nterest
in Vedic maths is growing in the field of education where math’s
teachers are looking for a new and better approach to the subject. Even
students at IIT (Indian Institute of Technology) are said to be using
this ancient technique for quick calculations. No wonder, a recent Convocation
speech addressed to the students of IIT, Delhi, Indian Minister for
Science & Technology, stressed the significance of Vedic math’s,
while pointing out the important contributions of ancient Indian
mathematicians, such as Aryabhatta, who laid the foundations
of algebra, Baudhayan, the great geometer, and Medhatithi and Madhyatithi,
the saint duo, who formulated the basic framework for numerals.
Few of Vedic examples (The Magic of Vedas)
SUTRA  MEANING  
1  Ekadhikina Purvena  By one more than the previous one 
COROLLARY: Anurupyena  
2  Nikhilam Navatashcaramam Dashatah  All from 9 and the last from 10 
COROLLARY: Sisyate Sesasamjnah  
3  UrdhvaTiryagbyham  Vertically and crosswise 
COR: Adyamadyenantyamantyena  
4  Paraavartya Yojayet  Transpose and adjust 
COR: Kevalaih Saptakam Gunyat  
5  Shunyam Saamyasamuccaye  When the sum is the same that sum is zero. 
COROLLARY: Vestanam  
6  (Anurupye) Shunyamanyat  Sankalanavyavakalanabhyam 
COROLLARY: Yavadunam Tavadunam  
7  Sankalanavyavakalanabhyam  By addition and by subtraction 
COR: Yavadunam Tavadunikritya Varga Yojayet  
8  Puranapuranabyham  By the completion or noncompletion 
COROLLARY: Antyayordashake'pi  
9  ChalanaKalanabyham  Differences and Similarities 
COROLLARY: Antyayoreva  
10  Yaavadunam  Whatever the extent of its deficiency 
COROLLARY: Samuccayagunitah  
11  Vyashtisamanstih  Part and Whole 
COROLLARY: Lopanasthapanabhyam  
12  Shesanyankena Charamena  The remainders by the last digit 
COROLLARY: Vilokanam  
13  Sopaantyadvayamantyam  The ultimate and twice the penultimate 
COR: Gunitasamuccayah Samuccayagunitah  
14  Ekanyunena Purvena  By one less than the previous one 
COROLLARY: Dhvajanka  
15  Gunitasamuchyah  The product of the sum is equal to the sum of the product 
COROLLARY: Dwandwa Yoga  
16  Gunakasamuchyah  The factors of the sum is equal to the sum of the factors 
COROLLARY: Adyam Antyam Madhyam 
1  EKADHIKENA PURVENA The Sutra (formula) Ekadhikena Purvena means: “By one more than the previous one”. 
i)
Squares of numbers ending in 5 :
Now we relate the sutra to the ‘squaring of numbers ending
in 5’. Consider the example 252.
Here the number is 25. We have to find out the square of the number.
For the number 25, the last digit is 5 and the 'previous' digit
is 2. Hence, 'one more than the previous one', that is, 2+1=3.
The Sutra, in this context, gives the procedure 'to multiply the
previous digit 2 by one more than itself, that is, by 3'. It becomes
the L.H.S (left hand side) of the result, that is, 2 X 3 = 6.
The R.H.S (right hand side) of the result is 52, that is, 25.


Thus:  25^{2} = 2 X 3 / 25 = 625.  
In the same way,  
35^{2}= 3 X (3+1) /25 = 3 X 4/ 25 = 1225;  
65^{2}= 6 X 7 / 25 = 4225;  
105^{2}= 10 X 11/25 = 11025;  
135^{2}= 13 X 14/25 = 18225;  
Algebraic proof:  
a) Consider (ax + b)^{2} ? a^{2}. x^{2} + 2abx + b^{2}.  
This identity for x = 10 and b = 5 becomes  
(10a + 5)^{2} = a^{2} . 10^{2} + 2. 10a . 5 + 5^{2}  
= a^{2} . 10^{2} + a. 10^{2} + 5^{2}  
= (a ^{2}+ a ) . 10^{2} + 5^{2}  
= a (a + 1) . 10^{2} + 25.  
Clearly 10a + 5 represents twodigit numbers 15, 25, 35, ,95 for the values a = 1, 2, 3, ,9 respectively. In such a case the number (10a + 5)^{2} is of the form whose L.H.S is a (a + 1) and R.H.S is 25, that is, a (a + 1) / 25.  
Thus any such two digit number gives the result in the same fashion.  
Example:
45 = (40 + 5)^{2}, It is of the form (ax+b)^{2}
for a = 4, x=10 and b = 5. giving the answer a (a+1) / 25 that is, 4 (4+1) / 25 + 4 X 5 / 25 = 2025. 

b) Any three digit number is of the form ax2+bx+c for x = 10, a ? 0, a, b, c ? W.  
Now (ax^{2}+bx+ c) ^{2} = a^{2} x4 + b^{2}x^{2} + c^{2} + 2abx^{3} + 2bcx + 2cax^{2}  
= a^{2} x^{4} +2ab. x^{3}+ (b^{2} + 2ca)x^{2}+2bc . x+ c^{2}.  
This identity for x = 10, c = 5 becomes (a . 102 + b .10 + 5)^{2}  
= a^{2}.10^{4} + 2.a.b.10^{3} + (b^{2} + 2.5.a)10^{2} + 2.b.5.10 + 5^{2}  
= a^{2}.10^{4} + 2.a.b.10^{3} + (b^{2} + 10 a)10^{2} + b.10^{2}+ 5^{2}  
= a^{2}.10^{4} + 2ab.10^{3} + b^{2}.10^{2}+ a . 10^{3} + b 10^{2} + 5^{2}  
= a^{2}.10^{4}+ (2ab + a).10^{3} + (b2+ b)10^{2} +5^{2}  
= [ a^{2}.10^{2} + 2ab.10 + a.10 + b^{2} + b] 10^{2}+ 5  
= (10a + b) ( 10a+b+1).10^{2} + 25  
= P (P+1) 10^{2} + 25, where P = 10a+b.  
Hence any three digit number whose last digit is 5 gives the same result as in (a) for P=10a + b, the ‘previous’ of 5.  
Example : 165^{2} = (1 . 10^{2} + 6 . 10 + 5)^{2}.  
It is of the form (ax^{2} +bx+c)^{2} for a = 1, b = 6, c = 5 and x = 10. It gives the answer P(P+1) / 25, where P = 10a + b = 10 X 1 + 6 = 16, the ‘previous’. The answer is 16 (16+1) / 25 = 16 X 17 / 25 = 27225.  
Similar to this other sutra’s has there benefits and mathematic implications to solve the problems.  
The other degree programs under this department will be  
Course & Duration  
BSc/ M B A in Moral science, a 3/ 2 years program  
BSc/ M B A in Human psychology a 3/ 2 years program  
BSc/ M Sc in Botany a 3/ 2 years program  
M B A in Human behavior (Marketing) 