Technical Books

This book contains below topics, Note to the reader, Overview of Galois theory, Group actions rings and fields, Polynomials, Field extensions, Degree, Splitting fields, Preparation for the fundamental theorem, The fundamental theorem of Galois theory, Solvability by radicals, Finite fields.

This book contains below topics, Topological groups and their toposes of continuous actions, A representation theorem, Concrete Galois theories, Other insights from the bridge technique, Examples, The four ways to topological Galois representations.

This note covers the following topics, Differentiable Manifolds, The Tangent Space, The Tangent Bundle, Riemannian Manifolds, The LeviCivita Connection, Geodesics, The Riemann Curvature Tensor, Curvature and Local Geometry.

This note covers the following topics, Smooth Manifolds, Tangent Spaces, Affine Connections on Smooth Manifolds, Riemannian Manifolds, Geometry of Surfaces in R3, Geodesics in Riemannian Manifolds, Complete Riemannian Manifolds and Jacobi Fields.

This book covers the following topics, Differentiable Manifolds, Differential Forms, Riemannian Manifolds, Curvature, Geometric Mechanics, Relativity.

This note covers curves and surfaces in the plane and in space, Riemannian manifolds, Connections, Geodesics, The second fundamental form.

This PDF covers the following topics related to Riemannian Geometry, Smooth manifolds, Some examples, Riemannian metrics, Geodesics, Curvature, Lie groups and homogeneous spaces, Characteristic classes, Hodge theory, Minimal surfaces.

This PDF covers the following topics related to Riemannian Geometry, Manifolds, Examples of manifolds, Submanifolds, Tangent spaces, Tangent map, Tangent bundle, Vector fields as derivations, Flows of vector fields, Geometric interpretation of the Lie bracket, Lie groups and Lie algebras, Frobenius theorem, Riemannian metrics, Existence of Riemannian metrics, Length of curves, Connections and parallel transport, Geodesics, The HopfRinow Theorem, The curvature tensor, Connections on vector bundles.

This PDF covers the following topics related to Riemannian Geometry, Introduction, Riemannian Metric, Geodesics, Connections, Curvatures, Space forms and Jacobi fields, Comparison Theorem, Candidates for Synthetic Curvature Conditions.

These lecture notes are based on the course in Riemannian geometry at the University of Illinois over a period of many years. This book contains below topics, Riemannian metrics, Minimizers, Connections, The Riemannian Connection, Calculus of variations, Riemannian curvature, Conjugate Points, Completeness, Curvature and topology.

This is a text for a twoterm course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Topics covered includes, Real Numbers, Differential Calculus of Functions of One Variable, Integral Calculus of Functions of One Variable, Infinite Sequences and Series, VectorValued Functions of Several Variables, Integrals of Functions of Several Variables and Metric Spaces.

These lecture notes are an introduction to undergraduate real analysis. They cover the real numbers and onevariable calculus.

This note covers the following topics, Topology Preliminaries, Elements of Functional Analysis, Measure Theory, Integration Theory, Product Spaces, Analysis On Locally Compact Spaces, Introduction to Harmonic Analysis.

This note is an activityoriented companion to the study of real analysis. It is intended as a pedagogical companion for the beginner, an introduction to some of the main ideas in real analysis, a compendium of problems, are useful in learning the subject, and an annotated reading or reference list. Topics covered includes, Sets, Functions, Cardinality, Groups, Vector Spaces, And Algebras, Partially Ordered Sets, The Real Numbers, Sequences And Indexed Families, Categories, Ordered Vector Spaces, Topological Spaces, Continuity And Weak Topologies, Normed Linear Spaces, Differentiation, Complete Metric Spaces, Algebras And Lattices Of Continuous Functions.

This note covers the following topics, mathematical reasoning, The Real Number System, Special classes of real numbers, Limits of sequences, Limits of functions, Continuity, Differential calculus, Applications of differential calculus, Integral calculus, Complex numbers and some of their applications, The geometry and topology of Euclidean spaces, Continuity, Multivariable differential calculus, Applications of multivariable differential calculus, Multidimensional Riemann integration, Integration over submanifolds.