Do you know any influential mathematicians that are visual thinkers? especially those who wrote books.
For example mathematicians that think and write like Roger Penrose,Benoit Mendelbrot,Vladimir Arnold,Sir M.Atiyah who are very keen on using diagrams and drawings in their writings.
From Special Relativity to Feynman Diagrams: A Course of Theoretical Particle Physics for Beginners (UNITEXT / Collana di Fisica e Astronomia)
by Riccardo D'Auria , Mario Trigiante
Galitski V., Karnakov B., Kogan V. Exploring Quantum Mechanics A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers-Oxford University Press (2013)
I found this: Thermodynamics:
A Dynamical Systems Approach
Wassim M. Haddad, Vijay Sekhar Chellaboina, & Sergey G. Nersesov and didn't like it
is there something similar but better written ?
Here's a one I just found online( it's free) : Radically elementary probability theory by Edward Nelson
https://web.math.princeton.edu/~nelson/books/rept.pdf
Marcel Berger's books(geometry revealed,differential geometry and a panoramic view of riemannian geometry) are apparently masterful,but I think they're research-level,am I wrong?
I would to know if anyone knows any books in mathematics or physics at any level :
-Which treat their subject in an unusual maybe even original ways?
-Treat topics rarely touched upon in standard ones?
-Any book that's not very known but which you regard as useful ?
-Whether this book is...
John Dirk Walecka's books are very good for this :https://www.amazon.com/dp/9812705856/?tag=pfamazon01-20
https://www.amazon.com/dp/9812812253/?tag=pfamazon01-20
The best establishments for higher education(I'm interested in only mathematics or/and physics) in France are not the universities but ''Les grandes écoles'',like l'Ecole Normale Supérieure (ENS for short),and l'Ecole Polytechnique. They produce a lot of great mathematicians,and have a very...
I've seen Stephen Smale say something similar on an interview on youtube,but I think you can get some ''guidance'' from class,but for learning something ,you can't do it except on your own,and yes, I also hate class.
When I'd like to know if there any advanced calculus book that doesn't adhere to axiomatic methods,is rigorous but with strong appeal to ‘geometric intuition'.
There's Vector Calculus, Linear Algebra, and Differential Forms by Hubbard ,the very difficult Advanced calculus by Loomis and Sternberg ,that's free on Sternberg's website.For something unusual and good there's Advanced Calculus: A Geometric View (James J. Callahan) and Harold M. Edwards'...
I've bought Mathematics: Its Content, Methods and Meaning Kolmogorov, Aleksandrov, and Lavrent'ev ( because it was cheap and had Kolmogorov as an author),it's very very interesting (that chapter on electric is kind of useless) ,sadly there are no problems .
I would like to ask for suggestions...
If you were to be an undergraduate in a run-of-the-mill university,would that mean that you'll be a second rate professional?Or does it all depend on the effort you put in?
(What I want is a solid technical ability,and a decent understanding of the profession,the money or the prestige are...
What books take the opposite approach? Rudin's book on analysis?the Bourbaki books?
By the way what do you think about V.A Zorich's books on analysis ? they make it very easy to work with physical problems ,and the exercices are very hard. I've read the 3 first chapters of Artin's book,it is...
Deductive reasoning is incapable of yielding essentially new knowledge,plausible reasoning can and does all the time,therefore it should occupy a larger part of the teaching and learning about math,the axiomatic method require that one accepts any axiom with a hope that its corollaries are...
Yes ,maybe, but I think that most of their mathematics was done ''experimentally''( there's a video you can google by V.I Arnold titled ''mathématique expérimentale'' online,you should see it).
Some very good mathematicians like Newton,Euler,Poincaré,Minkowski, Weyl, Kolmogorov were prominent users of it,according to Vladimir Arnold who's also one of them,on other side you may find Leibniz and Descatres,the Bourbakists,Artin,Noether.
I think the best discoveries in math were made...
I have an incredible distaste for the axiomatic approach ,it's a very bad method,I think ,for teaching or learning about mathematics.I don't understand why I feel this way, I always thought inductive reasoning in mathematics ,the sort you find with physicist,is better than the deductive...