Linear Algebra

Linear-Algebra-Feature-image

What is linear algebra? Graphically speaking, linear algebra deals with lines and their transformations. In short, linear algebra is linear transformation represented using vectors of numbers and matrices of two dimensional numbers.

We solve linear equations with unknown variables associated with each term of the linear equations. For example,

ax + by = c (linear equation)

Each term has unknowns (x, y) and coefficient (a, b) and equals a constant (c). Also, geometrically, each linear equation represents a straight line, hence, the name ‘linear’.

Imagine a few lines intersecting each other , then we could find the coordinates of intersections and we have a solution to the linear equations involved. Such equations form a system of linear equations which can solved using vectors and matrices. it is usually in the form of Ax = b.

Prerequisite To Learn Linear Algebra

The only prerequisite to learn linear algebra is basic algebra course and understanding of coordinate systems. This is because during our course we will have to apply concepts like exponents, solving equations by adding subtracting, multiplying with fractions,and so on.

If you know some programming, then its good idea to practice programming by creating programs for solution to linear equations. That’s totally up to you.

Topics From Linear Algebra

Here are the list of topics from linear algebra. You should read sequentially from top to bottom.

Introduction

Matrix Algebra

Determinants

more topics coming soon …

R Tutorial

What is R programming ?

R is a programming language developed by Ross Ihaka and Robert Gentleman in University of Auckland, New Zealand in the year 1995 and a stable version released in year 2000.

What can R do ?

R is a programming language and environment commonly used in statistical computing, data analytics and scientific research.

R and its libraries implement a wide variety of statistical and graphical techniques, including linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, and others. R is easily extensible through functions and extensions, and the R community is noted for its active contributions in terms of packages

Who Use R ?

R programming is popular choice among

  • Statisticians
  • Data analysts
  • Researchers and Academics
  • Business Houses
  • Data miners

Common R Features

R is free under GNU general public license and it is an interpreted language. R programming is written using C, FORTRAN and R itself. It has a Command Line Interface and a R IDE is also available which is a GUI interface called R-studio.

Prerequisite To Learn R

There are only two most important prerequisite to learn R programming. They are

  • R Programming Syntax and Basics
  • Learning Statistics

R Programming Syntax and Its Basics

Learning R syntax and language features are the first you have to take if you are new to this programming. If already have experience in programming such as C/C++, Java,etc, then learning the basics will not be hard for you.

Learning Statistics

R is a language for mathematics, especially statistics. You must be good in statistics to use R programming. It is good to watch some videos and learn statistics first before creating R programs.

If you are not good at statistics, then learn the basics of R and learn statistics later and come back to R for programming.

About R Tutorial

This tutorial is to help you learn the basics of R programming. We will include the statistical part eventually. Therefore, the tutorial is for beginners in R programming.

Engineering Mathematics

Engineering mathematics is a type of mathematics that is used in engineering and applied sciences. It is used in computer science as well. It helps to create mathematical models and these models solve engineering problems.

What do we learn in Engineering Mathematics?

Since, engineering math is a branch of applied mathematics, it is used with a specialized sciences from any engineering discipline.

In computer science, we learn linear algebra concepts, precalculus and calculus with advanced concepts like integration, differential equations and probability theory.

Why to learn Engineering Mathematics?

It depends on the goal of the learner whether to master mathematics or not. Computer science students more interested in programming and related topics do not learn mathematics, though we recommend they do.

Another group of students studies engineering math to build a solid foundation for research as a career option. Mastering mathematics will help them with research activities and provide them with an alternative career option.

finally, the benefit of learning engineering math is that it will open door for wide variety of opportunities in applied sciences.

Prerequisites

There is no prerequisite to learn from the tutorial because we covered the basics in precalculus section. We are developing the tutorial currently which requires time.

So either you can start reading available study materials on our site or get good books to learn and practice.

Engineering Mathematics Tutorial Topics

Here is a list of engineering math topics. Start from the top of the list and move through each lessons.

Functions And Graphs

Rational And Polynomial Functions

Calculus

Discrete Mathematics

The origin of discrete mathematics can be traced back to 1980s when it was taught as a part of the computer science course. Discrete Mathematics is a new kind of mathematics that has evolved with Computer Science.

There is no branch in mathematics called “Discrete Mathematics”. It is a term used for already existing math topics used in computer science that mostly deals with a discrete amount of data.

So you may ask, What is continuous mathematics? We mentioned earlier that there is nothing called Continuous mathematics, but it is a general term to describe the math that uses continuous data – speed, velocity, distance, etc.

What do we study in Discrete Mathematics ?

A lot of topics belong to discrete mathematics, other than calculus and different types of analysis. So, discrete math is broadly classified into combinatorics, sets and relations, graphs and trees, algebraic structures and modern algebra.

The list could be endless because it is finite mathematics dealing with finite quantities.

How does it help learning computer Science?

The rules that govern computer architecture and communication of internal parts of a computer are based on Boolean algebra. Any possible change in the Boolean algebra will change the entire structure of computer systems.

Graphs and Trees form a data structure for many computer algorithms. A lot of research is being done on these topics. Discrete math gives a proper understanding of principles on which these structures work or do not work.

Many computer science programs is proved correctly using discrete mathematics tool like mathematical induction.

Prerequisites

The prerequisite to learn from this tutorial is at least pre-calculus. Knowledge of calculus is not a compulsory  requirement for discrete math, but it builds a mathematical maturity.

Discrete Math Topics

All topics listed in top to bottom order. Start to learn from top as it is easier and foundation for subsequent topics.

Prepositional Logic

Graph Theory

Partial Relations

Groups