# Introduction To

Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry.

Historically, engineering mathematics consisted mostly of applied analysis, most notably: differential equations, real and complex analysis (including vector and tensor analysis).

The goal of this mathematics course is to provide high school students and college freshmen an introduction to basic mathematics and especially show how mathematics is applied to solve fundamental engineering problems. As well as to show the students why mathematics is important in an engineering career by demonstrating how simple engineering problems can be mathematically described and methodically analyzed to find a solution.

# Course Structure

## Propositional and First Order Logic

- Mathematics | Introduction to Propositional Logic | Set 1
- Mathematics | Introduction to Propositional Logic | Set 2
- Mathematics | Propositional Equivalences
- Mathematics | Predicates and Quantifiers | Set 1
- Mathematics | Predicates and Quantifiers | Set 2
- Mathematics | Some theorems on Nested Quantifiers
- Mathematics | Rules of Inference
- PDNF and PCNF in Discrete Mathematics

## Set Theory

- Mathematics | Introduction of Set theory
- Mathematics | Set Operations (Set theory)
- Inclusion-Exclusion and its various Applications
- Mathematics | Power Set and its Properties
- Mathematics | Partial Orders and Lattices
- Mathematics | Algebraic Structure
- Mathematics | Introduction and types of Relations
- Discrete Mathematics | Representing Relations
- Mathematics | Closure of Relations and Equivalence Relations
- Number of possible Equivalence Relations on a finite set
- Mathematics | Classes (Injective, surjective, Bijective) of Functions
- Mathematics | Total number of possible functions
- Discrete Maths | Generating Functions-Introduction and Prerequisites
- Mathematics | Generating Functions – Set 2
- Mathematics | Sequence, Series and Summations
- Mathematics | Independent Sets, Covering and Matching
- Mathematics | Introduction to Proofs
- Discrete Mathematics | Hasse Diagrams
- Introduction to Mojette transform
- Mathematics | Rings, Integral domains and Fields

## Combinatorics

- Mathematics | The Pigeonhole Principle
- Mathematics | Combinatorics Basics
- Mathematics | PnC and Binomial Coefficients
- Mathematics | Generalized PnC Set 1
- Mathematics | Generalized PnC Set 2
- Corollaries of Binomial Theorem
- Number of triangles in a plane if no more than two points are collinear
- Mathematics | 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

## Graph Theory

- Mathematics | Graph Theory Basics – Set 1
- Mathematics | Graph Theory Basics – Set 2
- Graph Types and Applications
- Mathematics | Euler and Hamiltonian Paths
- Mathematics | Planar Graphs and Graph Coloring
- Mathematics | Graph Isomorphisms and Connectivity
- Mathematics | 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

## Linear Algebra

- Mathematics | Matrix Introduction
- Different Operations on Matrices
- Mathematics | Representations of Matrices and Graphs in Relations
- Mathematics | Eigen Values and Eigen Vectors
- Mathematics | System of Linear Equations
- Mathematics | L U Decomposition of a System of Linear Equations
- Doolittle Algorithm : LU Decomposition

## Calculus

- Mathematics | Limits, Continuity and Differentiability
- Cauchy’s Mean Value Theorem
- Mathematics | Lagrange’s Mean Value Theorem
- Mathematics | Rolle’s Mean Value Theorem
- Mathematics | Unimodal functions and Bimodal functions
- Activation Functions
- Surface Area and Volume of Hexagonal Prism
- Inverse functions and composition of functions
- Mathematics | Indefinite Integrals

## Statistics and Numerical Methods

- Mathematics | Mean, Variance and Standard Deviation
- Newton’s Divided Difference Interpolation Formula
- Mathematics | Law of total probability
- Mathematics | Probability Distributions Set 1 (Uniform Distribution)
- Mathematics | Probability Distributions Set 2 (Exponential Distribution)
- Mathematics | Probability Distributions Set 3 (Normal Distribution)
- Mathematics | Probability Distributions Set 4 (Binomial Distribution)
- Mathematics | Probability Distributions Set 5 (Poisson Distribution)
- Homogeneous Poisson Process
- Nonhomogeneous Poisson Processes
- Mathematics | Renewal processes in probability
- Mathematics | Covariance and Correlation
- Scales of Measurement
- Univariate, Bivariate and Multivariate data and its analysis
- Mathematics | Hypergeometric Distribution model