## CSIR-NET Syllabus for Mathematical Sciences

CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship COMMON SYLLABUS FOR PART ‘B’ AND ‘C’ MATHEMATICAL SCIENCES UNIT –  1 Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel … Read more CSIR-NET Syllabus for Mathematical Sciences

## Vector Spaces and Linear Transformation

Vector Space- A set V is called vector space on which two operations are defined. 1- Vector Addition 2- Scalar Multiplication Further, vector addition must follow the following properties and laws for vector addition. 1- Closure Property If u and v are two vectors in V then u+v must be in V. 2- Commutative Law … Read more Vector Spaces and Linear Transformation

## Random variables and Probability Distribution Functions

To understand random variable first you have to know about events.  I will make you understand using examples. What are events? Example Tossing three coins on which one head turns up {HT,HH} A random variable quantify   events of  occurence. In other words, a random variable X is a function from set of events to real … Read more Random variables and Probability Distribution Functions

## Mutually Exclusive and Independent Events

Mutually Exclusive Events- Two or more events events are said to be mutually exclusive if only one can happen at a time. Example-1 In tossing a coin, event of tail up (T) and even of heads up (H) can not happen simultaneously. They are mutually exclusive events. Example-2 In rolling of a dice, event of  … Read more Mutually Exclusive and Independent Events

## Linear Dependence and Independence of Vectors

Linear  Independence of Vectors Suppose α1, α2, α3, α4…………αn are vectors  of V(F) where F is field.  And there exist scalers a1, a2, a3, a4………..an which belong to field F. α1, α2, α3, α4…………αn vectors are called lineary independent if a1 α1 + a2 α2 + a3 α3+ ……… + an αn = 0 and … Read more Linear Dependence and Independence of Vectors

## Create Bootable Pendrive and Install Ubuntu

Ubuntu only provides an iso image of the operating system and you need to make a pen drive bootable to install ubuntu. I will show  step-by-step how to make a pen drive bootable using  USB Installer. Step-1 Download USB installer  using this link  https://universal-usb-installer.en.uptodown.com/windows and keep in pendrive. Step-2 Download Ubuntu operating system  using this … Read more Create Bootable Pendrive and Install Ubuntu

## Divide and Conquer and Dynamic Programming Algorithms

Often students get confused what are differences between divide and conquer and dynamic programming. Since they solve problems in similar nature. Divide the problem into sub-problems combine them to get solution. Here I list the differences  between divide and conquer and dynamic programming in a table and also  made quizzes so that you can practice … Read more Divide and Conquer and Dynamic Programming Algorithms

## Mathematics for Machine Learning

Mathematics is an essential part for machine learning  without maths it is hard to get into core concepts. In addition, machine learning uses concepts from different branches, however, these branch of mathematics are the backbone of the machine learning. 1- Linear Algebra Matrix, Vector Spaces and Linear Transformations, Eigen Values and Eigen Vectors ( Principle … Read more Mathematics for Machine Learning

## Datasets for Machine Learning

For machine learning and data science projects data sets are necessary to train and test model. Furthermore, several datasets repository is available on the Internet. Some of them are freely available some need to pay money. Here I will list some popular datasets resources over the Internet for machine learning projects.   1-Kaggle Datasets Repository … Read more Datasets for Machine Learning

## Operating System

An Operating System is a system software which uses the software and hardware resources and provides an environment for application programs to execute appropriately.     Operating System Types 1.  Distributed Operating System With a distributed system, memory and clock are not shared by processors.     2. Real Time Systems In this type of … Read more Operating System