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Visual Real Analysis : Real Numbers & Real Sequences
Rating: 4.5 out of 5(12 ratings)
3,199 students

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
Created byEpsilonia Corp.
Last updated 4/2023
English

What you'll learn

  • Understand and have a mental representation of concepts related to real numbers (definition, density, supremum, upper bound, etc.)
  • Learn three ways to represent sequences in a visual way: on a line, as a mapping and using a function’s graph
  • 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.)

Explore related topics

Course content

2 sections • 14 lectures • 2h 44m total length

  • Meet real numbers (1/2)12:25

    This is an introduction to the course and the first part of the video on the definition of real numbers.

  • Meet real numbers (2/2)13:31

    This is the second part of the video on the definition of real numbers.

  • Upper bound, supremum, greatest element14:30

    What's an upper bound? supremum? Greatest element/maximum? And what is the difference between these three concepts?

  • Density of a subset of R14:17

    The difference between a subset of ℝ that is dense and one that is not is the difference between ℤ and ℚ... 

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.


Who this course is for:

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

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