Unlock the Secrets of Mathematical Induction: A Step-by-Step Guide to Mastering Both Regular and Strong Induction
Are you a first-year student struggling with mathematical induction? You’re not alone—many students find this concept difficult to grasp. But it doesn't have to be. In this course, you'll break down the fundamentals of both regular and strong induction with tons of fully worked out examples and clear explanations, all designed to make induction easy to understand.
What You’ll Learn
-
The core principles behind regular induction, walking you through base cases and inductive steps.
-
How to apply strong induction to more complex problems and see where it’s necessary over regular induction, especially involving recursive definitions / recursive functions.
-
Master the process of writing clear, step-by-step proofs using induction.
-
Understand common mistakes students make and how to avoid them.
-
Work through tons of examples so you can tackle even the hardest induction problems with confidence.
Who Is This Course For?
-
First-year college students taking a course in mathematical induction or discrete mathematics.
-
High school students preparing for advanced mathematics courses.
-
Anyone looking to solidify their understanding of induction for tests or exams.
Course Overview
Lectures And Examples
14 lessons
- VIDEO: Intro To Sigma Notation
- VIDEO: Introduction To Induction
- VIDEO: A Second Induction Example
- VIDEO: Induction Where The Induction Step Has More Than One Term
- Induction Examples - Sums
- Induction Examples - Inequalities
- VIDEO: Strong Induction & Recursive Definitions
- Induction Examples - Recursive Definitions
- VIDEO: Induction Example - Divisibility
- VIDEO: Induction With Other Variables
- Induction Examples - Number Theory
- Induction Example - Additional Number Theoretic
- Induction Examples - Matrices
- Induction Examples - Complex Numbers
Worksheets
1 lessons
- Sigma Notation Worksheet
Advanced Topics
4 lessons
- VIDEO: Induction Examples: Primes Dividing Products
- VIDEO: Strong Induction Example - Every Integer Can Be Written As A Product Of Primes
- VIDEO: Well Ordering Principle
- VIDEO: Proof of PMI By Well Ordering
Get To Know Your Instructor
Rob Borgersen is the lead minister of the Winnipeg Church of Christ and a former mathematics instructor at the University of Manitoba, where he taught for nearly 20 years. With a deep passion for helping students understand complex mathematical concepts, Rob specializes in making challenging topics like mathematical induction approachable and clear. His years of teaching experience have equipped him to guide students through the nuances of induction, ensuring that they build the confidence and skills needed to succeed in their studies. Whether you're struggling with regular induction or strong induction, Rob is dedicated to helping you master these critical concepts and excel in your logic courses.
Testimonials
"As a second degree student, Rob is one of the best instructors I’ve had. He does an excellent job of explaining content through real world applications which greatly helps in understanding and visualizing problems." - Dylan Z.
"Rob gave easy to follows instructions on how to pass the course, which was to work has many examples has possible in the text book and worksheet. Personally, I finished all examples and exercises in the worksheet and text books respectively while I also engaging the TA on area that needs clarification." - Taiwo O.
"Coming from another country, I was so sure that I wasn’t going to perform that well in my first course since I am new to the system and the teaching style is different from the one I am used to but Rob’s teaching made things really easy for me and to my surprise I performed so well in the course. Thank you so much Rob!" - Abimbola S.
"Rob's a dedicated teacher and clearly loves his job. He was always willing to look over a proof...and the constant feedback is the main reason I did so well in the class." - Luke W.
"Amazing professor. He’s real and friendly! He also helps a lot and is always within reach, he was the first professor I did not feel bad or scared reaching out to- that too, just over text. He’s also passionate about the course and that’s what really mattered to me in the end." - Sheikha W.
Mastering Mathematical Induction: From Basics to Strong Induction with Step-by-Step Examples
Course
C$49.97