5.0
Beginner
6h 30min
An Introduction to Basic Set Theory
Gain insights into fundamental set theory concepts and operations. Explore relations, functions, set ordering, and cardinality using Python. Delve into Cantor’s diagonalization and its applications in various fields.
This course aims to introduce fundamental concepts of set theory. It provides hands-on experience through practical tasks using Python programming language (Python 3.8) to enhance engagement.
You’ll start with the basics of sets, their properties, and set operations. Additionally, you’ll learn about relations, functions, ordering of sets, and cardinality of sets. You’ll also explore Cantor’s diagonalization method as a tool to demonstrate the uncountability of sets.
After completing this course, you’ll have a solid understanding of the foundations of set theory that are vital for understanding many mathematics and computer science concepts, such as discrete mathematics, design of algorithms, theory of automata, and problem-solving. These concepts can also be applied in other significant areas including Physics, Statistics, and Probability.
This course aims to introduce fundamental concepts of set theory. It provides hands-on experience through practical tasks using ...Show More
WHAT YOU'LL LEARN
An understanding of basic mathematical structures and concepts of set theory
Familiarity with the set operations and their properties
Working knowledge of the Cartesian product of sets, relations, and functions
An understanding of the cardinality of finite and infinite sets
Familiarity with the countable and uncountable sets
Hands-on experience with Cantor’s diagonalization method
An understanding of basic mathematical structures and concepts of set theory
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Content
2.
Fundamentals
3 Lessons
Look at the essence of sets, subsets, power sets, universal sets, and Venn diagrams.
3.
Basic Set Operations
12 Lessons
Work your way through fundamental operations, laws, and principles in set theory.
4.
Relations
7 Lessons
Grasp the fundamentals of binary, reflexive, symmetric, transitive, and order relations with examples.
5.
Functions
6 Lessons
Take a closer look at functions, their types, compositions, and inverses with practical examples.
6.
Indexing and Ordering of Sets
2 Lessons
Simplify complex topics of set indexing, sequences, tuples, and their practical applications.
7.
Cardinality of Sets
2 Lessons
Build on understanding countable and uncountable sets, demonstrating varied cardinalities in set theory.
8.
Concluding Remarks
2 Lessons
Learn how to use set theory fundamentals and logical operations for advanced applications.
Certificate of Completion
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