Free

Please find below a range of free books on the subject of Vedic Mathematics.

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:-

  • Provide your email address
  • Have to sign up to one of several offers
  • Provide your credit card details to verify your identity
  • Required to install a program to make the book available

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

Cover

Details

K R Williams
Pages 173-4 (depending on translation)
ISBN 978-1-902517-16-2

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

Hindi version

German version

French Translation

Romanian Translation

 Vertically and Crosswise

Cover

Details

169 + xii pages.
Author: A. P. Nicholas, K. R. Williams, J Pickles
ISBN 978-1-902517-21-6.

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.

Book

GEOMETRY FOR AN ORAL TRADITION

Cover

Details

Author: A. P. Nicholas, 1999. Paperback.
132 pages, A4 size.
ISBN 1 902517 05 9

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.

Book

INTRODUCTORY LECTURES ON VEDIC MATHEMATICS

Cover

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.

Description

Following various lecture courses in London an interest arose for printed material containing the course material. This book of 12 chapters was the result covering a range topics from elementary arithmetic to cubic equations.

Book

Chapters 8 and 9

Free Practice Sheets (& Sutras list etc.)

Details

These worksheets are designed for use with the DVD Basic Course, anyone is welcome to download and use them.
Answers are given at the end of each sheet.

 

Free books Hosted on other websites

 

Vedic Mathematical Concepts and Their Application
to Unsolved Mathematical Problems:
Three Proofs of Fermat's Last Theorem

Details

Author: S.K. Kapoor
Pages 30

Book

This document is hosted on the Maharishi University of Management website.

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

Description

Improving achievement, affect, and mental mathematics through Vedic sutra based computation

Book

This document is hosted on the Maharishi University of Management website.

Vedic Mathematics: Vedic or Mathematics: A Fuzzy and Neutrosophic Analysis

Cover

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

Amazon UK Kindle Link

Amazon US Kindle Link

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.

Book

Hosted on the University of New Mexico (Gallup's branch campus) website

Hosted on Cornell University Libraries website

 

GTranslate

English Chinese (Traditional) Dutch Finnish French German Hindi Korean Russian Ukrainian