**Discrete Structures Handwritten Notes**

## What is Discrete Structures ?

Discrete Structures is a branch of mathematics involving discrete elements that uses algebra and arithmetic. It is increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities.

## What is the difference between Continuous and Discrete Mathematics ?

**Continuous Mathematics**− It is based upon continuous number line or the real numbers. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. For example, a function in continuous mathematics can be plotted in a smooth curve without breaks.**Discrete Mathematics**− It involves distinct values; i.e. between any two points, there are a countable number of points. For example, if we have a finite set of objects, the function can be defined as a list of ordered pairs having these objects, and can be presented as a complete list of those pairs.

### Topics in our Discrete Structures Handwritten Lecture Notes PDF

In these “* Discrete Structures Handwritten Lecture Notes PDF*”, you will study the fundamental concepts of Sets, Relations and Functions, Mathematical Logic, Group theory, Counting Theory, Probability, Mathematical Induction and Recurrence Relations, Graph Theory, Trees and Boolean Algebra.

The topics we will cover will be taken from the following list:

**Introduction: **Sets – finite and infinite sets, uncountable infinite sets; functions, relations, properties of binary relations, closure, partial ordering relations; counting – Pigeonhole Principle, permutation and combination; mathematical induction, Principle of Inclusion and Exclusion.

**Growth of Functions: **asymptotic notations, summation formulas and properties, bounding summations, approximation by integrals.

**Recurrence: **recurrence relations, generating functions, linear recurrence relations with constant coefficients and their solution, recursion trees, Master Theorem

**Graph Theory: **basic terminology, models and types, multi-graphs and weighted graphs, graph representation, graph isomorphism, connectivity, Euler and Hamiltonian Paths and Circuits, planar graphs, graph coloring, Trees, basic terminology and properties of Trees, introduction to spanning trees.

**Propositional Logic**: logical connectives, well-formed formulas, tautologies, equivalences, Inference Theory.