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July 2nd, 2016, 05:47 PM
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IIT Bombay Lecture Notes
I want the lecture notes on Introduction to Algebraic Geometry of Indian Institute of Technology Bombay? Ok, as you want the lecture notes on Introduction to Algebraic Geometry of Indian Institute of Technology Bombay so here I am providing you. IITB Introduction to Algebraic Geometry notes Introduction to Algebraic Geometry Sudhir R. Ghorpade Department of Mathematics Indian Institute of Technology Bombay Theory of Equations The theory of equations is concerned with solving polynomial equations. In high-school, Algebra or Beejganit is almost synonymous with the art of formulating, manipulating and solving polynomial equations. We learn some basic techniques and work out a variety of examples, usually restricted to polynomials in one variable of a reasonably small degree. In college, Algebra appears to bemainly the study of abstract algebraic structures such as groups, rings, fields, and we learn a number of basic notions and results concerning these objects. Slowly, the ideas of theory of equations make a reappearance in the guise of notions such as euclidean domains, principal ideal domains and unique factorization domains. Also, one revisits the familiar formula for the roots of a quadratic equation in terms of its coefficients, and investigates if such a thing is possible for equations of higher degree. This culminates in a remarkable part of al- gebra, known as Galois Theory. For our purpose, it should suffice at the moment to stick to high-school algebra, and review some basic aspects of the theory of equations. However, we work in a little more generality by considering not only equations with rational or real coefficients, but equations with coefficients in a field. A field is basically a set in which we can add, subtract, multiply and divide. Of course division is only permissible by nonzero elements. Some examples of fields are: the set Q of all rational numbers, the set R of all real numbers, the set C of all complex numbers, and the set Fp = Z/pZ of residue classes of integers modulo a prime number p. If you are uncomfortable with the notion of a field, please think of C whenever a field is being talked about. Let K be a field and let K[X] denote the set of all polynomials in the variable X with coefficients in K. Elements of K[X] look like For complete notes here is the attachment Contact- Indian Institute of Technology Bombay Powai Mumbai, Maharashtra 400076 Last edited by Neelurk; April 2nd, 2020 at 11:22 AM. |
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