"As in the first edition, a historical introduction precedes each important new concept, tracing its development from an early intuitive physical notion to its precise mathematical formulation. The student is told something of the struggles of the past and of the triumphs of the men who contributed most to the subject. Thus the student becomes an active participant in the evolution of ideas rather than a passive observer of results. " (Tom M. Apostol, Calculus)
Surely you know it yet, but if not I would suggest you read volume I of Feller's "Introduction to probability theory and its applications". It is a very enjoyable and down-to-earth probability book. A gem.
Thank you for this great selection! I have read some of them already, such as Stillwell's book (and some others by him, I am a big fan of his style of writing). I never got very deep into number theory, I will try at least one of your recommendations to fill some gaps there. I had already planned on reading some of Edward's books like the one on Galois theory. Looking forward to your next book recommendations!
Thank you sir, these recommendations were quite different than the common recommendations I expected before clicking on the video. Happy that I have some radically New books for look for and read.
Did I say casual? Anyway I have great respect for the 'yellow" books - in that I try and avoid them especially the graduate level ones. But there are a few that are not that difficult - more calculational and historical - and fun to read.
I was puzzled - you said at the start you were "not interested in rigour", but then went on to recommended some highly rigorous advanced mathematical textbooks ! Can you enjoy reading this material without truly understanding it - which takes a LOT of hard work ? Unless there's some clever way to get the benefits and rewards of something without putting the work in - but that doesn't seem to be in keeping with the Conservation of Energy principle.
All of these books are math books, but I would hardly call them highly rigorous. Perhaps rigor is not the best choice of words for what I am trying to convey - maybe formal or pedantic would be a better choice. . These books don't follow the Bourbaki school of mathematics where everything is definition, lemma, lemma, theorem, corollary, etc. They instead use the process of intuition, calculation, example, application. They don't always treat everything in full generality, but often focus on the particular. They do require a lot of work to understand but no more than the usual theoretical physics books.
@@markweitzman I have recently re-read my undergraduate textbook "Complex Analysis" by Ian Stewart/David Tall (1983), apart from the final 2 chapters. This is a good book, but it does not spell out all the details, but it is a good exercise to work those out for yourself. I also like the book "Elements of Real Analysis" by Robert Bartle (1964) - this again omits a fair amount of details - but again good exercises to work out for yourself.
Alejandro Garciadiego, Bertrand Russell and the Origins of the Set-theoretic 'paradoxes.' This is the most important math book written in the last 50 years. In case you think you understand anything, read, in this book, Ricard's statement of his "paradox." What is wrong with the argument? When you can't tell what is wrong with it, and give up, then read, also in this book, Richard's description of what is wrong with his argument. Still think you know anything? Then read Godel's famous 1926 paper. Find Godel's reference to Richard's paradox. Note that Godel believes Richard 's argument is a paradox. What role does Richard's "paradox" play in Godel's argument? Still think you know anything?
