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Newton-Raphson Method, by Niket S.Kaisare

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Newton’s Divided Differences: Derivation, by Niket S.Kaisare

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Newton’s forward Difference Polynomial, by Niket S.Kaisare

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Orbits of the Integral Unimodular Group in the Upper Half-Plane, by T.E. Venkata Balaji

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Out of Syllabus: Improvements to NR Methods, by Niket S.Kaisare

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Out of Syllabus: Roots of a Polynomial, by Niket S.Kaisare

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Problems with Newton-Raphson, by Niket S.Kaisare

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Quadratic Forms, by Tanuja Srivastava

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Quasi-Compactness in the Zariski Topology; Regularity of a Function at a Point of an Affine Variety, by T.E. Venkata Balaji

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Quotients by Kleinian Subgroups Give Rise to Riemann Surfaces, by T.E. Venkata Balaji

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Recap: Formula for Linear Regression, by Niket S.Kaisare

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Regula-Falsi Method, by Niket S.Kaisare

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Regula-Falsi vs. Secant Method, by Niket S.Kaisare

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Richardson’s Extrapolation, by Niket S.Kaisare

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Riemann Surface Structures on Cylinders and Tori Via Covering Spaces, by T.E. Venkata Balaji

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Simple Examples of Riemann Surfaces, by T.E. Venkata Balaji

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Simpson’s Rules for Integration, by Niket S.Kaisare

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Some Special Cases, by Niket S.Kaisare

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Summary and Recap (Weeks 10 and 11), by Niket S.Kaisare

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Summary, by Niket S.Kaisare

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Summary: Regression and Interpolation, by Niket S.Kaisare

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The Birth of Local Rings in Geometry and in Algebra, by T.E. Venkata Balaji

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The Coordinate Ring of an Affine Variety Determines the Affine Variety and is Intrinsic to it, by T.E. Venkata Balaji

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The D-Uple Embedding and the Non-Intrinsic Nature of the Homogeneous Coordinate Ring of a Projective Variety, by T.E. Venkata Balaji

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The Field of Rational Functions Or Function Field of a Variety-The Local Ring at the Generic Point, by T.E. Venkata Balaji

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The first Order Degree Two Cubic Ordinary Differential Equation Satisfied by the Weierstrass Phe-Function, by T.E. Venkata Balaji

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The Formula for the Local Ring at a Point of a Projective Variety Or Playing with Localisations, Quotients, Homogenisation and Dehomogenisation !, by T.E. Venkata Balaji

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The Idea of a Riemann Surface, by T.E. Venkata Balaji

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The Importance of Local Rings-A Morphism is an Isomorphism if it is a Homeomorphism and Induces Isomorphisms at the Level of Local Rings, by T.E. Venkata Balaji

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The Importance of Local Rings-A Rational Function in every Local Ring is Globally Regular, by T.E. Venkata Balaji

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The Necessity of Elliptic Functions for the Classification of Complex Tori, by T.E. Venkata Balaji

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The Ring of Functions on a Basic Open Set in the Zariski Topology, by T.E. Venkata Balaji

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The Ring of Polynomial Functions on an Affine Variety, by T.E. Venkata Balaji

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The Unimodular Group is Kleinian, by T.E. Venkata Balaji

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The Uniqueness Property of the Weierstrass Phe-Function Associated to a Lattice in the Plane, by T.E. Venkata Balaji

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The Values of the Weierstrass Phe-Function at the Zeros of its Derivative are Nonvanishing Analytic Functions on the Upper Half-Plane, by T.E. Venkata Balaji

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The Various Avatars of Projective N-Space, by T.E. Venkata Balaji

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The Zariski Topology and Affine Space, by T.E. Venkata Balaji

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Translating Homogeneous Localisation into Geometry and Back, by T.E. Venkata Balaji

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Translating Morphisms into Affines as K-Algebra Maps and the Grand Hilbert Nullstellensatz, by T.E. Venkata Balaji

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Translating Projective Geometry into Graded Rings and Homogeneous Ideals, by T.E. Venkata Balaji

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Trapezoidal Rule and Derivation, by Niket S.Kaisare

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Understanding the Zariski Topology on the Affine Line; The Noetherian Property in Topology and in Algebra, by T.E. Venkata Balaji

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What is a Global Regular Function on a Quasi-Affine Variety?, by T.E. Venkata Balaji

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Why Local Rings Provide Calculus without Limits for Algebraic Geometry Pun Intended!, by T.E. Venkata Balaji

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Why should we Study Affine Coordinate Rings of Functions on Affine Varieties ?, by T.E. Venkata Balaji

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