## Part 1 - Linear Algebra

##
#### Introduction to Linear Algebra

Introduction, Definition

Linear Combination and Linear Equation

Linear Independence

System of Linear Equations

Geometry of Linear Equations

Solution of System of Linear Equations

*1) Geometrical Method*

*2) Substitution Method*

*3) Elimination Method *

#### Vectors

Introduction and Geometry

Notation

Basic Properties and Operations

*Scalar Multiplication, Addition, Subtraction, Angle *

Linear Combination of Vectors

Magnitude of a Vector

Dot Product

*Comutation and Geometric Interpretation *

Dot Product

Application of Dot Product

*Magnitude, Angle Between Vectors, Orthogonality, Norm, Distance*

Cross Product

* Comutation and Geometric Interpretation*

Application of Cross Product

#### Matrices

System of Linear Equations and Matrix Notation

Application

*Images as Multi-dimensional Arrays *

Basic Properties and Operations

*Images as Multi-dimensional Arrays *

Linear Transformation and Matrices

Basic Properties and Operations

*Scalar Multiplication, Addition, Subtraction, Transpose *

Matrix Product as Composition of Transformations

Types of Matrices

*Identity, Orthogonal, Sparse, Triangular *

Determinant

*Computation and Geometric Interpretation*

Inverse of a Matrix

* Comutation and Geometric Interpretation*

Solution of System of Linear Equations

*1) Cramer's Rule* *2) Matrix Inverse*

*3) Echelon Form * *4) Reduced Row Echelon Form*

Types of Solution

*Unique, Infinite, Inconsistent*

Eigenvalues

Eigenvectors

Applications of Matrices

*Application 1*

*Application 2*

#### Introduction to Linear Algebra

Introduction, Definition

Linear Combination and Linear Equation

Linear Independence

System of Linear Equations

Geometry of Linear Equations

Solution of System of Linear Equations*1) Geometrical Method* *2) Substitution Method 3) Elimination Method *

#### Vectors

Introduction and Geometry

Notation

Basic Properties and Operations*Scalar Multiplication, Addition, Subtraction, Angle *

Linear Combination of Vectors

Magnitude of a Vector

Dot Product *Comutation and Geometric Interpretation *

Dot Product

Application of Dot Product*Magnitude, Angle Between Vectors, Orthogonality, Norm, Distance*

Cross Product * Comutation and Geometric Interpretation*

Application of Cross Product

#### Matrices

System of Linear Equations and Matrix Notation

Application *Images as Multi-dimensional Arrays *

Basic Properties and Operations*Images as Multi-dimensional Arrays *

Linear Transformation and Matrices

Basic Properties and Operations *Scalar Multiplication, Addition, Subtraction, Transpose *

Matrix Product as Composition of Transformations

Types of Matrices*Identity, Orthogonal, Sparse, Triangular *

Determinant*Computation and Geometric Interpretation*

Inverse of a Matrix * Comutation and Geometric Interpretation*

Solution of System of Linear Equations *1) Cramer's Rule* *2) Matrix Inverse 3) Echelon Form 4) Reduced Row Echelon Form*

Types of Solution*Unique, Infinite, Inconsistent*

Eigenvalues

Eigenvectors

Applications of Matrices*Application 1**Application 2*

## Part 2 - Probability and Random Variables

##
#### Probability

Historical Background

Random Experiment

Sample Space, Event

Set Theory

Law of Large Numbers

Axiomatic Definition of Probability

Conditional Probability

Joint Probability

Marginal Probability

Multiplication Rule and Tree Diagrams

Bayes Theorem

#### Random Variables

Discrete Random Variable

Concept of Random Variable

Discrete Probability Distributions

*Binomial, Poisson, Hypergeometric, Bernoulli *

Continuous Random Variable

Continuous Probability Distributions

*Normal, Exponential*

#### Probability

Historical Background

Random Experiment

Sample Space, Event

Set Theory

Law of Large Numbers

Axiomatic Definition of Probability

Conditional Probability

Joint Probability

Marginal Probability

Multiplication Rule and Tree Diagrams

Bayes Theorem

#### Random Variables

Discrete Random Variable

Concept of Random Variable

Discrete Probability Distributions *Binomial, Poisson, Hypergeometric, Bernoulli *

Continuous Random Variable

Continuous Probability Distributions*Normal, Exponential*

## Part 3 - Statistics and Hypothesis Testing

##
#### Descriptive Statistics

What is Statistics?

Applicatons of Statistics

Terminologies

Measures of Location

Measures of Variability

Histograms

Measures of Association b/w variables

#### Inferential Statistics

Hypothesis Tests

*1) Null and Alternative Hypothesis* *2) Type I and Type II Errors*

*3) One Tailed and Two Tailed Tests*

Inferences about population mean

*Variance known and unknown*

Inferences about population proportion

*Variance known and unknown *

ANOVA

#### Regression

Linear Regression

Polynomial Regression

Goodness of fit

#### Descriptive Statistics

What is Statistics?

Applicatons of Statistics

Terminologies

Measures of Location

Measures of Variability

Histograms

Measures of Association b/w variables

#### Inferential Statistics

Hypothesis Tests *1) Null and Alternative Hypothesis* *2) Type I and Type II Errors*

*3) One Tailed and Two Tailed Tests*

Inferences about population mean *Variance known and unknown*

Inferences about population proportion *Variance known and unknown *

ANOVA

#### Regression

Linear Regression

Polynomial Regression

Goodness of fit

## Part 4 - Calculus

##
#### Derivatives

Derivative definition and meaning

Highe Order Derivatives

Chain Rule

#### Optimization

First Derivative Test

Second Derivative Test

Applications

#### Partial Derivatives

Definition and interpretation

Gradients

Gradient Descent

#### Derivatives

Derivative definition and meaning

Highe Order Derivatives

Chain Rule

#### Optimization

First Derivative Test

Second Derivative Test

Applications

#### Partial Derivatives

Definition and interpretation

Gradients

Gradient Descent