NUMBERS 1.8c GENERAL SUBTRACTION LESSON 2 SPECIAL METHODS 2.1 MULTIPLICATION NEAR A BASE 2.1a Numbers just below the base 2.1.b Above the base 2.1c Above and below 2.1d Proportionately 2.1e With different bases 2.2 MENTAL CALCULATIONS 2.3 SPECIAL NUMBERS 2.3a Repeating numbers 2.3b Proportionately 2.3c Disguises 2.4 DIVISION BY NINE 2.4a Adding Digits 2.4b A Short Cut 2.4c Dividing by 8 2.4d Algebraic Division 2.4e Dividing by 11, 12 etc. LESSON 3 RECURRING DECIMALS 3.1 DENOMINATOR ENDING IN 9 3.2 A SHORT CUT 3.3 PROPORTIONATELY 3.4 LONGER NUMERATORS 3.5 DENOMINATORS ENDING IN 8, 7, 6 3.6 DENOMINATORS ENDING IN 1 3.7 DENOMINATORS ENDING IN 2, 3, 4 3.8 WORKING 2, 3 ETC. FIGURES AT A TIME LESSON 4 TRIPLES 4.1 Definitions 4.2 Triples for 45°, 30° and 60° 4.3 Triple Addition 4.4 Double Angle 4.5 Variations of 3,4,5 4.6 Quadrant Angles 4.7 Rotations LESSON 5 GENERAL MULTIPLICATION 5.1 TWOFigure Numbers Explanation/ The Digit Sum Check 5.2 Moving Multiplier 5.3 Algebraic PRODUCTS The Digit Sum Check 5.4 ThreeFigure Numbers 5.5 FourFigure Numbers 5.6 Writing Left to Right Sums 5.7 From Right to Left setting the sums out 5.8 Using Bar Numbers LESSON 6 SOLUTION OF EQUATIONS 6.1 TRANSPOSE AND APPLY 6.1a SIMPLE EQUATIONS 6.1b MORE THAN ONE X TERM 6.2 SIMULTANEOUS EQUATIONS 6.2a GENERAL SOLUTION 6.2b Special Types 6.3 QUADRATIC EQUATIONS 6.4 ONE IN RATIO THE OTHER ONE ZERO 6.5 MERGERS 6.6 WHEN THE SAMUCCAYA IS THE SAME IT IS ZERO 6.6a Samuccaya as a common factor 6.6b Samuccaya as the Product of the Independent Terms 6.6c Samuccaya as the Sum of the Denominators 6.6d Samuccaya as a Combination or Total Proof/ EXTENSION 6.6e other typeS 6.7 THE ULTIMATE AND TWICE THE PENULTIMATE 6.8 ONLY THE LAST TERMS 6.9 SUMMATION OF SERIES 6.10 FACTORISATION LESSON 7 SQUARES AND SQUARE ROOTS 7.1 Squaring 2FIGURE NUMBERS 7.2 Algebraic Squaring 7.3 Squaring Longer Numbers 7.4 Written Calculations 7.4a Left to Right 7.4b Right to Left 7.5 Square Roots of Perfect Squares LESSON 8 APPLICATIONS OF TRIPLES 8.1 Triple Subtraction 8.2 Triple Geometry 8.3 Angle Between Two Lines 8.4 Half Angle 8.5 Coordinate Geometry 8.5a Gradients 8.5b Length of Perpendicular 8.5c Circle Problems 8.5d EQUATION OF A LINE 8.6 COMPLEX NUMBERS CONTENTS LESSON 9 DIVISIBILITY 9.1 Elementary Parts 9.2 The Ekadhika 9.3 Osculation Explanation 9.4 Testing Longer Numbers 9.5 Other Divisors 9.6 The Negative Osculator 9.7 OSCULATING WITH GROUPS OF DIGITS LESSON 10 STRAIGHT DIVISION 10.1 Single Figure on the Flag 10.2 Short Division Digression 10.3 Longer Numbers Multiplication Reversed 10.4 Decimalising the Remainder 10.5 Negative Flag Digits 10.6 Larger Divisors 10.7 ALGEBRAIC DIVISION LESSON 11 SQUARE ROOTS 11.1 Squaring 11.2 Square Root of a Perfect square 11.2a Preamble 11.2b TwoFigure Answer Reversing Squaring 11.2c ThreeFigure Answer Reversing Squaring 11.3 General Square Roots 11.4 Changing the Divisor Heuristic Proof 11.5 ALGEBRAIC SQUARE ROOTS LESSON 12 TRIPLE TRIGONOMETRY 12.1 COMPOUND ANGLES 12.2 INVERSE FUNCTIONS 12.3 THE GENERAL TRIPLE 12.4 TRIGONOMETRIC EQUATIONS 12.4a SIMPLE EQUATIONS 12.4b A SPECIAL TYPE LESSON 13 COMBINED OPERATIONS 13.1 Algebraic 13.2 Arithmetic 13.2a SUMS OF PRODUCTS 13.2b ADDITION AND DIVISION 13.2c STRAIGHT DIVISION 13.2d MEAN AND MEAN DEVIATION 13.2e DIVIDING SUMS OF PRODUCTS 13,2f VARIANCE 13.3 Pythagoras’ Theorem LESSON 14 SOLUTION OF POLYNOMIAL EQUATIONS 14.1 QUADRATIC EQUATIONS 14.1a x > 1 PROOF 14.1b x < –1 14.1c 0 < x < 1 14.1d 0 < x < 1 and x2 Coefficient > 1 14.1e –1 < x < 0 14.1f x LARGE 14.2 HIGHER ORDER EQUATIONS 14.2a CUBE ROOT 14.2b CUBIC EQUATIONS A SIMPLIFICATION A CUBIC WITH 0 < x < 1 14.2c QUINTICS LESSON 15 CALCULUS METHODS 15.1 Partial Fractions 15.2 Integration by ‘Parts’ TRUNCATING 15.3 BINOMIAL AND MACLAURIN THEOREMS 15.4 Derivatives of a Product 15.5 Derivative of A Quotient 15.6 Differential Equations – 1 15.7 Differential Equations – 2 15.8 Limits 220 LESSON 16 APPLIED MATHEMATICS 16.1 SIMPLE HARMONIC MOTION 16.2 PROJECTILES 16.3 FORCES IN EQUILIBRIUM 16.4 WORK AND MOMENT LESSON 17 TRIGONOMETRIC FUNCTIONS 17.1 DERIVATIVES 17.2 SERIES EXPANSIONS 17.3 INVERSE TRIGONOMETRIC FUNCTIONS 17.3a DERIVATIVES 17.3b SERIES 17.4 EVALUATING TRIGONOMETRIC FUNCTIONS 17.4a COSINE 17.4b SINE 17.4c INVERSE TANGENT LESSON 18 TRIGONOMETRIC AND TRANSCENDENTAL EQUATIONS 18.1 POLYNOMIAL EQUATIONS 18.2 TRIGONOMETRIC EQUATIONS 18.3 TRANSCENDENTAL EQUATIONS KEPLER’S EQUATION REFERENCES SUTRAS AND SUBSUTRAS INDEX OF THE VEDIC FORMULAE INDEX. CAT#470 $30.00 Motilal Banarsidass 

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