Please find below a range of free books on the subject of Vedic Mathematics.
N.B. these books are mostly in English, except for the "Vedic Mathematics Teacher's Manual - Elementary Level", which has been translated into six languages (See Book tab).
A good free introductory ebook in Spanish can be found here.
[We would like to point that when searching for free material on Vedic Mathematics, you may need to be cautious, as we found that often the material would not be provided unless you carried out one of the following:-
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N.B. for the last option we often found Adobe Acrobat books with file names like "<Book Title>.pdf.exe". The ".exe" implying installation of a program on your computer which is not necessary for a document to be readable by the Adobe Acrobat reader i.e. file names should just end with ".pdf". From our point of view, the best situation you can end up with is receiving spam email etc, with the worst scenario's being someone using your credit card or having virus's or spyware installed onto your computer. It should be noted that the above requirements are completely unnecessary to make material available for free and imply some non monetary cost to yourself.]
The free books available below are all simple Adobe Acrobat PDF documents.
We only ask that you do not upload them to any other place on the Internet without consulting us first (and where the document is hosted on another website, please consult with the original author first).
Vedic Mathematics Teacher's Manual - Elementary Level
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
TWO-FIGURE NUMBERS
CARRIES
MOVING MULTIPLIER
EXTENSION
MULTIPLYING BINOMIALS
MULTIPLYING 3-FIGURE 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
ONE-STEP EQUATIONS
TWO-STEP EQUATIONS
THREE-STEP 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
TWO-FIGURE 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 SUB-SUTRAS
9-POINT CIRCLES
REFERENCES
INDEX OF THE VEDIC FORMULAE
INDEX
Description
This book is designed for teachers of children in grades 3 to 7. It shows how Vedic Mathematics can be used in a school course but does not cover all school topics (see contents). The book can be used for teachers who wish to learn the Vedic system or to teach courses on Vedic mathematics for this level.
The Manual contains many topics that are not in the other Manuals that are suitable for this age range and many topics that are also in Manual 2 are covered in greater detail here.
Book
ENGLISH version
Homework exercises for Manual 1 (extracted from the book) - (click below)
Full solutions to the exercises for Manual 1 (click below)
HINDI version (click below)
GERMAN version (click below)
FRENCH Translation (click below)
ROMANIAN Translation (click below)
TAMIL Translation (click below)
JAPANESE Translation (click below)
Japanese Workbook (click below)
NORWEGIAN Translation (click below)
Vertically and Crosswise
Contents
Preface
Preface to 'Vedic Mathematics'
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 CURVE-FITTING
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 NON-LINEAR DIFFERENTIAL, INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS
16 THE SOLUTION OF LINEAR AND NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS
Description
This is an advanced book of sixteen chapters on one Sutra ranging from elementary multiplication etc. to the solution of non-linear 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.
GEOMETRY FOR AN ORAL TRADITION
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
Part 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
Description
This book demonstrates the kind of system that could have existed before literacy was widespread and takes us from first principles to theorems on elementary properties of circles. It presents direct, immediate and easily understood proofs. These 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 recognise valid reasoning). It includes discussion on the relevant philosophy of mathematics and is written both for mathematicians and for a wider audience.
INTRODUCTORY LECTURES ON VEDIC MATHEMATICS
Details
Authors: A. P. Nicholas, J. Pickles, K. Williams, 1982.
Paperback, 166 pages, A4 size.
Currently out of print.
Contents
Chapter 8 is on Addition. Chapter 9 is on Subtraction and combined addition and subtraction.
FREE PRACTICE SHEETS (& Sutras list etc.)
Mental Math Workouts
Vedic Math Genius
Free books Hosted on other websites
Fundamentals & Applications of Vedic Mathematics
Details
Published by : State Council of Educational Research & Training, New Delhi
and printed at
Educational Stores, S-5, Bsr. Road Ind. Area, Ghaziabad (U.P.)
Varun Marg, Defence Colony, New Delhi-110024
Chief Advisor
Anita Satia Director, SCERT
Guidance
Dr. Pratibha Sharma,
Joint Director, SCERT
Contributors
Dr. Anil Kumar Teotia (Sr. Lecturer, DIET Dilshad Garden)
Neelam Kapoor (Retired PGT, Directorate of Education)
Chander Kanta Chabria (PGT, RPVV Tyagraj Nagar, Lodhi Road)
Rekha Jolly (TGT, RPVV Vasant Kunj)
Dr. Satyavir Singh (Principal SNI College Pilana)
Editor
Dr. Anil Kumar Teotia
Sr. Lecturer, DIET Dilshad Garden
Publication Officer
Ms. Sapna Yadav
Publication Team
Navin Kumar, Ms. Radha, Jai Baghwan
Pages 65
Contents
Preface 03-04
Introduction 07-11
Chapter-1 Addition and Subtraction 12-24
1. Addition - Completing the whole
2. Addition from left to right
3. Addition of list of numbers - Shudh method
4. Subtraction - Base method
5. Subtraction - Completing the whole
6. Subtraction from left to right
Chapter-2 Digit Sums, Casting out 9s, 9-Check Method 25-28
Chapter-3 11-Check method 29-31
Chapter-4 Special Multiplication methods 32-52
1. Base Method
2. Sub Base Method
3. Vinculum
4. Multiplication of complimentary numbers
5. Multiplication by numbers consisting of all 9s
6. Multiplication by 11
7. Multiplication by two-digit numbers from right to left
8. Multiplication by three and four-digit numbers from right to left.
Chapter-5 Squaring and square Roots 53-57
Squaring
1. Squaring numbers ending in 5
2. Squaring Decimals and Fraction
3. Squaring Numbers Near 50
4. Squaring numbers near a Base and Sub Base
5. General method of Squaring - from left to right
6. Number splitting to simplify Squaring Calculation
7. Algebraic Squaring
Square Roots
1. Reverse squaring to find Square Root of Numbers ending in 25
2. Square root of perfect squares
3. General method of Square Roots
Chapter-6 Division 58-64
1. Special methods of Division
2. Straight Division
Vedic Math Presentation
Vedic Mathematics
Vedic Mathematics Methods
Contents
Vedic Mathematics - Methods
Preface 1
I. Why Vedic Mathematics? 3
II. Vedic Mathematical Formulae 5
1. Ekadhikena Purvena 7
2. Nikhilam navatascaramam Dasatah 18
3. Urdhva - tiryagbhyam 31
4. Paravartya Yojayet 41
5. Sunyam Samya Samuccaye 53
6. Anurupye - Sunyamanyat 64
7. Sankalana - Vyavakalanabhyam 65
8. Puranapuranabhyam 67
9. Calana - Kalanabhyam 68
10. Ekanyunena Purvena 69
11. Anurupyena 75
12. Adyamadyenantya - mantyena 82
13. Yavadunam Tavadunikrtya Varganca Yojayet 86
14. Antyayor Dasakepi 93
15. Antyayoreva 96
16. Lopana Sthapanabhyam 101
17. Vilokanam 106
18. Gunita Samuccayah : Samuccaya Gunitah 113
III Vedic Mathematics - A briefing 115
1. Terms and Operations 116
2. Addition and Subtraction 130
3. Multiplication 139
4. Division 144
5. Miscellaneous Items 151
IV Conclusion 158
Vedic Mathematical Concepts and Their Application
to Unsolved Mathematical Problems:
Three Proofs of Fermat's Last Theorem
MAHARISHI'S VEDIC MATHEMATICS AT THE ELEMENTARY LEVEL
Details
Author John M Muehlman, 1993.
Publisher: Dissertation Information Service
Pages 72 (although pages are numbered from 36 for some reason)
ASIN: B0006PAVSA
Contents
Introduction 39
Maharishi's Description of the Veda 41
Self-Interacting Dynamics of Consciousness 41
Laws of Nature 42
Pure Knowledge and Infinite Organizing Power 43
Development of Consciousness through MaharishiÕs Vedic Technologies 43
Experience of Pure Consciousness 45
Higher States of Consciousness 47
Nature of All Knowingness in MaharishiÕs Teaching 49
Infinite Correlation 49
Principle of Least Action 50
Mathematics Without Steps 50
Introduction to Vedic Sªtra Based Computation 55
Literature Review on Characteristics of Vedic Sªtra Based Computation
Relevant to the Experimental Study 61
Efficient Algorithms and Ease of Learning 61
Flexible Format 62
Conducive to Mental Computation 63
Upsurges of Joy 63
Pilot Research on Vedic Sªtra Based Computation 63
Pilot Study Number One 63
Pilot Study Number Two 64
Pilot Study Number Three 65
An Experimental Study on Vedic Sªtra Based Multiplication and Checking 69
Subjects and Setting 69
Overview of the Curricula 70
Comparison of the Algorithms 71
Instruments Used to Evaluate Hypotheses 75
Design 76
Discussion of Results from the Study 76
Hypothesis One: Multiplication Skill 77
Hypothesis Two: Checking Skill 80
Hypothesis Three: Multiplication and Checking Affect 81
Hypothesis Four: Mental Mathematics 86
Extension of Results to Explain Possible Growth in the Direction of
All Knowingness 87
Appendix: Review of Additional Characteristics of a Full Vedic Sªtra Based
Computation Program 90
Vedic Mathematics: Vedic or Mathematics: A Fuzzy and Neutrosophic Analysis
Details
W. B. Vasantha Kandasamy (Author)
Florentin Smarandache (Author)
Meena Kandasamy (Illustrator)
Perfect Paperback: 220 pages
Publisher: Automaton; 1 edition (December 5, 2006)
Language: English
ISBN-10: 1599730049
ISBN-13: 978-1599730042
Product Dimensions: 8.7 x 6 x 0.5 inches
Contents
Preface 5
Chapter One
INTRODUCTION TO VEDIC MATHEMATICS 9
Chapter Two
ANALYSIS OF VEDIC MATHEMATICS BY MATHEMATICIANS AND OTHERS 31
2.1 Views of Prof. S.G.Dani about Vedic
Mathematics from Frontline 33
2.2 Neither Vedic Nor Mathematics 50
2.3 Views about the Book in Favour and Against 55
2.4 Vedas: Repositories of Ancient Indian Lore 58
2.5 A Rational Approach to Study Ancient Literature 59
2.6 Shanghai Rankings and Indian Universities 60
2.7 Conclusions derived on Vedic Mathematics and the
Calculations of Guru Tirthaji - Secrets of
Ancient Maths 61
Chapter Three
INTRODUCTION TO BASIC CONCEPTS AND A NEW FUZZY MODEL 65
3.1 Introduction to FCM and the Working of this Model 65
3.2 Definition and Illustration of
Fuzzy Relational Maps (FRMS) 72
3.3 Definition of the New Fuzzy Dynamical System 77 4
3.4 Neutrosophic Cognitive Maps with Examples 78
3.5 Description of Neutrosophic Relational Maps 87
3.6 Description of the new Fuzzy Neutrosophic model 92
Chapter Four
MATHEMATICAL ANALYSIS OF THE VIEWS ABOUT VEDIC MATHEMATICS USING FUZZY MODELS 95
4.1 Views of students about the use of Vedic
Mathematics in their curriculum 97
4.2 Teachers views on Vedic Mathematics and
its overall influence on the Students Community 101
4.3 Views of Parents about Vedic Mathematics 109
4.4 Views of Educationalists about Vedic Mathematics 114
4.5 Views of the Public about Vedic Mathematics 122
Chapter Five
OBSERVATIONS 165
5.1 Students’ Views 165
5.2 Views of Teachers 169
5.3 Views of Parents 180
5.4 Views of the Educated 182
5.5 Observations from the Views of the Public 193
REFERENCE 197
INDEX 215
ABOUT THE AUTHORS 220
Description
The Vedas are considered divine in origin and are assumed to be revelations from God. In traditional Hinduism, the Vedas were to be learnt only by the upper caste Hindus. The lower castes (Sudras) and so-called untouchables (who were outside the Hindu social order) were forbidden from even hearing to its recitation. In recent years, there have been claims that the Vedas contain the cure to AIDS and the production of electricity. Here the authors probe into Vedic Mathematics (that gained renown during the revivalist Hindutva rule in India and was introduced into school syllabus in several states); and explore if it is really Vedic in origin or Mathematics in content. To gain a better understanding of its imposition, we interviewed students, teachers, parents, educationists and activists. We analyze this problem using models like Fuzzy Cognitive Maps (FCM), Fuzzy Relational Maps (FRM) and newly constructed Fuzzy Dynamical System (and their Neutrosophic Analogues). The issue of imposition of Vedic Mathematics into the school curriculum involves religious politics, caste supremacy, apart from elementary arithmetic so we use fuzzy and neutrosophic techniques to gain acute insight into how students have been affected because of this politically motivated syllabus revision.
Our Comments
We believe this paper was a reaction by some in the academic community to certain elements of the Hindu community trying to use Vedic Mathematics to promote Hinduism by teaching Vedic Mathematics in schools. It is our understanding that much of this initial teaching of Vedic Mathematics may have been implemented poorly by people who did not have a good grounding in their subject matter as they may have been more interested in promoting Hinduism than Vedic Mathematics, hence the academic reaction.
This paper was produced in 2006 and often appears in searches for Vedic Mathematics. The understanding and teaching of Vedic Mathematics has moved on a lot since this point in time.
