# CSIR

## PROBLEM SOLVERS’ TOPOLOGY:- A COMPLETE SOLUTION GUIDE TO ANY TEXTBOOK

Thorough coverage is given to the fundamental concepts of topology, axiomatic set theory, mappings, cardinal numbers, ordinal numbers, metric spaces, topological spaces, separation axioms, Cartesian products, the elements of homotopy theory, and other topics. A comprehensive study aid for the graduate student and beyond. Jigs Solanki provides you with the best chosen study material like …

## REAL ANALYSIS:- ALTERNATING AND ARBITRARY SERIES HAND WRITTEN NOTE

In mathematics, real analysis is the theory of real numbers and real functions, which are real-valued functions of a real variable. Real analysis studies properties of real functions like convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis and complex analysis are both branches of mathematical analysis. The theorems of real analysis rely intimately upon …

## CALCULUS OF VARIATION HAND WRITTEN NOTE

Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals …

## TOPOLOGY AND MATRIC SPACES NOTE BY PI AIM INSTITUTE

In mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. The most …

## MATRIX THEORY HAND WRITTEN NOTE

Properties of matrices and determinants (Matrix Algebra). Linear independence and dependence.Rank of a matrix and its properties. System of linear equations. Eigenvalues and eigenvector. Gate Syllabus:Vector space,Basis,Linear dependence and independence,Matrix algebra, Eigen values and eigen vectors,Rank. Solution of linear equations – existence and uniqueness. This material is helpful for both Gate and placements. It consists …

## REAL ANALYSIS:-TOPOLOGY ON R AND R HAND WRITTEN NOTE

In mathematics, real analysis is the theory of real numbers and real functions, which are real-valued functions of a real variable. Real analysis studies properties of real functions like convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis and complex analysis are both branches of mathematical analysis. The theorems of real analysis rely intimately upon …

## COMPLEX ANALYSIS HAND WRITTEN NOTE

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.  It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly …

## MOLE CONCEPT AND STOICHIOMETRY HAND WRITTEN NOTE

The mole concept is one of the topics with which you kick-off your preparation of physical chemistry in class 11. One of the reasons for it being taught earlier is that the concept of mole will be required in almost every other topic of physical chemistry that you study later, irrespective of the complexity of …

## AROMATICITY NOTE FOR CAIR NET/SET/GATE/IIT-JAM

In organic chemistry, the term aromaticity is used to describe a cyclic (ring-shaped), planar (flat) molecule with a ring of resonance bonds that exhibits more stability than other geometric or connective arrangements with the same set of atoms. Aromatic molecules are very stable, and do not break apart easily to react with other substances. Organic …

## Group Theory Hand Written Note

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.  Groups recur throughout mathematics, and the methods of …