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
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
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...
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.
Mathematics and its History - Stillwell.
Wonderfully written. From the ancients to the 20th century, covers the mathematics (in a lot of detail) and lives of major mathematicians (potted bios).
Concrete Mathematics - Knuth et al.
Discrete maths, number theory, generating functions, covers most of the maths that pops up continually in programming.
All You Wanted To Know About Mathematics But Were Afraid To Ask. Mathematics for Science Students 2 Vols. - Louis Lyons.
Pretty basic, but covers all the mathematical basics for physics. (1st year uni level I guess) I learned a lot from this years ago, I still consult it as a reference. It's a pleasure to read.
Also, all of Hamming's books.
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.
It covers nearly all aspects of electronics both theory and practice. It’s still relevant after all these years.
Concise, clear, thorough. Strang is a great author.
There's just so much "how does all this shit actually work" in there ....
It is extremely readable and presents very theoretical concepts in a pragmatic way. Love it.
There is a bewildering confusion of editions and versions of this book, but look for a book called "Biology" or "Campbell Biology" with Neil A. Campbell and Jane B. Reece in the author list, but not necessarily listed first. There is what I believe to be an abridged version called "Biology: Concepts and Connections", and something called "Biology: A Global Approach", which may just be the name for the newest editions.
"It goes really deep" is, unfortunately, a relative description. Half-way through my undergraduate studies, I had pretty much outgrown it and needed more specialized books.
Nonetheless, it is a superb entry-level college textbook that covers the entire breadth of modern biology. The text is very understandable and gives more background information than is needed for a typical introductory lecture to any given topic (while still emphasizing the salient points so you don't get confused). Apart from the above-mentionend interviews, it also includes sections on current methods in biology, which are pretty handy when you're new to the field. Plus, the illustrations are simply excellent: pretty to look at and a huge help for understanding. On the whole, I find it to be one of the most aesthetically pleasing textbooks I know. (Beaten only by Futuyma's "Evolution".)
My best investment in university so far!
(I think I've read the first volume, at least, even though I don't claim to have understood it all.)
Its the only book i still have from uni. It breaks the language down, and made it easy for a techie like me to learn german. Can still speak a fair bit
Lots of worked examples. Very easy to follow and really helped me "teach myself" calculus and advanced calculus.
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.)
A hands on introduction to both Python and Linear Algebra using real world cases (ex. you are given a high res image, make a low res version to put on your website so that it could load more quickly).
Picture of the cover, with text in Spanish: https://es.wikipedia.org/wiki/%C3%81lgebra_de_Baldor
1. Elements of Computing Systems
2. On Lisp
3. Game Engine Architecture
Edit: 2 -> 3
I hope the "Learning Perl 6" book by brian d. foy will be as good.
Spacetime and Geometry an Introduction to General Relativity by Sean Carroll.
Also the textbooks by David Griffiths and Gill Strang mentioned in other comments.
Entertaining and insightful.