Reddit Reddit reviews Visual Complex Analysis

We found 29 Reddit comments about Visual Complex Analysis. Here are the top ones, ranked by their Reddit score.

Books
Engineering & Transportation
Engineering
Civil & Environmental Engineering
Visual Complex Analysis
Oxford University Press USA
Check price on Amazon

29 Reddit comments about Visual Complex Analysis:

u/ArthurAutomaton · 18 pointsr/math

The Mis-Education of Mathematics Teachers made a huge impression on me, in particular its emphasis on content knowledge and the fundamental principles of mathematics. More recently, the following comment by Ian Stewart has persuaded me to put more emphasis on the visual aspects of the subjects I teach:

> One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual tradition by silly games with 2x2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's Visual Complex Analysis with its elegantly illustrated visual approach. Yes, he has 2x2 matrices―but his are interesting. (Ian Stewart, New Scientist, 11 October 1997) (source)

u/CD_Johanna · 12 pointsr/math

If visualizing complex analysis is your thing, I'd suggest "Visual Complex Analysis" by Tristan Needham.

u/jacobolus · 11 pointsr/math

Your post has too little context/content for anyone to give you particularly relevant or specific advice. You should list what you know already and what you’re trying to learn. I find it’s easiest to research a new subject when I have a concrete problem I’m trying to solve.

But anyway, I’m going to assume you studied up through single variable calculus and are reasonably motivated to put some effort in with your reading. Here are some books which you might enjoy, depending on your interests. All should be reasonably accessible (to, say, a sharp and motivated undergraduate), but they’ll all take some work:

(in no particular order)
Gödel, Escher, Bach: An Eternal Golden Braid (wikipedia)
To Mock a Mockingbird (wikipedia)
Structure in Nature is a Strategy for Design
Geometry and the Imagination
Visual Group Theory (website)
The Little Schemer (website)
Visual Complex Analysis (website)
Nonlinear Dynamics and Chaos (website)
Music, a Mathematical Offering (website)
QED
Mathematics and its History
The Nature and Growth of Modern Mathematics
Proofs from THE BOOK (wikipedia)
Concrete Mathematics (website, wikipedia)
The Symmetries of Things
Quantum Computing Since Democritus (website)
Solid Shape
On Numbers and Games (wikipedia)
Street-Fighting Mathematics (website)

But also, you’ll probably get more useful response somewhere else, e.g. /r/learnmath. (On /r/math you’re likely to attract downvotes with a question like this.)

You might enjoy:
https://www.reddit.com/r/math/comments/2mkmk0/a_compilation_of_useful_free_online_math_resources/
https://www.reddit.com/r/mathbooks/top/?sort=top&t=all

u/desquared · 9 pointsr/math

There's "A Mathematical Coloring Book": http://www.lulu.com/content/4858716 (free download!)

Somewhat more serious, I like "Visual Complex Analysis": http://www.amazon.com/Visual-Complex-Analysis-Tristan-Needham/dp/0198534469/

u/rarededilerore · 8 pointsr/math
u/nanami-773 · 6 pointsr/math

I like this book.

u/gin_and_clonic · 6 pointsr/AskReddit

tl;dr: you need to learn proofs to read most math books, but if nothing else there's a book at the bottom of this post that you can probably dive into with nothing beyond basic calculus skills.

Are you proficient in reading and writing proofs?

If you aren't, this is the single biggest skill that you need to learn (and, strangely, a skill that gets almost no attention in school unless you seek it out as an undergraduate). There are books devoted to developing this skill—How to Prove It is one.

After you've learned about proof (or while you're still learning about it), you can cut your teeth on some basic real analysis. Basic Elements of Real Analysis by Protter is a book that I'm familiar with, but there are tons of others. Ask around.

You don't have to start with analysis; you could start with algebra (Algebra and Geometry by Beardon is a nice little book I stumbled upon) or discrete (sorry, don't know any books to recommend), or something else. Topology probably requires at least a little familiarity with analysis, though.

The other thing to realize is that math books at upper-level undergraduate and beyond are usually terse and leave a lot to the reader (Rudin is famous for this). You should expect to have to sit down with pencil and paper and fill in gaps in explanations and proofs in order to keep up. This is in contrast to high-school/freshman/sophomore-style books like Stewart's Calculus where everything is spelled out on glossy pages with color pictures (and where proofs are mostly absent).

And just because: Visual Complex Analysis is a really great book. Complex numbers, functions and calculus with complex numbers, connections to geometry, non-Euclidean geometry, and more. Lots of explanation, and you don't really need to know how to do proofs.

u/OphioukhosUnbound · 6 pointsr/3Blue1Brown

A wonderful source for those that want to know questions better: Naive Lie Theory by John Stillwell

(Google excerpts)

This book is a wonderful read and it jumps into quaternions very early on. It really helps one learn about them and other spaces. Is also a remarkably Easy to access book on Lie Theory — (basic calculus, linear algebra only real read. Having seen group theory before is nice, but not necessary)

I’m about half way through and just love it.

Also, somewhat related, Visual Complex Analysis by Tristan Needham is a ridiculously good and powerful book.

(Google excerpts)

Anyone that has to interact with complex numbers should read at least the first two chapters in my opinion.

u/tip_ty · 6 pointsr/math

For your particular case I highly recommend the textbook Visual Complex Analysis. Helped bring the "math talk" down to earth for me at least.

u/robbie · 5 pointsr/reddit.com

> what's supposed to be nice about a math book is that the author distills the content down to the bare essentials with nothing necessary omitted and nothing unnecessary included (this makes time spent reading the book and doing problems from it fulfilling and efficient)

I disagree. That's what's nice about math. What's nice about a math book is that it teaches you math. If you're taking lectures and seminars at a university and discussing the subject with other students then a minimal, rigorous and terse textbook maybe just what you need. However, if you're learning math as a hobby in your spare time and on your own, a book that gives copious examples, and motivates the subject from many angles, is much more useful.

Visual complex analysis is a shining example of this kind of writing http://www.amazon.com/gp/product/0198534469/103-9283683-9227825?v=glance&n=283155

u/freyrs3 · 5 pointsr/math

I don't know if complex analysis is your cup of tea but Visual Complex Analysis by Needham is probably the best math book I've bought in a long time.

u/two_if_by_sea · 3 pointsr/math
u/redditor62 · 3 pointsr/math

Saff and Snider is great for applied complex analysis. In my opinion it strikes a perfect balance between accessibility and rigor for a first course on the subject.

Visual Complex Analysis is another good choice, but it might be a little more advanced than what you're interested in.

The first half of Lang might also be a good choice, but Lang takes a slightly more formal, proof-based approach.

I've also skimmed through Brown and Churchill, which looks quite good but is prohibitively expensive.

Finally, you can find many cheap (~$10) books on the subject by Dover. The only one I've looked at is Knopp, which is quite formal and light on computation, but might be a good supplement. Here's another Dover book with outstanding Amazon reviews.

Complex analysis is both very elegant and very useful. Best of luck with your class!

u/mantrap2 · 3 pointsr/ECE

https://en.wikipedia.org/wiki/Affine_transformation

https://www.math.tamu.edu/~stecher/LinearAlgebraPdfFiles/chapterThree.pdf

https://www.khanacademy.org/math/linear-algebra/matrix-transformations/linear-transformations/v/linear-transformations

A linear time-invariant circuit system is a linear system. You can represent it as a linear matrix - which is what SPICE does to solve circuits: V = Z I or I = Z^(-1) V.

An affine transform is merely a form of linear matrix transformation that has particular constraints on its elements that cause it to be "affine". Without more information this makes no sense to do on a circuit but maybe there's a case I don't know about.

There are issues with general circuit representation in this form so systems like SPICE do NOT use these in this form but in a combined matrix form (so you can have zero or infinite values of V or I or Z without blowing things up).

A really, really amazing book on linear transformations and how they tie to complex math is Tristan Needham's Visual Complex Analysis.

If you've ever been fascinated by circuit theory with regards to linear algebra, Fourier transforms, Euler's Identity, Stability Analysis, etc., and wanted to understand the underlying math better, this is the book to read. It's easy to read but has plenty of rigor. Also highly relevant to graphics transformations used in GPUs.

u/Banach-Tarski · 3 pointsr/math

Neither of those is the complex plane. The first is 3-dimensional in the real manifold sense and the latter is 4-dimensional.

It seems that you are confused about what the complex plane is, so I would suggest that you read Needham's Visual Complex Analysis. It's a very gentle introduction to complex analysis that also conveys very good visual intuition for what is going on.

u/acetv · 3 pointsr/math

Complex analysis, my friend. If you can understand even the basics intuitively it can smooth out a lot of the higher classes. I like Needham's Visual Complex Analysis but I've been told it's not a good introduction. I'm not really sure what would be, but you might want to look at Introductory Complex Analysis by Silverman (Dover books are cheap and awesome).

Graph theory certainly wouldn't be too bad either. It's actually pretty fun and has applications in programming and algorithms. Dover publishes this book which I expect would be excellent to read at work (pretty basic, moves slowly). Same goes for linear algebra if you can find a book on it (look for one with "matrix analysis" in the title).

Learning advanced set theory or category theory will probably not be useful at all. (*ducks*).

u/PrancingPeach · 3 pointsr/math

Pick up the book Visual Complex Analysis by Tristan Needham. You can probably find a free copy online, but this one is, I assure you, worth every penny. Not only is it the most intuitive book on complex analysis ever written in my opinion; it is probably among the very best mathematical books in general.

Let me put it this way. I happened upon that book in high school and was so captivated that I read it cover to cover. Upon entering college, my understanding of the subject was so strong and intuitive I could jump into graduate-level complex analysis with little to no difficulty.

u/indutny · 2 pointsr/AskPhysics

Check out Visual Complex Analysis by T. Needham . This covers complex analysis in a very original and vivid way!

u/po2gdHaeKaYk · 2 pointsr/funny

Part of the problem is that there are a lot of little things that are subtly wrong, and I'm sorry if this sounds patronizing, but it's because you're still ignorant of the larger theory. Let's take a few statements.

> Trigonometry is not the same as geometry by any means,

Trigonometry is the branch of mathematics that studies relationships between lengths and triangles. If it is not geometry, I do not know what is.

Now I think that people are being suckered into these statements because they associate the manipulation of sin/cos/tan as functional quantities. So they start thinking that this is not geometry because it involves purely algebraic manipulation of functions. Which is absurd. What do you think the graph of sin/cos/tan comes from?

It reminds me of a student who once had to punch into her calculator the value of sin(0). If you understand the origin of the definition of sine, you understand its value at the origin.

> especially the trigonometry used in electrical engineering (where it's really about complex exponentials, eiθ = cosθ + isinθ).

The notion of a complex exponential (typically) requires the notion of geometry in the complex plane. I say (typically) because there are different ways of defining the complex function. For example, you can define it as the addition of two separate infinite series that make up the real and imaginary parts. However you define it, you won't escape the notion that it is linked to points on the unit circle. This is geometry.

Tristan Needham basically claims (around Chapter 1) that the importance of complex numbers in many scientific pursuits is based on the fact that it is effectively equivalent to the definition of Euclidean Geometry. Hence again geometry.

> Electrical engineers aren't using trig to represent geometry, but to represent oscillations

Again, where are these oscillations coming from? They are defined via ratios of side lengths in a triangle as a point is rotated around the unit circle. This is geometry.

> Also, they're used in Fourier transforms and series - also completely unrelated to geometry.

A Fourier series is defined via an expansion of certain functions into more basic components of sines and cosines. The reason why you are able to do this boils down to geometric extensions of the notion of orthogonality and projections. Basically, the individual modes are orthogonal to each other (except their twin), and by projecting things in a judicious manner, you can derive formulae on the Fourier coefficients. Projections and orthogonality...this is geometry. What functions can or can't be Fourier summed? This relates to notions of continuity, differentiability, integrality, and periodicity. All of these, in the case of Fourier Series, are intimately linked to circles and ratios of side lengths.

As I pointed out in another post, the definition of Fourier transform inversion requires contour integration in the complex plane. Where do you think all those tables Engineers use are taken from? Contour integration is geometry. It involves notions of decomposing line segments and curves into sub-elements, integrating over circles and arcs, etc. Hell, even integration is geometry. If you can't figure out what area means, then how do you define the concept of an integral?

The problem is that students lose this geometric understanding of mathematics. Then you have to explain to them what happens when you actually integrate, or why an integral they calculated is obviously positive or negative based on the parity or sign of the function.

u/legendariers · 2 pointsr/askscience

You might like this book by Coxeter, who also co-wrote Geometry Revisited. Tristan Needham covers a bit of non-Euclidean geometry in Visual Complex Analysis. Really though I believe non-Euclidean geometry isn't a discipline of its own; it's part of differential geometry, so you might be better served looking for differential geometry references.

u/gmartres · 2 pointsr/math

Visual Complex Analysis looks interesting, haven't read it yet.

u/lamson12 · 2 pointsr/math

Here is an actual blog post that conveys the width of the text box better. Here is a Tufte-inspired LaTeX package that is nice for writing papers and displaying side-notes; it is not necessary for now but will be useful later on. To use it, create a tex file and type the following:

\documentclass{article}
\usepackage{tufte-latex}

\begin{document}
blah blah blah
\end{document}

But don't worry about it too much; for now, just look at the Sample handout to get a sense for what good design looks like.

I mention AoPS because they have good problem-solving books and will deepen your understanding of the material, plus there is an emphasis on proof-writing when solving USA(J)MO and harder problems. Their community and resources tabs have many useful things, including a LaTeX tutorial.

Free intro to proofs books/course notes are a google search away and videos on youtube/etc too. You can also get a free library membership as a community member at a nearby university to check out books. Consider Aluffi's notes, Chartrand, Smith et al, etc.

You can also look into Analysis with intro to proof, a student-friendly approach to abstract algebra, an illustrated theory of numbers, visual group theory, and visual complex analysis to get some motivation. It is difficult to learn math on your own, but it is fulfilling once you get it. Read a proof, try to break it down into your own words, then connect it with what you already know.

Feel free to PM me v2 of your proof :)

u/sillymath22 · 2 pointsr/math

Book of proof is a more gentle introduction to proofs then How to Prove it.

​

No bullshit guide to linear algebra is a gentle introduction to linear algebra when compared to the popular Linear Algebra Done Right.

​

An Illustrated Theory of Numbers is a fantastic introduction book to number theory in a similar style to the popular Visual Complex Analysis.

u/rhab13 · 1 pointr/math

I recommend you to take a look at Visual Complex Analysis in particular the chapter on differentiation. In the first sections he explains the rationale for this restriction.

u/HastyToweling · 1 pointr/AskReddit

What is the square root of i? If it takes you longer than .5 seconds to figure this in your head, you are blind.

You need to read visual complex analysis by Tristan Needham. This book utterly opened my eyes to what complex number actually are (hint: The correct question is "what is multiplication?"). I used to be mystified by them, as you are. No more. They are as unmystical as anything in math. I also gained a supreme ability to use them, in practice. Read the book, and you will join the ranks of the enlightened.

u/DataCruncher · 1 pointr/math

For complex analysis, Visual Complex Analysis by Needham is often recommended along these lines. I haven't read it though, so I can't vouch for it.

u/dp01n0m1903 · 1 pointr/math

Congratulations are in order, to you as well as lysa_m, shizzy0 and all the other helpful redditors here. It must feel really great to get over this hurdle!

I just wanted to add a link to the book of Tristram Needham, Visual Complex Analysis. As lysa_m pointed out, you are not the first person in history to find "imaginary" numbers baffling. You can read the first 5 or 6 pages of Needham's book online at the Amazon page above. There he outlines the history of the subject and explains some of the same points made in the comments here.

u/[deleted] · 1 pointr/math

Side note: You might enjoy this book

u/cderwin15 · 1 pointr/math

What book have you been using? My undergraduate course is using Brown & Churchill, which a lot of people seem to really like, and I've also heard really great things about Tristan Needham's Visual Complex Analysis and I've loved what I've seen of it (mostly just the chapter on winding numbers and the argument principle from a geometric viewpoint).