Visual Real Analysis : Real Numbers & Real Sequences

A visual and brain-friendly course that makes real analysis fun and easy for college and university students

What you'll learn

Understand and have a mental representation of concepts related to real numbers (definition, density, supremum, upper bound, etc.)

Know how to represent sequences in a visual way

Understand an be able to manipulate concepts related to real sequences (induction, convergence, divergence, subsequence, monotonicity, etc.)

Understand and have a mental representation of tools and theorems related to real sequences (adjacent sequences, squeeze theorem, fixed point theorem, etc.)

Requirements

High school math, mainly calculus (functions and graphs, continuity, and differentiability)

Description

If you’re a college/university student in a STEM field and you’re taking a course on real sequences, this is for you. This course contains visual and brain-friendly videos that will help you better understand concepts related to real numbers and real sequences.This course is hands-on. You will have to pause several times during the videos and answer some questions that will help you make progress. Hopefully, at the end of this course, assignments and exams will look a lot easier for you.The first section of this course deals with real numbers. It defines real numbers and presents concepts related to the set ℝ of real numbers. These concepts are the floor and ceiling of a real number, the absolute value, the density of a subset of ℝ, the supremum, the upper bound, and the greatest element.The second section of this course is about real sequences. It starts with the definition and the different ways to visualize a real sequence. Then it clarifies several concepts related to real sequences: mathematical induction, convergence, divergence, monotonicity, and subsequences. Further, it presents tools and theorems related to real sequences: adjacent sequences, squeeze theorem, fixed point theorem, etc. And finally, it discusses particular sequences you will see a lot during your academic journey: arithmetic and geometric sequences, first- and second-order recursive sequences, and general recursive sequences.

Overview

Section 1: Real numbers

Lecture 1 Meet real numbers (1/2)

Lecture 2 Meet real numbers (2/2)

Lecture 3 Upper bound, supremum, greatest element

Lecture 4 Density of a subset of R

Section 2: Real sequences

Lecture 5 Definition and visualization of real sequences

Lecture 6 Mathematical induction

Lecture 7 Limit of a sequence

Lecture 8 Subsequences

Lecture 9 The Toolbox

This course is for college and university students who take math courses dealing with sequences.