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1 point

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15th Dec 2021

It’s also a little off since complex (and imaginary) numbers can be described using real numbers…. So… theories based “only” on real numbers would work fine for whatever the others explain.

It’s really a pity. I don’t think “imaginary/complex” numbers need to be obscure to no experts.

Just explain them as ‘**rotating** numbers’ or the like and suddenly you’ve accurately shared the gist of the idea.

Full disclosure: I don’t think I “*got*” complex numbers until after I read the first chapter of Needham’s Visual Complex Analysis. [Though with the benefit of also having seen complex numbers from a couple other really useful perspectives as well.] So I can only partially rag on a random journalist given that even in science engineering meeting I think the general spirit of the numbers is usually poorly explained.

1 point

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27th Jun 2015

One I'm currently working my way through: Visual Complex Analysis

Sadly, I put it down a few weeks ago and haven't worked on it much since.

1 point

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4th Jul 2011

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.

18 points

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27th Feb 2019

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)

1 point

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8th May 2022

Visual Complex Analysis - Tristan Needham

The first chapter of that book hugely helped me understand ‘what’ complex numbers are / why they are so useful and ubiquitous.

(TLDR: complex numbers represent the marriage of an infinite line and a self connected line, magnitude and rotation — the “real” and “imaginary” parts are just their projections into a double infinite line space [typical plane] — the “im” & “re” parts we normally work with are an awkward, but often needed, perspective on a very “natural”/simple construction)

I strongly support purchasing books to support their creation if at all reasonably possible, but here’s a pdf in the potential interim:

<strong>VCA, pdf</strong>.

Read the first chapter. And jump around and get a sense of some of the subject.

1 point

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15th Nov 2021

1 point

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17th Aug 2021

I learned complex analysis before real, so you probably can. I've heard good things about Visual Complex Analysis by Needham. Understanding Analysis by Abbot is also supposed to be great. In terms of geometry, Introduction to Algebraic Geometry by Smith has great reviews, I myself have recently bought it. It covers all of the necessary commutative algebra and sheaf theory in appendices. Be warned, however, there are typos. Introduction to Topology by Mendelson is great if you want a quick introduction to metric spaces, topological spaces, (path) connectedness & the fundamental group, and compactness. I have learned most of the differential geometry/topology that I know from Lee's Introduction to Smooth Manifolds, however, it is very wordy and contains a lot more information that one needs to know, so I suggest asking someone who knows some differential geometry (a professor or graduate student) what you should and shouldn't cover.

1 point

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17th Jul 2020

If you know multivariable and you like analysis so far, then how about complex analysis? There is a great book: https://www.amazon.com/Visual-Complex-Analysis-Tristan-Needham/dp/0198534469

To start studying algebra there is a similar book: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/088385757X#reader_088385757X

If I were you I'd hold off on axiomatic set theory for a bit longer, as out of all the subjects, it doesn't have the most applicability or opportunity to branch out. That said, you should study what you're interested in!

1 point

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19th Mar 2020

Not on amazon.

There are very expensive textbooks that peak in price around school start, but most thick textbooks are easy to get $70-$90. And many thinner textbooks are 40-60. With a ton of surprisingly cheap books here and there (like Dover books).

This is from someone who spends ~90% of his book reading on math (and some physics) books and compares different authors as a past time.

And those are all new prices.

Used is often significantly cheaper and still great. Also, Amazon has “rent a book” for a semester options for most of the expensive course books. (Though I like worrying and taking notes in my bobs — that’s part of the point for me, so I rarely use that option.)

Examples (just good books from my shelf, no price biasing)

Complex Analysis by Needham $66 paperback

Toplogy Illustrated by Savliev $64 paperback

Differential Geometry of Curves and Surfaces by Tapp $38 hardback

Nonlinear Dynamics and Chaos by Strogatz $70 paperback

A Book of Abstract Algebra by Pinter $9 paperback

An Illustrated Theory of Numbers $58 hardcover w/ large and beautiful layouts

No-Nonsense Electrodynamics by Schwichtenberg $30 paperback

Etc.

Etc.

1 point

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17th Jun 2017

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.

1 point

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11th Dec 2011

Side note: You might enjoy this book

< $50

< $50

< $50