Discrete Structures | Free Online Course | Alison

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Advanced Diploma in Discrete Structures

This free online course introduces you to the elements of mathematics that form the basis of computer science.

Free Course
This free online course introduces you to the elements of mathematics such as sets, functions and relations that form the basis of computer science. You will receive a basic understanding of formal logical statements and their proofs,as well as counting techniques, the concept of algebraic structures and how they are used in defining mathematical applications. Start this course today and learn more about discrete structures.
  • Duration

    20-30 Hours
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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.

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Introduction to Propositional Logic

Predicate Logic

Methods of Proof and Induction

Sets and Functions

Relations and their Properties


Recurrence Relations

Counting Techniques and Pigeonhole Principle


Algebraic Structures

Rings and Modular Arithmetic

Finite Fields and Applications

Course assessment

Learning Outcomes

Having completed this course you will be able to:

  • Define logic and proposition
  • Explain the concept of Predicate Logic
  • Explain how to solve problems using mathematical induction techniques
  • List the different unary and binary set operations
  • Define relations and how they are expressed in mathematical notation
  • Distinguish between functions and relations
  • List the properties of a partially ordered set (POSET)
  • Explain how a POSET is represented by a Hasse diagram
  • Define functions, sets and sequences recursively
  • Explain how to frame and solve recurrence relations
  • Apply the pigeonhole principle to solve problems
  • Compute permutations and combinations of sets and multisets
  • Distinguish between the different algebraic systems based on their properties
  • Explain how modular polynomial arithmetic governs the construction of a field


All Alison courses are free to enrol, study and complete. To successfully complete this Diploma course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Diploma course, you have the option to acquire an official Diploma, which is a great way to share your achievement with the world. Your Alison Diploma is:

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