Set Theory: A Brief Introduction

Course details

Hello and Welcome to Set Theory: A Brief Introduction

This course poses a brief introduction to the fundamentals of set theory. The main topics that comprise the course are sets and operations between sets, relations, equivalence relations and functions. Along the way, students taking this course will learn a few methods of proof and see how they arise while dealing with mathematical problems. Further, they will obtain the required knowledge for understanding courses that are formalized with the help of sets, relations between sets, operations between sets and functions defined on sets - For instance, in probability theory, a probability space is a triple - a set called the sample space, a collection of subsets of this set that satisfy specific properties and a function that maps each of these sets to a number in the real interval [0,1] , called a probability measure.

How Is The Course Structured?

The course is organized so that, when there're documents attached to lectures, they should be read after going over the lecture and before proceeding any further. Make sure to read and understand these - relatively short - documents thoroughly and DO NOT skip any supplementary material. In the last section, there are five problem sets. It's recommended that students solve the problems relevant to each section before they move to new sections. However, if you feel comfortable with the material, you can skip the problem set and get back to it later. This course is relatively short, and it takes the average student around 7 days to fully understand the material, interiorize it and solve the exercises that appear in the last section. The solutions for these exercises will be uploaded in about two weeks from the day the course is published. However, if you need any help solving any question, or if you're so excited about having a good solution for any problem, I'd be happy to know. A few days after the solutions are online, a downloadable pdf file - holding the name All in One will be published in the last section. This file will include all the material taught in this course in the form of an ebook, broken up into sections including the problem sets and solutions - this file would make an easy access and a good assistant if you plan on viewing the whole course at once. More lectures and sections might be added to the course in the future. In case any modifications have been made to the course, it will be written in the announcements forum, thus it's your responsibility to go over the annoucements.

Do you find problems understanding the material or solving any exercise? Please let me know. I hope you'll enjoy this course and benefit a lot from it =)

your instructor,