By V. S. Varadarajan

This article bargains a different account of Indian paintings in diophantine equations in the course of the sixth via twelfth centuries and Italian paintings on ideas of cubic and biquadratic equations from the eleventh via sixteenth centuries. the amount lines the historic improvement of algebra and the idea of equations from precedent days to the start of contemporary algebra, outlining a few glossy issues corresponding to the basic theorem of algebra, Clifford algebras, and quarternions. it's aimed at undergraduates who've no history in calculus.

**Read Online or Download Algebra in Ancient and Modern Times PDF**

**Similar algebra & trigonometry books**

In 1914, E. Cartan posed the matter of discovering all irreducible actual linear Lie algebras. Iwahori gave an up to date exposition of Cartan's paintings in 1959. This thought reduces the type of irreducible actual representations of a true Lie algebra to an outline of the so-called self-conjugate irreducible complicated representations of this algebra and to the calculation of an invariant of one of these illustration (with values $+1$ or $-1$) often called the index.

ICM 2010 complaints includes a four-volume set containing articles according to plenary lectures and invited part lectures, the Abel and Noether lectures, in addition to contributions in line with lectures introduced through the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. the 1st quantity also will comprise the speeches on the starting and shutting ceremonies and different highlights of the Congress.

"Furnishes vital study papers and effects on staff algebras and PI-algebras provided lately on the convention on tools in Ring idea held in Levico Terme, Italy-familiarizing researchers with the most recent subject matters, options, and methodologies encompassing modern algebra. "

**Additional info for Algebra in Ancient and Modern Times**

**Sample text**

27 ALGEBRA I N ANCIENT AN D MODERN TIME S 1. Find po , #o? ™o s o tha t PQ

Bu t w e shal l no t tak e thi s shor t cu t bu t procee d strictl y a s require d b y the cakravala. The n 0 < x\ < 3 and 3 + X\ i s to b e divisibl e b y 4 giving x\ = 1 . S o Pi=4,g i= l,rai= 3 giving u s (4,1 ;3) . The n 1 < x 2 < 3 an d 4 + x 2 i s t o b e divisibl e b y 3 , s o tha t x2 = 2 . S o P2 = 7 , q 2 = 2 , ra 2 = - 3 giving us (7 , 2; —3). Proceedin g i n thi s manne r w e get i n successio n (11,3; 4), 1( 8,5 ; - 1), 1 1 ( 9,33 (256,71; 3), (393, 1 09 ; 4), 1( 37,38 ; - 4 ), (649, 1 80 ; -3) ; 1) We hav e alread y see n tha t (649,180) is a solutio n i n thi s case .

X^ n,... replac e y/X, &X, ... J/X, .... There wa s anothe r obstacl e face d b y th e mathematician s eve n upt o th e 1 6 th century, namel y the unwillingness t o use negative numbers, eve n though th e Hindu s had successfull y introduce d the m centurie s earlier . Thus , Al~Khwarizm i , with th e convention o f writin g onl y positiv e quantities , ha d t o distinguis h betwee n differen t types o f quadrati c equation s suc h a s X2 = BX + C , X 2 + BX = C , X 2 4 - C = BX Moreover thes e woul d hav e t o b e referre d t o i n descriptiv e for m a s square equal s thin g an d numbe r square an d thin g equa l numbe r square an d numbe r equa l thin g ALGEBRA I N ANCIENT AN D MODER N TIME S 45 Al-Khwarizmi gav e rule s fo r solvin g thes e equations , presente d example s t o illustrate hi s rules , an d essentiall y als o givin g demonstration s o f th e rule s throug h these example s a s wel l a s geometrically .