In this free online course, you will be introduced to the fundamentals of logic and proposition. You will learn how to construct truth tables and how to verify the validity of arguments. You will also learn about propositional logic and predicate logic and understand how laws of inference are used on quantified statements to solve practical problems.

Next, you will learn about mathematical systems, proof techniques and the concept of mathematical induction. You will be exposed to set theory, including the different unary and binary set operations and representations of set relationships by Venn and Arrow diagrams. Following set theory, you will learn about relations and their properties, including equivalence relation and POSET. You will also learn how to define set relations using recursion and how to frame or design recursive algorithms. Next, you will delve into recurrence relations, the pigeonhole principle and the inclusion-exclusion principle.

The next part of the course will introduce you to combinatorics and permutations and combinations of sets and multisets. You will also get to know about different algebraic systems and their properties, including ring, group, and field. Finally, you will be exposed to modular and polynomial arithmetic, that governs the construction of finite fields. This course will be of interest to students of mathematics, engineering and science, or those interested in learning more about the advanced principles of mathematical and logical systems.