40
$\begingroup$

Perhaps this question has already been asked (if so, please let me know) but I am looking for books that appeal to visual learners.

I discovered that I am able to understand concepts much quicker and better when they are explained/taught in a visual way. For example the epsilon-delta definition of a limit of a sequence/function only became really clear to me when explained with the help of a graph similar to this one:

enter image description here

I also love the Visually stunning math concepts which are easy to explain

thread on this site because it helped me understand so many things that made no sense to me when I was "just" reading them in a book with no visual illustrations.

Can you recommend some books ,from all areas of mathematics (especially analysis and linear algebra), that would appeal to visual learners like myself?

$\endgroup$
12
  • 4
    $\begingroup$ This was downvoted without explanation. Upvoting. $\endgroup$
    – wlad
    Commented May 26, 2015 at 18:35
  • 3
    $\begingroup$ @Rzeta I think being able to more easily understand things you can visualise is a fairly common trait (certainly one I have). I would definitely recommend "Visual Complex Analysis" by Tristan Needham $\endgroup$
    – Dan
    Commented May 26, 2015 at 19:44
  • $\begingroup$ @Dan Thanks. Will take a look at it. $\endgroup$
    – qmd
    Commented May 26, 2015 at 22:03
  • 1
    $\begingroup$ Are there particular concepts you are looking to learn? $\endgroup$
    – Jas
    Commented May 28, 2015 at 18:50
  • 2
    $\begingroup$ @Rzeta Glad you like it, the lectures from Tokieda are very motivational as well, so in case you want to find yourself eager to learn more, I'd recommend that. He uses a lots of pictures, and probably is less rigorous in the eyes of many mathematicians, but builds your imagination, which only few people, from those I've met, did. I wrote Dr $T^2$ (his own abbreviation), asking for the exercise sheet, but did not receive a reply yet, I might post it here later. And since you seem to like, it I'll also link videos to Louis H. Kauffman's lectures. $\endgroup$
    – quapka
    Commented May 29, 2015 at 10:23

3 Answers 3

Reset to default
23
+100
$\begingroup$

Here are some of my favorites that I recommend with pleasure.

Maybe the following recommendations are not so often cited:

  • Beautiful Evidence by Edward Tufte is a wonderful book about how to present data and statistics. I deeply appreciate all his books around this theme and from my point of view it's a must have for statisticians.

  • The Ashley Book of Knots: Although this book is not written for mathematicians, I recommend it to all who like topology. The theme of the last chapter from the Topological Picture Book is knot theory. And if you are a visual learner with a faible for knots you will appreciate this book . It is a guide containing thousands of wonderfully drawn knots most of them are masterpieces of art. You can delve into an incredible world of different knots and after that you will look at Topology with different eyes.

Some additional hints regarding OPs comment:

  • Analysis by Its History by E. Hairer and G. Wanner is an approach to Analysis following the chronological order of the subject. It's a valuable supplement to ordinary textbooks in calculus providing also a wealth of highly instructive graphics. When looking at the many graphics it's obvious, that hundreds of hours had been invested with great sensitivity by the authors to serve the visual needs of the students.

  • Calculus by Michael Spivak is a well known (modern) classic which also contains a lot of good drawings. The contents is great of course, the drawings are numerous and instructive, but they do not play in the same league as those by E. Hairer and G. Wanner.

One more regarding topology:

  • Aspects of Topology by C.O. Christenson and W.L. Voxman is a particularly suited easy to read and informative text about topology which also contains a lot of instructive graphics.
$\endgroup$
5
  • $\begingroup$ Thankyou very much. I looked at most of them in the library today and Visual Complex Analysis by T Needham seems really good. Do you know of any other similar books for differential equations and real analysis? $\endgroup$
    – qmd
    Commented May 29, 2015 at 14:37
  • $\begingroup$ @Rzeta: Sorry, I don't have books about differential equations adressing your needs, but I've added books regarding real analysis (and topology) in my answer above. $\endgroup$
    – Markus Scheuer
    Commented May 30, 2015 at 8:16
  • $\begingroup$ Thankyou again for your answer. It was very helpful. $\endgroup$
    – qmd
    Commented May 30, 2015 at 9:16
  • $\begingroup$ T Needham released a new book in 2021 about differential geometry ("Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts") that could be an interesting addition to this list :) $\endgroup$
    – shamisen
    Commented Feb 28, 2023 at 9:57
  • 1
    $\begingroup$ @shamisen: Many thanks, I agree. I bought the book some time ago and I appreciate it too. :-) I will add it after work. $\endgroup$
    – Markus Scheuer
    Commented Feb 28, 2023 at 10:38
3
$\begingroup$

Something I think should be mentioned is Robert Ghrist's "Elementary Applied Topology". Ghrist's illustrations in this book are some of the best I've seen; in fact, he allegedly had wanted to develop a career in graphic design, but eventually chose math instead!

Another great reference in my experience is Nathan Carter's "Visual Group Theory". Lucid explanations of the fundamentals of group theory.

Hope you enjoy these!

$\endgroup$
3
$\begingroup$

  1. For some proofs with good visual input are (I think these are the books that most agree with the question asked, in fact some demonstrations have almost only drawings.) : Proofs without Words I, II and III, R. B. Nelsen.

  2. If you want to know a little groups more quickly, one of my favorites is: Visual Group Theory, N. Carter.

  3. To know some of the concepts of number theory it can be interesting to see: An Illustrated Theory of Numbers, M. H. Weissman. Nuggets of Number Theory: A Visual Approach, R. B. Nelsen.

  4. If the mathematical logic is of your interest, i.e. the reasoning of the arguments with diagrams:

Visual Reasoning with Diagrams, A. Moktefi, S. Shin (Editors).

  1. Visual Complex Analysis, T. Needham. Visual Complex Functions: An Introduction with Phase Portraits, E. Wegert.

  2. For the most abstract themes of differential forms and varieties, A Visual Introduction to Differential Forms and Calculus on Manifolds. J. P. Fortney.

  3. For those who have an interest in graph theory, the combination with algorithms and drawing the graph can be interesting. Graph Drawing: Algorithms for the Visualization of Graphs, I. G. Tollis, G. Di Battista, P. Eades, R. Tamassia (Authors).

  4. Beautiful Evidence, E. Tufte: some photos help explain concepts.

  5. From numbers, trigonometric functions, geometry, transformations that preserve area, and much more: Math Made Visual, C. Alsina and R. Nelsen.

Some other references can be found here, mainly topology books.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .