Back to Introduction to Complex Analysis

4.8

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666 ratings

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208 reviews

This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into territories at the edge of what is known today. Each module consists of five video lectures with embedded quizzes, followed by an electronically graded homework assignment. Additionally, modules 1, 3, and 5 also contain a peer assessment.
The homework assignments will require time to think through and practice the concepts discussed in the lectures. In fact, a significant amount of your learning will happen while completing the homework assignments. These assignments are not meant to be completed quickly; rather you'll need paper and pen with you to work through the questions. In total, we expect that the course will take 6-12 hours of work per module, depending on your background....

Apr 06, 2018

The lectures were very easy to follow and the exercises fitted these lectures well. This course was not always very rigorous, but a great introduction to complex analysis nevertheless. Thank you!

Mar 21, 2017

With this wonderful complex analysis course under your belt you will be ready for the joys of Digital Signal Processing, solving Partial Differential Equations and Quantum Mechanics.

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By James B

•May 15, 2019

Lots of neat math! It's challenging and requires a substantial time commitment. Though in CS, my love of math was re-awakened. If you are in CS and only want to know the basics of how to rotate objects with complex numbers and polar coordinates, then this course is way more than you need. If you enjoy math, have had little or no complex analysis and are curious about what's up with the complex plane, I recommend this course.

By Rens K

•Apr 06, 2018

The lectures were very easy to follow and the exercises fitted these lectures well. This course was not always very rigorous, but a great introduction to complex analysis nevertheless. Thank you!

By Hrvoje B

•Mar 23, 2018

The course covers beautiful corner of mathematics and is a wonderful introduction to the topic of Complex Analysis. I would highly recommend this course for undergraduate students. In my opinion maybe it`s too tough for highschool graduates.

Material was well motivated and clearly presented. The quizes and homework assignments generally may took longer than the stated time, but that`s just fine. Feedback on quizzes was excellent and useful.

In the end, Prof. Petra Bonfert-Taylor, does an excellent job at explaining concepts simply. The main reason for that are her extraordinary pedagogic skills. She made a well organized and concise course. I hope there will be an opportunity to take another course with her again Overall, I`m very satisfied and grateful!

By Arpon P

•Feb 25, 2017

This course is fairly appropriate for those who have completed high school eduaction and opt to pursue higher studies in the field of science and engineering. This is an introductory course on complex analysis and does not cover advanced topics like zeta function, Manderbolt set etc in great detail. If you are doing major on Mathematics and looking for a graduate level course, this is not for you.This course offers an introduction to complex numbers, then discusses briefly on function iteration. In this course, you will learn on complex functions, complex derivative and integration, Cauchy-Riemann equation, Residues. The topics required to pursue undergraduate science education are covered nicely in this course.It is essential to do the quizzes and assignments to get hold of this topic. I thought the exercises in the course are not enough. I would recommend to do more exercises from any standard textbook on Complex Analysis. This course does not specifically follow any textbook. You will get some suggestions for textbook in the discussion forum.To get a deeper understanding, it is a great idea to follow the discussion forum. If you have any difficulty in understanding any topic, you can share in the discussion forum. Also following other people's questions helps you to develop an insight on this topic. Discussion forum is an integral part of this course. Use it wisely.To conclude, any high school graduate can take the course without any difficulty.

By Marcin B

•Apr 07, 2020

Petra Bonfert-Taylor did a great job constructing this course. Her video lectures are clear and easy to follow. I took this course because I had lousy instructors at the university and this course filled the gap. There are a lot of examples and exercises where you actually have to do a lot of counting and playing with mathematical expressions. Much less focus is put on proofs, although some simple proofs are presented and sometimes the instructor outlines the main ideas behind other formal proofs. It may be beneficial to follow a standard textbook on complex analysis along with the online course. Last thing, the course is not easy. Unless you already have substantial experience with complex analysis prepare to study intensively. My experience is that it is important to re-do on your own all material covered during lectures. And indeed, without a good background on calculus and some general mathematical fluency, this course would be hard to complete.

By 黄鹏锟

•Apr 02, 2018

It's the first time I join a class like this, I think it's a fantastic experience for me, Although I was busy after I came back to school, it's the course itself that encourage me to finish all kinds of work in my spare time, and I do learn something about complex analysis, which I will learn in detail in my follow college years. Thanks to the course, I could have a overview about my class. Last but not least, I think the way that let us check homework for each other is really nice, I spend a few hours to finish the first one because I really want to leave an good impression for my classmates, who are really nice because they gave me warm and nice judgement. I think I would highly recommend this course for whoever want to have a overview and application of complex analysis.

By Assaf B

•Feb 22, 2018

This is a beautiful area, delivered in a brilliant manner here. It succeeds in delivering most of the material in a near-uncompromising way, even though it also targets those who remember single variable calculus and nothing more.

This does not mean that the course is easy, especially if you just have the basic prerequisites, or are separated years from the last time you learned math like myself, when trying to complete tasks, you will find yourself getting back to the material and reviewing slides and videos again, and this challenge really adds to the understanding of the material. Also, as an added bonus, if you are distant many years from the time you last learnt mathematics, it will remove a little of the rust.

Brilliantly done.

By Gary U

•Oct 02, 2017

Excellent course for an introduction to complex analysis. Beginning from basic concepts, the instructor develops the basis of complex analysis. The first two weeks having to do with Julia sets and Mandelbrot sets are colorful lessons, the real analysis starts on week 3. The instructor is excellent, providing step by step instructions in the presentation and also some proofs of the theorems. Week 4 lessons 4 and 5 deal with the Riemann Zeta function and the Prime Number Theorem, very interesting and addition to the course. There is much more that could be added, perhaps a further course can be developed for the MOOC.

By Meir S

•Jan 17, 2017

Excellent entry into the world of complex analysis. Dr. Petra Bonfert-Taylor carefully constructs the foundations for complex functions while constantly providing enriching examples. Complications in advanced proofs are sometimes obviated (she will mention what she chooses to skip). If you only need to learn to use complex analysis Dr. Petra Bonfert-Taylor provides more than enough guidance. Since I enjoy understanding mathematics from the axioms up, I found myself turning to outside resources to fill in the nuanced complications. Consider doing the same if you are like me.

By shouvik d

•Oct 02, 2016

A great course for beginners and engineers looking to just apply concepts of Complex Analysis without going too much into mathematical rigour. This course does not require any knowledge of "Real Analysis" or "Multi-variable/Vector" calculus as a prerequisite which is one of it's greatest strengths.

This has especially helped in my preparation for a graduate-entrance exam called GATE that we have here in India.

Although, I believe the course could include some more number of problems and solutions.

By Daniel S

•Sep 26, 2016

This is an outstanding course; one of the gems of the Coursera platform. It is only the launching point for my study of and fascination with complex analysis. I'd say the course covers about three-fifths of the content for an engineering mathematics treatment of functions of complex variables. I'm a student of fluid mechanics and my ignorance of advanced concepts in complex analysis has kept me from mastering some of the advanced topics in FM. I'm well on my way to go beyond those barriers, now.

By Sam G

•Jun 25, 2017

This course was incredible. The teacher was made the experience understandable and fun giving light onto a new world of mathematics that I had only dreamed of investigating.

The lectures each week were insightful and interesting for all skill levels. (Although it may have been easier had I not had external exams to do)

I would highly recommend this course which spans from A-level to Year 3 university studies as it is presented in a clever and accessible way.

By Stanley Y

•Jan 12, 2019

Excellent pacing of materials. The assignments strike that rare balance of enforcing key concepts that were discussed during that week's lectures and not being too difficult. And more than that, in my opinion, you can certainly tell that the instructor really cares about teaching in general. I took this class on a whim because I saw it was available and thought "eh, why not?", and I am delighted to say that this feels stumbling on some hidden treasure.

By Jerry H

•Aug 03, 2018

This is an excellent and challenging course! A great introduction to complex analysis. I feel some materials covered in the course might lack rigorous derivations, but the proofs are really intuitive. I hope Professor can make more courses like this one on Coursera about other topics in mathematics like linear algebra, number theory, abstract algebra, topology, differential geometry and functional analysis etc.

By Dr. S N

•Jan 16, 2017

Very nice course. It was very informative. Even though I did it in Audit mode, I am going to recommend my PhD students to do the course for improving themselves as physicists and computer science by knowing what actually goes behind the scene mathematically. I will recommend the course for all students of electronics (with strong desire to understand the mathematical basis) in general.

By Colin Y

•Dec 22, 2018

The course covers quite a wide range of topics but are very approachable. Nice lecturer, and very clear pdf slides available for read at any time. One can follow the lecture contents either by watching the videos or by walking through the reading resources provided, either way serves my need. The assessment questions are well-designed to test the learner's understandings. Good course!

By Victor P

•Sep 21, 2016

This course has been very exciting and powerfull. The lectures are very clear and the professor use many didactic tools for improving our learning. The content of this course is completed with some other advanced topics in mathematics (for example: topology), and the course is well enriched. I recommend this course for all learners who want to learn something of advanced mathematics.

By Samopriya B

•Jun 12, 2016

Wonderful. I have been waiting for this course for some time. It begins somewhat basic, and progresses really fast, to cover some deep topics in complex analysis theory. Also, the instructor, Prof. Petra Bonfert-Taylor, does a very good job at explaining concepts simply, by not being too pedantic (e.g., with the topological preliminaries). Overall, really satisfied and grateful!

By Raymond M

•Aug 21, 2019

Enjoyable. There seemed to be a few math rendering errors in some of the assignments. The homework assignments involving peer review were good.

You've got to appreciate how the originally recorded class needed more, but then the author added more! The lesson 7, Calculus of Residues was an appropriate addition, I didn't mind it being last, but it did not go into Branch Cuts.

By Kevin R

•Oct 09, 2017

This course is a wonderful Introduction to the topic of Complex Analysis. Many thanks to Prof Bonfert-Taylor for taking the time to put together a well-organized and concise course. The quizes and homework assignments generally took me longer than the stated time, but I was OK spending the extra time re-reviewing lectures to ensure I knew the material appropriately.

By Harish M

•Apr 04, 2020

The course is excellent and Dr. Petra Bonfert-Taylor is an excellent instructor. This course is not rigorous but it touches on a lot of topics which are quintessential in Physics and to a smaller extent, Engineering. I would also recommend this to anyone who is interested in Math or is pursuing an undergraduate degree in Math.

By Ayush T

•Jan 26, 2019

This is really good course for complex analysis. Things have discussed in details and assignents are also very good. It covers most of the topics which I felt were relevent for my work and studies. I wish it had Reimannian Optimization, but even without it the course is really well designed as well as well taught.

By Brahadeesh S

•Sep 05, 2017

The course content as well as the presentation of the material by the instructor are both wonderful. The quizzes and peer-graded assignments are optimally designed. Although there are few proofs of theorems, the applications and examples are in sufficient number that the understanding of the theorems is obtained.

By Henry P k

•Sep 22, 2017

This was a well thought out and taught course in complex analysis. A good amount of detail and examples were nicely done. A particularly attractive feature of the course is that all slides were available in a downloadable .pdf format. The instructor was quite good and presented well prepared lectures.

By Charles K

•Jan 16, 2017

While there are a plethora of MOOCs around aimed at first-year maths, Prof Bonfert-Taylor should be congratulated for being one of the few to bring a course on higher mathematics to the masses. This is a particularly valuable effort that's accessible to anyone with a grasp of first-year calculus.

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