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Fibonacci Numbers and the Golden Ratio
This is the paperback edition of my lecture notes for my online Coursera course, Fibonacci Numbers and the Golden Ratio . These lecture notes are divided into chapters called Lectures, and each Lecture corresponds to a video on Coursera.
Most of the Lectures also contain problems for students to solve. Less experienced students may find some of these problems difficult. Do not despair! The Lectures can be read and watched, and the material understood and enjoyed without actually solving any problems. But mathematicians do like to solve problems and I have selected those that I found to be interesting. Try some of them, but if you get stuck, full solutions can be read in the Appendix.
My aim in writing these lecture notes was to place the mathematics at the level of an advanced high school student. Proof by mathematical induction and matrices, however, may be unfamiliar to a typical high school student and I have provided a short and hopefully readable discussion of these topics in the Appendix. Although all the material presented here can be considered elementary, I suspect that some, if not most, of the material may be unfamiliar to even professional mathematicians since Fibonacci numbers and the golden ratio are topics not usually covered in a University course. So I welcome both young and old, novice and experienced mathematicians to peruse these lecture notes, watch my lecture videos, solve some problems, and enjoy the wonders of the Fibonacci sequence and the golden ratio.
Most of the Lectures also contain problems for students to solve. Less experienced students may find some of these problems difficult. Do not despair! The Lectures can be read and watched, and the material understood and enjoyed without actually solving any problems. But mathematicians do like to solve problems and I have selected those that I found to be interesting. Try some of them, but if you get stuck, full solutions can be read in the Appendix.
My aim in writing these lecture notes was to place the mathematics at the level of an advanced high school student. Proof by mathematical induction and matrices, however, may be unfamiliar to a typical high school student and I have provided a short and hopefully readable discussion of these topics in the Appendix. Although all the material presented here can be considered elementary, I suspect that some, if not most, of the material may be unfamiliar to even professional mathematicians since Fibonacci numbers and the golden ratio are topics not usually covered in a University course. So I welcome both young and old, novice and experienced mathematicians to peruse these lecture notes, watch my lecture videos, solve some problems, and enjoy the wonders of the Fibonacci sequence and the golden ratio.
112 pages, Paperback
Published February 2, 2023
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