 # Discrete Math

Discrete math, also known as “math for computer science” is usually a required course for students of computer science. The material typically covered in this class for CS students overlaps with fields such as cryptography, logic, information theory, theoretical computer science, artificial intelligence, design of algorithms, and others, and teaches the basic language and structures used by computer scientists. Sometimes discrete math is listed as a mathematics course. As a math class, it mainly deals with other abstract concepts (algebra, groups, or combinatorics) with a correspondingly heavier focus on proofs. A common characteristic of these classes is that for most students this is their first encounter with mathematical structures and proof. Unlike, for example, calculus classes, there is no commonly accepted definition or syllabus for this course and its content varies by school. The goal of this topic is to provide important representation models for data sets. This class provides ways for refining the original data model to something more easily understandable in respect to 1) representation format and 2) operations that can be executed on discrete data.

Most discrete math – computer science classes cover the following topics in some order and with varying degree of depth:

• Basics of logic and mathematical proof (proof by contradiction, proof by induction)
• Set theory and notation
• Representation of integers (bits, bitstring Boolean algebra)
• Basic number theory, computing modules and integer definitions of relations (what is a relational data base? A hash table?), and functions
• Basics of graph theory – directed and undirected graphs, useful to understand networking and telecommunications
• Introduction to methods of counting – permutations, combinations etc.
• Combinatorics
• Algorithms – for example sorting algorithms
• Algorithm complexity and estimation of run time – Big O Notation
• Computational Models, finite state machines, pseudocode – basic principles of programming
• Methods of encryption and secure communication – for example RSA algorithms- an introduction to cryptography

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