Mathematics

Categories Computer Science Studies

Description

Mathematics is an exact language for description, calculation, deduction, modeling, and prediction — more a systematic way of thinking than a set of rules. Using a legal analogy, mathematics is a language for writing contracts with Nature that Nature accepts as legally binding. The practical importance of mathematics lies in its ability to describe the real world.

This tutorial will give you the knowledge from the scratch as a beginner level to intermediate level.

It consists of 2 parts 1. Discrete Mathematics 2. Engineering Mathematics

Topics for this course

86 Lessons

Discrete Mathematics

Introduction

Propositional and First Order Logic

Set Theory

Introduction

Set Operations

Inclusion-Exclusion and its various Applications

Power Set and its Properties

Partial Orders and Lattices

Groups

Introduction and types of Relations

Discrete Mathematics | Representing Relations

Relations | Representations in Matrices and Graphs

Closure of Relations and Equivalence Relations

Number of possible Equivalence Relations on a finite set

Classes (Injective, surjective, Bijective) of Functions

Total number of possible functions

Generating Functions | Introduction and Prerequisites

Generating Functions – Set 2

Sequence, Series and Summations

Independent Sets, Covering and Matching

Introduction to Proofs

Hasse Diagrams

Introduction to Mojette transform

Rings, Integral domains and Fields

Combinatorics

Probability

Graph Theory

Graph Theory Basics – Set 1

Graph Theory Basics – Set 2

Graph Types and Applications

Euler and Hamiltonian Paths

Planar Graphs and Graph Coloring

Graph Isomorphisms and Connectivity

Matching (graph theory)

Betweenness Centrality (Centrality Measure)

Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph

Graph measurements: length, distance, diameter, eccentricity, radius, center

Relationship between number of nodes and height of binary tree

Engineering Mathematics

Linear Algebra

Calculus

Statistics and Numerical Methods

Mean, Variance and Standard Deviation

Newton’s Divided Difference Interpolation Formula

Law of total probability

Probability Distributions Set 1 (Uniform Distribution)

Probability Distributions Set 2 (Exponential Distribution)

Probability Distributions Set 3 (Normal Distribution)

Probability Distributions Set 4 (Binomial Distribution)

Probability Distributions Set 5 (Poisson Distribution)

Homogeneous Poisson Process

Nonhomogeneous Poisson Processes

Renewal processes in probability

Mathematics | Covariance and Correlation

Scales of Measurement

Univariate, Bivariate and Multivariate data and its analysis

Hypergeometric Distribution model

Free

Enrolment validity: Lifetime

Mathematics

Description

Topics for this course

Discrete Mathematics

Introduction

Propositional and First Order Logic

Introduction to Propositional Logic

Introduction to Propositional Logic | Set 2

Propositional Equivalences

Predicates and Quantifiers

Predicates and Quantifiers | Set 2

Some theorems on Nested Quantifiers

Rules of Inference

PDNF and PCNF in Discrete Mathematics

Set Theory

Introduction

Set Operations

Inclusion-Exclusion and its various Applications

Power Set and its Properties

Partial Orders and Lattices

Groups

Introduction and types of Relations

Discrete Mathematics | Representing Relations

Relations | Representations in Matrices and Graphs

Closure of Relations and Equivalence Relations

Number of possible Equivalence Relations on a finite set

Classes (Injective, surjective, Bijective) of Functions

Total number of possible functions

Generating Functions | Introduction and Prerequisites

Generating Functions – Set 2

Sequence, Series and Summations

Independent Sets, Covering and Matching

Introduction to Proofs

Hasse Diagrams

Introduction to Mojette transform

Rings, Integral domains and Fields

Combinatorics

Pigeon Hole Principle

Combinatorics Basics

PnC and Binomial Coefficients

Generalized PnC Set 1

Generalized PnC Set 2

Corollaries of Binomial Theorem

Sum of squares of even and odd natural numbers

Finding nth term of any Polynomial Sequence

Discrete Mathematics | Types of Recurrence Relations – Set 2

Probability

Mathematics | Probability

Conditional Probability

Bayes’s Formula for Conditional probability

Prosecutor’s Fallacy

Random Variables

Graph Theory

Graph Theory Basics – Set 1

Graph Theory Basics – Set 2

Graph Types and Applications

Euler and Hamiltonian Paths

Planar Graphs and Graph Coloring

Graph Isomorphisms and Connectivity

Matching (graph theory)

Betweenness Centrality (Centrality Measure)

Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph

Graph measurements: length, distance, diameter, eccentricity, radius, center

Relationship between number of nodes and height of binary tree

Engineering Mathematics

Introduction

Linear Algebra

Matrix Introduction

Different Operations on Matrices

Representations of Matrices and Graphs in Relations

Eigen Values and Eigen Vectors

System of Linear Equations

LU Decomposition of a System of Linear Equations

Doolittle Algorithm : LU Decomposition

Calculus

Limits, Continuity and Differentiability

Cauchy’s Mean Value Theorem

Lagrange’s Mean Value Theorem

Rolle’s Mean Value Theorem

Unimodal functions and Bimodal functions