In this course you will learn discrete mathematics and study mathematical logic, mathematical proofs, set theory, functions, relations, graph theory, number theory as well as combinations and permutations. Each chapter of the course can be taken independently if required, and each chapter covers all of the listed topics in details so you will study everything that is necessary and in the order that most suits you as a student. As students usually come to this course for specific topic(s) and exercises, here is the comprehensive list of what you will learn from each chapter of this course: Logic: Propositions, Connectives, Truth Tables, Logic Gates, Conditional and Biconditional Propositions, Rules of Inference, Predicates and Quantifiers Proofs: Direct and Indirect Proofs, Proof by Induction and other Methods of Proof Sets: Sets and Number Sets, Complement Sets, Cartesian Product, Operations, Boolean Algebra and De Morgan's Law Functions and relations: Ordered Pair, Dom, Range, Inverse Relations Graphs: Simple and Complete Graph, Bipartite Graph, Paths and Circuits, Euler Circuit and Euler Path, Hamiltonian Circuit and Hamiltonian Path, Trees Numbers: Divisibility and Division Algorithm, Euclidean Algorithm Combinatorics: Combinations, Permutations, Fundamental Principle of Counting

Learn the fundamentals of Java 8.0 Work with primitive types and expressions Work with non-primitive types (classes, structs, arrays and enums) Learn the difference between value types and reference types Control the flow of programs using conditional statements Use arrays and lists Work with files and directories Work with text Work with date and time

Learn the fundamentals of C# Work with primitive types and expressions Work with non-primitive types (classes, structs, arrays and enums) Learn the difference between value types and reference types Control the flow of programs using conditional statements Use arrays and lists Work with files and directories Work with text Work with date and time Debug C# applications effectively

Learn all Important Concepts of C Understand Keywords, Variables and Data Types Understand Comments and Operators Implement Statements Apply Loops Implement Functions Use Arrays Apply Pointers Use String and Method Understand File Handling Complete Projects

I offer support courses in programming languages C, C ++, Java for beginners the course will begin with the architecture of computers to fully understand the world of computing C course: initiation + data structures + system programming C ++ course: initiation + data structures + ... Java: initiation + initiation the OOP + .....