Mathematics: Proofs by induction

Mathematics: Proofs by induction, available at Free, has an average rating of 4.7, with 13 lectures, based on 118 reviews, and has 6660 subscribers.

You will learn about How to conduct proofs by induction and in what circumstances we should use them. Prove (by induction) some formulas holding for natural numbers. Prove (by induction) some statements about divisibility of natural numbers. Prove (by induction) explicit formulas for sequences defined in a recursive way. Prove (by induction) some simple inequalities holding for natural numbers. You will also get an information about more advanced examples of proofs by induction. You will get a short explanation how to use the symbols Sigma and Pi for sums and products. This course is ideal for individuals who are High school students who want to learn conducting proofs by induction. or University or college students who have discovered that they need to master proofs by induction for some university level courses, and they want to re-learn this method of proving theorems. or Everybody who likes mathematics and want to learn more of it. It is particularly useful for High school students who want to learn conducting proofs by induction. or University or college students who have discovered that they need to master proofs by induction for some university level courses, and they want to re-learn this method of proving theorems. or Everybody who likes mathematics and want to learn more of it.

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Summary

Title: Mathematics: Proofs by induction

Price: Free

Average Rating: 4.7

Number of Lectures: 13

Number of Published Lectures: 13

Number of Curriculum Items: 13

Number of Published Curriculum Objects: 13

Original Price: Free

Quality Status: approved

Status: Live

What You Will Learn

How to conduct proofs by induction and in what circumstances we should use them.
Prove (by induction) some formulas holding for natural numbers.
Prove (by induction) some statements about divisibility of natural numbers.
Prove (by induction) explicit formulas for sequences defined in a recursive way.
Prove (by induction) some simple inequalities holding for natural numbers.
You will also get an information about more advanced examples of proofs by induction.
You will get a short explanation how to use the symbols Sigma and Pi for sums and products.

Who Should Attend

High school students who want to learn conducting proofs by induction.
University or college students who have discovered that they need to master proofs by induction for some university level courses, and they want to re-learn this method of proving theorems.
Everybody who likes mathematics and want to learn more of it.

Target Audiences

High school students who want to learn conducting proofs by induction.
University or college students who have discovered that they need to master proofs by induction for some university level courses, and they want to re-learn this method of proving theorems.
Everybody who likes mathematics and want to learn more of it.

How would you prove that a theorem or a formula is true for *all* natural numbers? Try it for n=0, n=1, n=2, etc? It seems to be a lot of work, or even completely impossible, as there are infinitely many natural numbers!

Don’t worry, there is a solution to this problem. This solution is called “proof by induction” and this is the subject of this short (and free) course. The Induction Principle is often compared to the “domino effect”, which will be illustrated in the course. (This is also the reason for our course image.)

In this course you will learn how induction proofs work, when to apply them (and when not), and how to conduct them. You will get an illustration of this method on a variety of examples: some formulas, some inequalities, some statements about divisibility of natural numbers. You will also get some information about other courses where you can see some theory, and more advanced proofs based on the same principle.

Sadly, there is no possibility of asking question in free courses, but you can ask me questions about this subject via the QA function in my other course: “Precalculus 1: Basis notions”, where the topic of proofs by induction is covered, both theoretically (Peano’s axioms) and practically, with several examples.

Extras

You will learn: about all the courses we offer. You will also get a glimpse into our plans for future courses, with approximate (very hypothetical!) release dates.

Course Curriculum

Chapter 1: What is mathematical induction and how it works

Lecture 1: Introduction to the course

Lecture 2: What kinds of statements can be proven by induction

Lecture 3: Induction: this is how it works

Lecture 4: Both cases are necessary

Chapter 2: Examples of proofs by induction

Lecture 1: Proving formulas, Problem 1

Lecture 2: Sequences: guess and prove, Problem 2

Lecture 3: Sequences: guess and prove, Problem 3 with two base cases

Lecture 4: Proving divisibility, Problem 4

Lecture 5: Not necessarily for all natural numbers: an inequality, Problem 5

Lecture 6: A difficult proof, Problem 6

Lecture 7: Another difficult proof, Problem 7

Lecture 8: Proofs by induction, Wrap-up

Chapter 3: Extras

Lecture 1: Bonus Lecture

Instructors

Hania Uscka-Wehlou
University teacher in mathematics, PhD
Martin Wehlou
Editor at MITM AB

Rating Distribution

1 stars: 0 votes
2 stars: 1 votes
3 stars: 5 votes
4 stars: 8 votes
5 stars: 104 votes

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