Finally I studied the Fibonacci sequence and the golden spiral. I used to say: one day I will.

Very interesting course and made simple by the teacher in spite of the challenging topics

This course did a great job of giving me an amazing understanding of the Fibonacci numbers and the golden ratio. I found it super interesting, and I was delighted whenever a connection was found between the two large subjects was found. One recommendation that I have to improve the course is to provide a little more assistance/hints with solving the HW proofs/problems. I found some of them tricky at times, and giving up made me feel unsatisfied, so help in solving or giving out strategies on how to do difficult proofs would be greatly appreciated.

This course gives a fascinating insight in the logic behind some of nature's beauty. It requires a lot of maths, far more than I did at school (A Level) many years ago. It is definitely aimed at keen maths students. I found that many of the examples in the videos and the model answers to the questions missed lots of steps that I needed. These logic jumps may be second nature to somebody regularly studying maths , but for the 'casual' MOOCer at home who thinks "Ooh! that looks interesting", it left me struggling.

I enjoyed the course well presented and documented. One suggestion Professor Chasnov mentioned other Maths courses that are available. A problem I have being retired but interested in maths, what other classes are suitable, I often go into high school courses that I did years ago, or head off into really challenging areas that I have no chance of completing. I suggest that there should be a course tree maybe for number theory as a topic that gives guidance.

The theory explained and the exercises are not at the same level.

Embarking on the journey through Coursera’s “Fibonacci Numbers and the Golden Ratio” course, guided by Prof. Jeffrey Chasnov, was akin to uncovering the hidden threads that weave the fabric of our universe. The course stands out not only for its comprehensive exploration of the mathematical concepts but also for its rich tapestry of historical context that breathes life into numbers and ratios. Prof. Chasnov masterfully intertwines the abstract with the tangible, presenting the Fibonacci sequence and the golden ratio as more than mere topics of mathematical intrigue—they are the underpinnings of beauty in nature and art. The course’s structure is meticulously crafted, ensuring a smooth progression from fundamental principles to complex applications, making it accessible to enthusiasts of all levels. What sets this course apart is its immersive approach. Each lesson is a revelation, showcasing how these mathematical principles manifest in the world around us

The class is fantastic! The material is fascinating and just challenging enough. The length of the class was good—for keeping motivated for the entire 3 weeks. The instructor’s videos are very clear, precise, thorough and I loved being able to print out the class notes as well as solutions to problems and practice tests. The only thing that I think could be improved would be to include a clear definition of “origin” of the golden spiral. It seems to me that in the problems the origin is sometimes assumed to be the accumulation point, whereas in the proof of problem one for lecture 13 the origin is used as the origin ( of the coordinate system) and assumed to be the lower left hand corner of the largest golden rectangle. This confused me.

This is a very exciting course. I was pleased the instructor told us we could continue without worrying about the maths. Although I passed the initial diagnostic maths test and mostly scored high on the quizzes I found the maths well beyond me and could not even follow the solutions to the extra problems at the end of each section let alone attempt the questions. I would nevertheless recommend this course to anyone who finds numbers fascinating. Even if some of the maths goes over your head it is still possible to appreciate the main ideas. The enthusiasm of the instructor encouraged me to persist, thank you

I really liked this course, and I think the instructor is great. Everything is well explained, both in algebra as well as in theory and geometrically. Music and visual representations both fit, as well. I find incredible how these patterns are reproduced in nature and in ancient forms, and, how they inner correlate numerically with each other, also. I've always wanted to explore better this issue, as I find it very interesting and I know these patterns are used in trading. It is still incredible to think that nature replicated this pattern into many of its designs.

This course is wonderfully composed to give you a good foundation to the Fibonaccci numbers. A basic knowledge in Algebra is sufficient to follow this course since much of the other required information are delivered during the lecture or as supplementary videos. The best thing about this course is how Professor Casnov step by step explains interesting details which when combines gives a beautiful meaning even towards the nature. Loved every minute of the lecture, and I highly recommend this course to anyone who is curious about this topic.

Great course, as expected from Prof. Chaznov. This course was fun and very interesting. As an Informatics Engineer student, I thought I knew about Fibonacci numbers but wow, I really didn't. There's a whole more to it, and anyone can learn from it. The course is challenging, but fun as well. It takes a while to get used to prove a lot of identities by mathematical induction, with wasn't my favorite thing ever but after this course I think I've learned to like it, it's very satisfying. Looking forward to more math courses like this.

Instructor was very clear and easy to follow and the lessons had a logical flow to them. To get the most out of this course you need to be comfortable with algebraic manipulation generally, factorization of quadratics, rationalization of irrational fractions, and proofs by induction. Although the lecturer does go through matrices from scratch, if you've not met these before I think you'd need to supplement this a bit before being able to handle the lectures which use matrices and determinants. Overall, time well spent.

This is a great course which delivered an in-depth of analysis on Fibonacci number to many more related topic like golden ratio to Cassini's / Catalans identity and many more. It was an exceptional course on introduction to advanced mathematical thinking and how Fibonacci number appears in nature like construction of sunflower head with respect to florets arrangement by using golden angle. To complete each assignment need thorough understanding of each derivations.

I learned to do calculations on the sequences of Fibonacci but I did not know more than the recurrent definition of this one. But in this course Fibonacci Numbers and the Golden Ratio, I really learned a lot, and I'm so excited to know all these things about the Fibonacci numbers and the famous golden ratio. One of the most interesting things besides the calculations are the discoveries they reveal and their stories.

Very interesting course. By far the most interesting and challenging I have found so far in my preparation to go study maths at uni in a years time. Used some of my previous mathematical knowledge such as matrices and proof by induction, whilst pushing me to use them in different problems and derive new formulas and use new mathematical methods. Will definitely be talking about this on my personal statement!

I joined this course out of interest about the existence and visibility of Fibonacci sequence and the Golden Ratio in nature as also its connection with ancient Indian texts. Found this course very interesting. The instructor was very clear with the concepts and presented them very lucidly. Would recommend this course to those who want to understand the basics of Fibonacci Numbers and golden ratio.

One of the best course ive taken so far. The assignments were fun to solve due to its challenging nature, cant deny the booklet of being extremely beneficial at such times. Overall, i had an interest on Fibonacci Numbers and after taking this course, it completely changed what i thought and how i thought about Fibonacci. Feeling lucky and grateful to have taken this course.

This class has a very beautiful and practical topic. Professor Chasnov's mastery of the subject along with his beautiful teaching method will make you interested to. Also, the presence of numerous practical examples in this course will help you if the application of abstract mathematical concepts in your life is unclear. Many thanks to the teacher!

This course is well explained. Interesting. Surprisingly takes less time to complete but consumes a lot of time to dwell deeper into it with proofs and their applications. I would like to repeat all the exercises and want to learn more about the topic, whenever I get a chance. It has opened new world to think. Thanks for the beautiful course.

Very good course, interesting and well conducted. Topics were introduced little by little, the lectures were short, providing good fixation. At the end, the concluding remarks section was quite remarkable, as it recalled and unified the content learned. Congratulations and thanks to Professor Chasnov, a very good instructor, and to Coursera.

I really enjoyed this course. I have always been a fan of the golden ratio and this was a wonderful exploration of a variety of mathematical topics that are connected to them. It was presented in an interesting manner and in manageable chunks. I would definitely recommend this course to anyone interested in this topic.

This is my third course with Prof. Chasnov on Coursera. I really love his teaching styles and truly appreciate the greatness of mathematics and its application to our real world. Through this course, I enjoyed seeing the beauty of Fibonacci Numbers, the sequence, the Golden Ratios, the model of sunflowers, etc.

I had a great time going through this course. I highly recommend students to take up this course as it will change the very imaginative concept of mathematics. I also liked the mentor Mr.Jeffrey. He is so much interested and patient in taking classes. I really liked this course a lot. Thank you.

The professor is one of the top instructors. It is a 3 week course which completely covers all the material plus the preliminaries. There is a 120 page syllabus with lecture notes, practice problems, and solutions. For fun or for a certificate, this is an excellent course! Highly Recommend!

Very interesting Course!

It has so much enriched resource and was so useful for me, a high school's math teacher, who looking forward to the material to develop my course and keep it touching to the spirit of Math.

Thank you so much for sharing a delightful course like this!