Textbooks for visual learners

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:

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?

Solution 1:

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

• Proofs without words - Exercises in visual thinking: Volume I and II by Roger B. Nelson are a nice way to work on relatively easy problems. But since they are presented with very nice and sometimes enlightning graphics, it's fun to work through them.

• Visual Complex Analysis by T. Needham is a guided tour through complex Analysis with plenty of illuminating pictures providing additional insight (and additional aesthetic pleasure).

• A Topological Picturebook by George K. Francis is a classical introductory text with focus on visual perception.

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.

Solution 2:

1: For some proofs with good visual input are (I think this 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. A good choice to read:

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

5: The complex analysis has always had a visual version, some good ideas can be seen in:

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

6: If the topic of interest are the most abstract themes of differential forms and varieties, My recommendation is to see this book: A Visual Introduction to Differential Forms and Calculus on Manifolds. J. P. Fortney.

7: 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).

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

9: 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 in the following link, mainly topology books.

http://www.math.com.mx/books_on_visual_mathematics.html

enjoy it.

Solution 3:

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!