The present book is an endeavor to let the enthusiasts comprehend the fundamentals of algebra as founded by the seers of the ancient period and get acquainted with the traditional antiquities. The methods adopted for the fundamental operations is much simpler than the present conventional methods. The Sutra 'Paravartya Yojayet' has made the division process less time taking, simple and error free. The different methods adopted for the factorizations, particularly of cubic polynomials, is really interesting and makes the solutions of subsequent equations less cumbrous. The comprehensive texts on solution of equations covering the special forms are of immense use. The procedures for finding H.C.F. involving only addition and subtraction of expressions is far away from long divisions. Resolving a fractional expression into its partial form is simple and involves less computations. The binomial expansions with the help of Meru Prastar are easy and free from lengthy calculations.
In each unit the illustrations along with the detailed steps of procedures will make the learners understand it easily. The sets of variety of questions along with the answers have been provided for practice. The approaches followed in the book will certainly be useful in arithmetical calculations also.
Dr. S.L. Maurya Got awarded M.A. (Maths) degree from Allahabad University and Ph.D. from Banaras Hindu University, Varanasi. Served the then Hindalco Vidya Niketan, Renukoot, Sonebhadra (U.P.) and thereafter Central Hindu Boys School, Kamachha, B.H.U.. Varanasi as Post Graduate Teacher (Maths). Retired from active service in 2014 but continued services to the school till 2019. Recently, extending services to the Centre for Vedic Sciences, B.H.U., Varanasi as Guest Faculty teaching Vedic Mathematics. Authored the book Vedic Geometry (Baudhayan Triples) published by this Centre.
It gives me immense pleasure to dedicate this book to the readers keenly interested in learning Vedic approaches in modern form of symbolism in algebra. The symbolic algebra as of today emerged around 16th century. The origin of algebra dates to the scripting of Vedas or even before that but it was not in symbolic form. The constraints to determine unknown quantities were expressed in words. Gradually symbolism got introduced to denote the quantities and the relations among them. The word problems to determine the value of a quantity could get expressed in symbolic form as equations. The Siddhant Shiromani of Bhaskaracharya II has four volumes Leelavati, Bijganit, Grahganit and Goladhyaya. It is presumed that the algebra in present form could started taking shape during the period of Bhaskara II.
The first unit is on the four fundamental operations and the method adopted for addition and subtractions is undoubtedly simpler than the present traditional method. The Sutras 'Nikhilam' and 'Urdhvatiryakbhyam' have been used to obtain the product of two or more expressions. For division of two algebraic expressions 'Paravartya Sutra has been applied which yields simple, less time taking and error free results. In second unit of factorizations of algebraic expressions 'Anurupyen' and 'Adyamadyenantyamantyen' Sutras have been used. The Sutra 'Gunitsamuccyayah Samuccaya Gunitah', not only checks the correctness of the factors but facilitates find the factors of higher degrees of polynomials.
The third unit comprises H.C.F. and L.C.M. of algebraic expressions. For finding H.C.F. of two expressions 'Lopanastha-panabhyam' Sutra has been incorporated and the procedure is simpler than that of conventional division method. L.C.M. of the expressions is calculated after finding their H.C.F. The mixed operations comprising four fundamental operations to reflect in this unit. In the fourth unit one-line solutions of simple equations using 'Paravartya Yojayet Sutra has been introduced. Quite a few special cases of equations have been dealt along with other forms which are transformed to these forms.
Solutions of quadratic equations have been computed using calculus (derivatives) method which of course coincides with Shreedharacharya method. The nature of roots of quadratic equations and the algebra there on has been discussed in detail. The solution of cubic equations using factor and 'Puranabhyam' methods have been dealt with. Alongside, the relation among the roots and the coefficients of the terms of the equations too has been established effectively.
The fifth unit is on Partial Fractions. Splitting the rational expression into partial fraction is the process of expressing it as the sum of the fractions. Disguised forms too have been taken into consideration and values of the unknowns have been obtained in easy way without many computations. Resolution of the rational expression into partial fraction facilitates obtaining its integration in easy way. The sixth unit deals with the binomial theorem. The Meruprastar has been used to determine the coefficients of terms of binomial expansions. The related results and properties too have been discussed in detail.
At the end of each unit a set of exercises has been provided to the learners for practice. Efforts are on to make the Vedic Sutras more adoptive in wider range. Elementaries in the beginning of each section help comprehend related basics and subsequent applications there on.
I extend my profound gratitude to the editor Prof. Upendra Kumar Tripathi, coordinator, Centre for Vedic Sciences and Professor, Department of Veda, Faculty of Sanskrit Vidya Dharm Vigyan, Banaras Hindu University Varanasi, whose cooperation, guidance, and encouragement boosted my morale to furbish the work in the form of this book. I express my deepest thanks to Dr. Daya Shankar Tripathi for valuable suggestions to consolidate the work in the present form. The valuable suggestions from readers end will be gracefully accepted. Computational errors, if any, should be brought to our notice so that same can be removed in future editions.
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