Technical Books

The objective of this book is to lay down and illustrate the more elementary principles of those Geometrical Methods which, in recent times, have been so successfully employed to investigate the properties of figured space.

This is a course note on Euclidean and nonEuclidean geometries with emphasis on i the contrast between the traditional and modern approaches to geometry, and ii the history and role of the parallel postulate. This course will be useful to students who want to teach and use Euclidean geometry, to students who want to learn more about the history of geometry, and to students who want an introduction to nonEuclidean geometry.

In this little treatise on the Geometry of the Triangle are presented some of the more important researches on the subject which have been undertaken during the last thirty years. The author ventures to express not merely his hope, but his confident expectation, that these novel and interesting theorems some British, but the greater part derived from French and German sources will widen the outlook of our mathematical instructors and lend new vigour to their teaching.

This book explains all the fundamental concepts in modern geometry.

This note explains the following topics, Euclidean geometry, Geometry in Greek astronomy, Constructions using a compass and straightedge, Geometers sketchpad, Higher dimensional objects, Hyperbolic geometry, The poincare models of hyperbolic geometry, Tilings and lattices, Foundations, Spherical geometry, Projective geometry, The pseudosphere in lorentz space, Finite geometries, Nonconstructibility, Modern research in geometry, A selective time line of mathematics.

This note covers the notions of convergence of sequences and series and the nature of the real numbers.

This note covers the following topics related to Infinite Series: Cauchy Root Test, Comparison Test, D�alembert (or Cauchy) Ratio Test, Alternating Series, Absolute And Conditional Convergence, Improvement Of Convergence, Rearrangement Of Double Series, Taylor�s Expansion, Power Series, Indeterminate Forms, Binomial Theorem, Mathematical Induction, Operations On Series Expansions Of Functions, Bernoulli Numbers, Euler-maclaurin Integration Formula and Dirichlet Series.

This note covers the following topics related to Infinite Series: Definitions and basic examples, Positive series, Series with mixed signs and Power series

This book explains the following topics, Some Elementary Logic, The Real Number System, Set Theory, Vector Space Properties of Rn, Metric Spaces, Sequences and Convergence, Cauchy Sequences, Sequences and Compactness, Limits of Functions, Continuity, Uniform Convergence of Functions, First Order Systems of Differential Equations

Goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. The lecture notes contain topics of real analysis usually covered in a 10week course, the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many wellselected exercises of various levels.

The contents include, Introduction, Metric Spaces, Compactness, Cauchy Sequences in Metric Spaces, Sequences in Rn, Continuous Functions on Metric Spaces, Sequences of Functions.

The contents include, Introduction, Axioms for arithmetic in R, Properties of arithmetic in R, Ordering the real numbers, Inequalities and arithmetic, The modulus of a real number, The complex numbers, Upper and lower bounds, Supremum, infimum and completeness, Existence of roots, More consequences of completeness, Countability, More on countability, Introduction to sequences, Convergence of a sequence, Bounded and unbounded sequences, Complex sequences, Subsequences, Orders of magnitude, Monotonic sequences, Convergent subsequences, Cauchy sequences, Convergence for series, More on the Comparison Test, Ratio Test, Integral Test, Power series, Radius of convergence, Differentiation Theorem.

The contents include, The Real And Complex Number Systems, Sets And Functions, Basic Topology, Sequences And Series, Continuity, Sequences And Series Of Functions, Figures.

This note explains the following topics, preliminaries, The real numbers, Sequences and series, Complex numbers.

This book contains below topics, Euclidean Spaces, Limits of Multivariable Functions and Continuity, Continuous Functions on Connected Sets and Compact Sets, Differentiating Functions of Several Variables, The Inverse and Implicit Function Theorems, Multiple Integrals, Fourier Series and Fourier Transforms, Sylvester s Criterion, Volumes of Parallelepipeds, Riemann Integrability.