New PDF release: Algebra in Ancient and Modern Times

By V. S. Varadarajan

ISBN-10: 082180989X

ISBN-13: 9780821809891

This article bargains a distinct account of Indian paintings in diophantine equations throughout the sixth via twelfth centuries and Italian paintings on strategies of cubic and biquadratic equations from the eleventh via sixteenth centuries. the quantity strains the historic improvement of algebra and the idea of equations from precedent days to the start of recent algebra, outlining a few sleek issues similar to the basic theorem of algebra, Clifford algebras, and quarternions. it's aimed at undergraduates who've no heritage in calculus.

Show description

Read or Download Algebra in Ancient and Modern Times PDF

Similar algebra & trigonometry books

Download PDF by A. J. Berrick: An Introduction to Rings and Modules With K-theory in View

This concise advent to ring thought, module conception and quantity concept is perfect for a primary yr graduate pupil, in addition to being an outstanding reference for operating mathematicians in different components. ranging from definitions, the publication introduces primary structures of earrings and modules, as direct sums or items, and by way of special sequences.

Download e-book for iPad: Tangents and secants of algebraic varieties by Francesco Russo

This ebook is an advent to the use and learn of secant and tangent forms to projective algebraic types. As pointed out within the Preface, those notes may be regarded as a ordinary guidance to components of the paintings of F. L. Zak [Tangents and secants of algebraic varieties}, Translated from the Russian manuscript via the writer, Amer.

Additional resources for Algebra in Ancient and Modern Times

Example text

S . VARADARAJA N 10. Sho w tha t i f th e positiv e intege r k i s no t th e squar e o f anothe r positiv e integer , i t canno t be th e squar e o f a rationa l numbe r either , s o tha t Vk i s a n irrationa l number . (Hin t : If k = 77 1 jn wher e 771 , 77 are positiv e integer s withou t a commo n factor , deduc e fro m kn = 77 1 tha t 7 7 divides 77 1 an d us e th e previou s exercis e t o sho w tha t 7 7 must b e 1 . 1090/mawrld/012/03 3 ARYABHATA-BRAHMAGUPTA-BHASKARA Aryabhata (476-c . 550) , Brahmagupt a (c .

Colebrook e o f th e work s o f Brahmagupta an d Bhaskar a : Algebra, with arithmetic and mensuration, from the Sanscrit of Brahmagupta and Bhascara, London, 1 81 7. 1090/mawrld/012/04 4 IRRATIONAL NUMBER S : CONSTRUCTIO N AND APPROXIMATIO N The Greek s alread y kne w tha t no t al l segment s tha t aris e i n geometrica l con structions hav e length s whic h ar e rationa l fractions . Thu s y/2 i s no t rational , al though i t i s the lengt h o f th e diagona l o f a squar e o f sid e 1 . A ver y genera l propositio n i n Eucli d show s ho w t o construc t a squar e whos e area i s equa l t o tha t o f a give n rectangle .

96-1 02 ) (i) arcta n \ + arcta n \ — \ (ii) arcta n | + arcta n ^ + arcta n \ — \ (iii) 4 arctan \ — arctan ^ = f (iv) 4 arctan \ — arctan ^ + arcta n ^ = f (Hint : Fo r (iii ) an d (iv) , sho w firs t tha t 3 a r c t an \ = a r c t a n | | ) 6. Us e th e formula e i n exercis e 5 to calculat e 7 T accurately t o severa l decima l places . 7. Sho w tha t x = y 3 4- y 5 4- V2 is algebrai c b y constructin g a n equatio n o f th e 1 2 degre by X. e wit h intege r coefficient s satisfie d Hilbert's famou s addres s liste d 2 3 problems an d th e proble m o f transcendentalit y o f a i s the 7 .

Download PDF sample

Algebra in Ancient and Modern Times by V. S. Varadarajan

by Steven

Rated 4.95 of 5 – based on 41 votes