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.

Math
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
  • Certification

    Yes
  • Mobile Friendly

    Yes
  • Publisher

    NPTEL
  • Accreditation

    CPD

Description

Modules

Outcome

Certification

View course modules

Description

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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Modules

Introduction to Propositional Logic

Predicate Logic

Methods of Proof and Induction

Sets and Functions

Relations and their Properties

Recursion

Recurrence Relations

Counting Techniques and Pigeonhole Principle

Combinatorics

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

Certification

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:

Ideal for sharing with potential employers - include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning

Alison offers 3 types of Diplomas for completed Diploma courses:

Digital Diploma - a downloadable Diploma in PDF format, immediately available to you when you complete your purchase
Diploma - a physical version of your officially branded and security-marked Diploma, posted to you with FREE shipping
Framed Diploma - a physical version of your officially branded and security-marked Diploma in a stylish frame, posted to you with FREE shipping

All Diplomas are available to purchase through the Alison Shop. For more information on purchasing Alison Diplomas, please visit our FAQs. If you decide not to purchase your Alison Diploma, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Diploma pricing, please visit our Pricing Page.

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