"Best" is a vague metric, but one textbook I am always happy to recommend is the Princeton Companion to Mathematics.
The book is a selective review of the most significant ideas in maths and mathematical research.
The great editorial process is what sets this book apart from the rest: each chapter is authored by an outstanding expert in his/her particular field (among which several fields medalist the likes of Terence Tao) and the editing by Timothy Gowers does an amazing job of uniforming the tone, notation and rigor across the whole text.
The authors were evidently chosen also for their communication skills since the articles come across as quite discoursive and really convey the beauty of modern maths.
In the book you'll find not only the articles on mathematical concepts, but also an introduction to modern mathematics, chapters on the relationship of maths with other sciences, a thorough history of mathematics and a collection of biographies of famous mathematicians.
Well recommended to anybody with an interest in maths. My background is in CS and I found it approachable (except minor sections) and illuminating!
I read almost all of it cover to cover when I was an undergrad in math, when I still had intention of going to grad school, to get a sense of which area(s) of math I'd like to pursue further.
It is incredibly illuminating and I also recommend it highly.
I've only worked through Chapter 1. The text is interesting, but most of my learning has come from the exercises. You should plan to do the exercises. Also, don't worry if you have to skip a few exercises and come back to them later. Don't allow yourself to be bogged down and loose interest over a single difficult exercise.
and you are right, the value lies in the exercises. I started doing them in Clojure. I recommend doing as many as you can and then you'll find plenty of solutions online to compare your results. It's worth it
There is an interactive version of that textbook you can read. It actually helps to do the exercises with the text. You can Google it. I read that book using that version and it was amazing.
An excellent and very fun read about compilation, interpretation, and programming semantics.
I don’t think you already have to know LISP, although there isn’t an introduction, but if you know any programming it would be enough to pick up the programs that are used as examples. Source code from the book is available and you will end up programming as you move along and it is a delight to see yourself make a program that can interpret another program.
A dear favorite of mine was Baldor's Algebra. Everyone else in high school was scared of it, but I found it to be very methodical and easy to follow from one topic to another.
I liked the first edition of K&R a lot. Today I suspect it shines most when compared to recent intro language books. It was succinct yet offered insight into both the language's design concepts and its implementation -- an introduction to software based on Strunk & White's spartan model of exposition.
Given the abstract nature and swiss-army knife mission creep of today's languages, it's a rare intro PL book today that's smaller than 600 pages. (K&R 1978 fit into a mere 220.)
I watched so far the first 7 or 8 lectures on youtube of his linear algebra course. (Which something like a million people have watched) He's such a great lecturer, extremely impressive. So mysteriously good it makes me wonder what it is about them that seem so good. He says somewhere about how he gets a lot of mail thanking him, that people appreciate that he's on their side. It's just done with what the experience is like for the student always in mind. Sounds simple, but there are plenty of lecture/course videos on youtube where that obviously wasn't given a thought.
Introduction of Quantum Mechanics and Introduction to Electrodynamics, both by David J. Griffiths. He also wrote Introduction to Elementary Particles, but I have not read that one.
Both books masterfully take exceptionally complex fields and break them down into easily digested chunks, with a clear progression of ideas as you go through the book. Do note that these are "Introduction" books written for Junior/Senior Physics majors.
You should also have a solid background in calculus before fully understanding these books. Typically, Physics majors take every undergrad calculus class offered in the math dept. at a college, then a few more in Physics just to be sure.
I had to learn some quantum for a graduate class, and even with my engineering background, Intro to Quantum by Griffiths was both extremely helpful and an awesome read. It's the first book that came to mind when I read the question.
I didn't learn electronics with this book, but I really wish I did. I used it to give tutorials for an undergraduate electronics course for physics students and it was immensely useful and well organized.
Have been recommending CASI to everyone who listens.
Everyone has their own unique datasets. And anyone can install data science platforms such as Anacondas. But being able to map a particular algorithm to the inference you wish to make. And understanding, from a historical context, precisely what that inferences means at a philosophical level. That is where this text will assist on your path to mastery.
It's actually not all that useful for Machine learning and is more focused on other aspects of AI. It talks a lot about propositional logic, knowledge representation, etc.
It's not the best textbook ever, but Shankar's book on quantum mechanics is interesting. It builds everything from ideas about vector spaces and the underlying mathematics (in an accessible way) before quantum magically pops out. You end up understanding bra-ket notation without realising it.
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[ 2.9 ms ] story [ 113 ms ] threadhttps://www.amazon.com/dp/1558601910
The book is a selective review of the most significant ideas in maths and mathematical research. The great editorial process is what sets this book apart from the rest: each chapter is authored by an outstanding expert in his/her particular field (among which several fields medalist the likes of Terence Tao) and the editing by Timothy Gowers does an amazing job of uniforming the tone, notation and rigor across the whole text.
The authors were evidently chosen also for their communication skills since the articles come across as quite discoursive and really convey the beauty of modern maths.
In the book you'll find not only the articles on mathematical concepts, but also an introduction to modern mathematics, chapters on the relationship of maths with other sciences, a thorough history of mathematics and a collection of biographies of famous mathematicians.
Well recommended to anybody with an interest in maths. My background is in CS and I found it approachable (except minor sections) and illuminating!
It is incredibly illuminating and I also recommend it highly.
In case you didn't know, have a look at http://lesswrong.com/lw/3gu/the_best_textbooks_on_every_subj...
I've only worked through Chapter 1. The text is interesting, but most of my learning has come from the exercises. You should plan to do the exercises. Also, don't worry if you have to skip a few exercises and come back to them later. Don't allow yourself to be bogged down and loose interest over a single difficult exercise.
and you are right, the value lies in the exercises. I started doing them in Clojure. I recommend doing as many as you can and then you'll find plenty of solutions online to compare your results. It's worth it
(I think I've read the first volume, at least, even though I don't claim to have understood it all.)
1. Elements of Computing Systems
2. On Lisp
3. Game Engine Architecture
Edit: 2 -> 3
It is extremely readable and presents very theoretical concepts in a pragmatic way. Love it.
An excellent and very fun read about compilation, interpretation, and programming semantics.
I don’t think you already have to know LISP, although there isn’t an introduction, but if you know any programming it would be enough to pick up the programs that are used as examples. Source code from the book is available and you will end up programming as you move along and it is a delight to see yourself make a program that can interpret another program.
Picture of the cover, with text in Spanish: https://es.wikipedia.org/wiki/%C3%81lgebra_de_Baldor
Given the abstract nature and swiss-army knife mission creep of today's languages, it's a rare intro PL book today that's smaller than 600 pages. (K&R 1978 fit into a mere 220.)
Lots of worked examples. Very easy to follow and really helped me "teach myself" calculus and advanced calculus.
Concise, clear, thorough. Strang is a great author.
Both books masterfully take exceptionally complex fields and break them down into easily digested chunks, with a clear progression of ideas as you go through the book. Do note that these are "Introduction" books written for Junior/Senior Physics majors.
I'm still upset that my copies of Griffiths' texts were stolen my senior year of college...
Yes!
I actually jumped in this thread to recommend Griffiths' Electrodynamics.
Even the review sections on how to think about things like divergence and curl is particularly well done by Griffiths.
It covers nearly all aspects of electronics both theory and practice. It’s still relevant after all these years.
Everyone has their own unique datasets. And anyone can install data science platforms such as Anacondas. But being able to map a particular algorithm to the inference you wish to make. And understanding, from a historical context, precisely what that inferences means at a philosophical level. That is where this text will assist on your path to mastery.
Computer Age Statistical Inference
https://web.stanford.edu/~hastie/CASI/