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Chandogya Upanishad's [[Narada Sanatkumara Samvada (नारदसनत्कुमारयोः संवादः)|Narada Sanathkumara Samvada]], clearly elucidates the existence of the subjects of sciences and arts depicting their antiquity in ancient India. Narada, entreated by Sanathkumara, enumerates the various sciences and arts studied by him and this list includes astronomy (nakshatra-vidya) and arithmetic (rasi-vidya). The culture of science of astronomy and mathematics classified under Aparavidya were not considered to be a hindrance to Paravidya or spiritual knowledge; they were part of the Chaturdasha and Asthadasa vidyas which was the basic curriculum of education. On the contrary they were considered as helpful adjuncts and were studied to aid the progress of Paravidya as expounded in Mundakopanishad (1.1.3-5).

Chandogya Upanishad's [[Narada Sanatkumara Samvada (नारदसनत्कुमारयोः संवादः)|Narada Sanathkumara Samvada]], clearly elucidates the existence of the subjects of sciences and arts depicting their antiquity in ancient India. Narada, entreated by Sanathkumara, enumerates the various sciences and arts studied by him and this list includes astronomy (nakshatra-vidya) and arithmetic (rasi-vidya). The culture of science of astronomy and mathematics classified under Aparavidya were not considered to be a hindrance to Paravidya or spiritual knowledge; they were part of the Chaturdasha and Asthadasa vidyas which was the basic curriculum of education. On the contrary they were considered as helpful adjuncts and were studied to aid the progress of Paravidya as expounded in Mundakopanishad (1.1.3-5).

The elementary stage in ancient education system lasted from the age of five till about the age of twelve. The main subjects of study were Lipi or lekha (alphabets, reading and writing), rupa (drawing and geometry) and ganita (arithmetic). It is said in the Arthashastra of Kautilya that having undergone the Choula ceremony (tonsure), the student shall learn the alphabets (lipi) and arithmetic (samkhyana). <blockquote>वृत्त-चौल-कर्मा लिपिं संख्यानं चौपयुञ्जीत ।। ०१.५.०७ ।। (Arth. Shast. 1.5.7)7</blockquote>Mention of lekha, rupa and ganana is also found in the Jaina canonical works.

The elementary stage in ancient education system lasted from the age of five till about the age of twelve. The main subjects of study were Lipi (लिपि) or lekha (alphabets, reading and writing), rupa (drawing and geometry) and ganita (arithmetic). It is said in the Arthashastra of Kautilya that having undergone the Choula ceremony (tonsure), the student shall learn the alphabets (lipi) and arithmetic (संख्यानम् । samkhyana).<ref>Shamasastri, R. () Kautilya's Arthasastra, English Translation. (Page 14)</ref> <blockquote>वृत्त-चौल-कर्मा लिपिं संख्यानं चौपयुञ्जीत ।। ०१.५.०७ ।। (Arth. Shast. 1.5.7)<ref>Arthashastra of Kautilya ([https://sa.wikisource.org/wiki/%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A5%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D/%E0%A4%85%E0%A4%A7%E0%A4%BF%E0%A4%95%E0%A4%B0%E0%A4%A3%E0%A4%AE%E0%A5%8D_%E0%A5%A7/%E0%A4%85%E0%A4%A7%E0%A Adhikarana 1 Adhyaya 5])</ref></blockquote>Mention of lekha, rupa and ganana is also found in the Jaina canonical works.

Our ancestors were well aware that mathematics is the language by which one can express any associated science compactly. It involved simplified ways of manipulation and calculations, helping one to develop the mind and also to communicate well. Thus mathematics was considered to be a very important subject in ancient India taught from a very young age.

Our ancestors were well aware that mathematics is the language by which one can express any associated science compactly. It involved simplified ways of manipulation and calculations, helping one to develop the mind and also to communicate well. Thus mathematics was considered to be a very important subject in ancient India taught from a very young age.

== Scope of Ganita ==

== Scope of Ganita ==

In Vedangas Astronomy (jyotisha) became a separate subject and geometry (kshetra-ganita) came to be included within its scope. It is to be noted that the Jain and Buddhist scholars have played a significant role in the development of astronomy and mathematics in India. Importance of Ganita is also given by the Jainas in their religious literature. Ganitanuyoga, meaning the exposition of the principles of mathematics and Samkhyana meaning the science of numbers, in terms of arithmetic and astronomy, is stated to be one of the principal accomplishments of the Jaina priest (Bhagavati-sutra, 90 and Uttaradhyayana-sutra, 25). Buddhist literature regards arithmetic (ganana and samkhyana) as the first and noblest of the arts. In ancient Buddhist literature we find a mention of three classes of Ganita:<ref name=":0" />

In Vedangas Astronomy (jyotisha) became a separate subject and geometry (kshetra-ganita) came to be included within its scope. It is to be noted that the Jain and Buddhist scholars have played a significant role in the development of astronomy and mathematics in India. Importance of Ganita is also given by the Jainas in their religious literature. Ganitanuyoga, meaning the exposition of the principles of mathematics and Samkhyana meaning the science of numbers, in terms of arithmetic and astronomy, is stated to be one of the principal accomplishments of a Jaina priest (Bhagavati-sutra, 90 and Uttaradhyayana-sutra, 25). Buddhist literature regards arithmetic (ganana and samkhyana) as the first and noblest of the arts. In ancient Buddhist literature we find a mention of three classes of Ganita:<ref name=":0" />

# Mudra ("finger arithmetic")

# Mudra ("finger arithmetic")

# Ganana ("mental arithmetic")  

# Ganana ("mental arithmetic")  

== Subject Matter of Ganita ==

== Subject Matter of Ganita ==

The subjects treated in Ganita of the early periods consisted of the following:  

The subjects treated in Ganita, in early centuries, consisted of the following:  

The development of numerical symbolism is intimately connected with the writing in ancient India.  

 

 

 

Rasi ("rule of three")

 

Kalasavarna ("operations with fractions")

 

 

 

 

 

Vikalpa ("permutations and combinations").

== References ==

== References ==