##### Document Text Contents

Page 1

3

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

Page 2

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

Page 109

111

etc. Some teachers ask them to recite it individually; They

feel so shy to pronounce meaningless Sanskrit words which

is difficult to run smoothly through their mouth. For this act

they become a laughing stock in the class and the Vedic

Mathematics teachers take it as an insult and doubly punish

the children.”

11. Some of the uneducated and not-so-literate parents said,

“after all my son is going to become a computer engineer,

how is this sutra in Sanskrit going to help him?” The

children say that the mathematical content is elementary

arithmetic of primary level. One lady said, “they waste our

money and our children’s time by these Vedic Mathematics

classes” though she has only studied up to 5th standard. The

questions she put to us about Vedic Mathematics was very

pertinent. She laughed and said, “in temples they blabber

something like this and get money, that too like beggars in a

plate; now they have started to come to this school and get

money in hundreds by saying some meaningless sutras.”

She further added that she was happy because her second

son is studying in a Convent. She says in that school no

such sloka-stuff is taught. Only after enquiring this, she put

him in a different school. She says only Hindu schools teach

Vedic Mathematics. Convents and Corporation schools or

Government-run schools do not teach Vedic Mathematics.

She says “I am uneducated. I want my children to get good

education.” She asked us, “Why is Vedic Mathematics

having slokas? Are they training them as temple priests?”

We have put this mainly to show how even uneducated

parents take interest in their children’s education!

12. Most of the parents said Vedic Mathematics teachers do not

have tolerance or patience, they easily punish children for

very simple things like laughing or not concentrating or

attentive in the class by looking at the teachers. Only this

atmosphere made the classes noisy, uncontrollable and

unruly. The Vedic Mathematics teachers do not appear to be

well-trained teachers. Some ask the students in Vedic

Page 110

112

Mathematics classes whether they take bath daily and so on

which is irrelevant, apart from being too personal.

13. Some parents said Vedic Mathematics teachers speak of

epics and characters like Mahabaratha’s ‘Kamsa’ and so on.

They feel a mathematics class cannot have place for epics;

why Krishna or Kamsa should come while teaching

mathematics? One may adore Krishna, some other person

may worship Kamsa it is after all individual freedom,

choice and taste! No one should preach Hinduism in

Mathematics class because there are Christian and Muslim

boys who might feel offended! Also some teachers gave

long lecture on Vedas and Vedic tradition, which they

consider as the high heritage of Indians. Some parents said,

“Are not Christians and Muslims living in India; Indians?

Why did they become or converted to Christianity and

Islam? They were humiliated and treated worse than

animals by the Brahmins so to live and lead a life of self

respect they sought Christianity or Islam.” Some parents

asked us, “if alone Christians and Muslims had not entered

India; can ever a non-Brahmin dream of education?” They

felt Vedic Mathematics was imposing brahminism i.e.,

casteism on children so they strongly objected to it. Some

parents had already changed the school (and many had

plans for changing their wards to a different school) because

they felt it was unbearable to impose “Hindutva” in the

name of Vedic Mathematics. (Several other charges were

made which we have not given fully).

14. Vedic Mathematics classes had become the seed of

discrimination on the basis of caste in schools! This was a

view shared by non-Brahmin parents.

15. A tiny section of the educated parents said they have read

the book on Vedic Mathematics and they had found it very

elementary. Yet they felt that it was a powerful means of

establishing the supremacy of the Aryans over the entire

world. We wonder why they need mathematics to do this

dirty trade?

Page 217

219

U

rdhva – tiryagbhy m, 11, 19

V

Vestanam, 11

Vilokanam, 11

Vyastisamastih, 11, 23

W

Weighted NRM, 88

Y

Y vad nam T vad nam, 11

Y vad nam T vad n krtya Varga ca Yojayet, 11, 23

Y vad nam, 11, 23

Page 218

220

ABOUT THE AUTHORS

Dr.W.B.Vasantha Kandasamy is an Associate Professor in the

Department of Mathematics, Indian Institute of Technology

Madras, Chennai. In the past decade she has guided 11 Ph.D.

scholars in the different fields of non-associative algebras,

algebraic coding theory, transportation theory, fuzzy groups, and

applications of fuzzy theory of the problems faced in chemical

industries and cement industries. Currently, four Ph.D. scholars

are working under her guidance.

She has to her credit 636 rese arch papers. She has guided

over 51 M.Sc. and M.Tech. projects. She has worked in

collaboration projects with the Indian Space Research

Organization and with the Tamil Nadu State AIDS Control Society.

This is her 29 th book.

On India's 60th Independen ce Day, Dr.Vasantha was

conferred the Kalpana Chawla Award for Courage and Daring

Enterprise by the State Government of Tamil Nadu in recognition

of her sustained fight for social justice in the Indian Institute of

Technology (IIT) Madras and for her contribution to mathematics.

(The award, instituted in the memory of Indian-American

astronaut Kalpana Chawla who died aboard Space Shuttle

Columbia). The award carried a cash prize of five lakh rupees (the

highest prize-money for any Indian award) and a gold medal.

She can be contacted at [email protected]

You can visit her on the web at: http://mat.iitm.ac.in/~wbv or:

http://www.vasantha.net

Dr. Florentin Smarandache is an Associate Professor of

Mathematics at the University of New Mexico in USA. He

published over 75 books and 100 articles and notes in

mathematics, physics, philosophy, psychology, literature, rebus.

In mathematics his research is in number theory, non-Euclidean

geometry, synthetic geometry, algebraic structures, statistics,

neutrosophic logic and set (genera lizations of fuzzy logic and set

respectively), neutrosophic probab ility (generalization of classical

and imprecise probability). Also, small contributions to nuclear

and particle physics, information fusion, neutrosophy (a

generalization of dialectics), law of sensations and stimuli, etc.

He can be contacted at [email protected]

3

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

Page 2

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

Page 109

111

etc. Some teachers ask them to recite it individually; They

feel so shy to pronounce meaningless Sanskrit words which

is difficult to run smoothly through their mouth. For this act

they become a laughing stock in the class and the Vedic

Mathematics teachers take it as an insult and doubly punish

the children.”

11. Some of the uneducated and not-so-literate parents said,

“after all my son is going to become a computer engineer,

how is this sutra in Sanskrit going to help him?” The

children say that the mathematical content is elementary

arithmetic of primary level. One lady said, “they waste our

money and our children’s time by these Vedic Mathematics

classes” though she has only studied up to 5th standard. The

questions she put to us about Vedic Mathematics was very

pertinent. She laughed and said, “in temples they blabber

something like this and get money, that too like beggars in a

plate; now they have started to come to this school and get

money in hundreds by saying some meaningless sutras.”

She further added that she was happy because her second

son is studying in a Convent. She says in that school no

such sloka-stuff is taught. Only after enquiring this, she put

him in a different school. She says only Hindu schools teach

Vedic Mathematics. Convents and Corporation schools or

Government-run schools do not teach Vedic Mathematics.

She says “I am uneducated. I want my children to get good

education.” She asked us, “Why is Vedic Mathematics

having slokas? Are they training them as temple priests?”

We have put this mainly to show how even uneducated

parents take interest in their children’s education!

12. Most of the parents said Vedic Mathematics teachers do not

have tolerance or patience, they easily punish children for

very simple things like laughing or not concentrating or

attentive in the class by looking at the teachers. Only this

atmosphere made the classes noisy, uncontrollable and

unruly. The Vedic Mathematics teachers do not appear to be

well-trained teachers. Some ask the students in Vedic

Page 110

112

Mathematics classes whether they take bath daily and so on

which is irrelevant, apart from being too personal.

13. Some parents said Vedic Mathematics teachers speak of

epics and characters like Mahabaratha’s ‘Kamsa’ and so on.

They feel a mathematics class cannot have place for epics;

why Krishna or Kamsa should come while teaching

mathematics? One may adore Krishna, some other person

may worship Kamsa it is after all individual freedom,

choice and taste! No one should preach Hinduism in

Mathematics class because there are Christian and Muslim

boys who might feel offended! Also some teachers gave

long lecture on Vedas and Vedic tradition, which they

consider as the high heritage of Indians. Some parents said,

“Are not Christians and Muslims living in India; Indians?

Why did they become or converted to Christianity and

Islam? They were humiliated and treated worse than

animals by the Brahmins so to live and lead a life of self

respect they sought Christianity or Islam.” Some parents

asked us, “if alone Christians and Muslims had not entered

India; can ever a non-Brahmin dream of education?” They

felt Vedic Mathematics was imposing brahminism i.e.,

casteism on children so they strongly objected to it. Some

parents had already changed the school (and many had

plans for changing their wards to a different school) because

they felt it was unbearable to impose “Hindutva” in the

name of Vedic Mathematics. (Several other charges were

made which we have not given fully).

14. Vedic Mathematics classes had become the seed of

discrimination on the basis of caste in schools! This was a

view shared by non-Brahmin parents.

15. A tiny section of the educated parents said they have read

the book on Vedic Mathematics and they had found it very

elementary. Yet they felt that it was a powerful means of

establishing the supremacy of the Aryans over the entire

world. We wonder why they need mathematics to do this

dirty trade?

Page 217

219

U

rdhva – tiryagbhy m, 11, 19

V

Vestanam, 11

Vilokanam, 11

Vyastisamastih, 11, 23

W

Weighted NRM, 88

Y

Y vad nam T vad nam, 11

Y vad nam T vad n krtya Varga ca Yojayet, 11, 23

Y vad nam, 11, 23

Page 218

220

ABOUT THE AUTHORS

Dr.W.B.Vasantha Kandasamy is an Associate Professor in the

Department of Mathematics, Indian Institute of Technology

Madras, Chennai. In the past decade she has guided 11 Ph.D.

scholars in the different fields of non-associative algebras,

algebraic coding theory, transportation theory, fuzzy groups, and

applications of fuzzy theory of the problems faced in chemical

industries and cement industries. Currently, four Ph.D. scholars

are working under her guidance.

She has to her credit 636 rese arch papers. She has guided

over 51 M.Sc. and M.Tech. projects. She has worked in

collaboration projects with the Indian Space Research

Organization and with the Tamil Nadu State AIDS Control Society.

This is her 29 th book.

On India's 60th Independen ce Day, Dr.Vasantha was

conferred the Kalpana Chawla Award for Courage and Daring

Enterprise by the State Government of Tamil Nadu in recognition

of her sustained fight for social justice in the Indian Institute of

Technology (IIT) Madras and for her contribution to mathematics.

(The award, instituted in the memory of Indian-American

astronaut Kalpana Chawla who died aboard Space Shuttle

Columbia). The award carried a cash prize of five lakh rupees (the

highest prize-money for any Indian award) and a gold medal.

She can be contacted at [email protected]

You can visit her on the web at: http://mat.iitm.ac.in/~wbv or:

http://www.vasantha.net

Dr. Florentin Smarandache is an Associate Professor of

Mathematics at the University of New Mexico in USA. He

published over 75 books and 100 articles and notes in

mathematics, physics, philosophy, psychology, literature, rebus.

In mathematics his research is in number theory, non-Euclidean

geometry, synthetic geometry, algebraic structures, statistics,

neutrosophic logic and set (genera lizations of fuzzy logic and set

respectively), neutrosophic probab ility (generalization of classical

and imprecise probability). Also, small contributions to nuclear

and particle physics, information fusion, neutrosophy (a

generalization of dialectics), law of sensations and stimuli, etc.

He can be contacted at [email protected]