By G.Emch, M.D.Srinivas, R.Sridharan (editors)
Articles at the background of Indian arithmetic, in accordance with the talks given on the periods on "History of Indian arithmetic" held through the first Joint-India-AMS assembly on arithmetic 2003
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This is often the 9th e-book of difficulties and recommendations from the yank arithmetic Competitions (AMC) contests. It chronicles 325 difficulties from the 13 AMC 12 contests given within the years among 2001 and 2007. The authors have been the joint administrators of the AMC 12 and the AMC 10 competitions in the course of that interval.
Nach der Bedeutungsanalyse ist der zweite in dies em Buch eror terte Hauptgegenstand die modale Logik, d. h. die Theorie der Modalitaten, wie Notwendigkeit, Zufalligkeit, Moglichkeit, Unmog lichkeit usw. Verschiedene Systeme der modalen Logik sind von ver schiedenen Autoren vorgeschlagen worden. Es scheint mir jedoch, daiS es nicht moglich ist, ein befriedigendes process zu konstruieren, bevor die Bedeutungen der Modalitaten geniigend klargestellt sind.
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Additional info for Contributions to the History of Indian Mathematics
In general, metrical music deals with three factors: the sound value of a syllable, syllabic quantity and the time taken for the utterence of a syllable. In vedic metres, the music depends only on the modulation of the voice in the pronunciation of the syllables; the essential features of the syllables, namely whether they are short or long do not matter. On the other hand, the music of classical metres depends on the essential features of the syllables, their variations and their order of succession.
As and the Aran branches of knowledge but were only indicated as ﬁelds of study, essential for the understanding of the Vedas. As time went by, it was realised that there was a real need to develop them as auxiliary subjects associated with the study of the Vedas. Hence, independent texts were written in the (mnemonic) s¯ utra style to expound these subjects. () . It is perhaps worthwhile to mention, by the way, that the s¯ utra style of writing is something unique to Indian literature. aram asandigdham aravat vi´svatomukham .
Tta chandas. ama. ttas are those which consist of the same number of syllables in each p¯ ada, while ardhasamavr. ttas have the same number of syllables in the ﬁrst and the third p¯ adas, as well as in the second and the fourth p¯ adas. ttas are those in which all the p¯ adas have unequal number syllables. The aim of the sixth chapter of Pingala’s ˙ Chandas S¯ utra is principally to deﬁne the notion of yati (caesura). The s¯ utra which describes yati is yati vicchedah. The word vicchedah. signiﬁes ‘resting place’.
Contributions to the History of Indian Mathematics by G.Emch, M.D.Srinivas, R.Sridharan (editors)