Reddit reviews Calculus

My main hobby is reading textbooks, so I decided to go beyond the scope of the question posed. I took a look at what I have on my shelves in order to recommend particularly good or standard books that I think could characterize large portions of an undergraduate degree and perhaps the beginnings of a graduate degree in the main fields that interest me, plus some personal favorites.

Neuroscience: Theoretical Neuroscience is a good book for the field of that name, though it does require background knowledge in neuroscience (for which, as others mentioned, Kandel's text is excellent, not to mention that it alone can cover the majority of an undergraduate degree in neuroscience if corequisite classes such as biology and chemistry are momentarily ignored) and in differential equations. Neurobiology of Learning and Memory and Cognitive Neuroscience and Neuropsychology were used in my classes on cognition and learning/memory and I enjoyed both; though they tend to choose breadth over depth, all references are research papers and thus one can easily choose to go more in depth in any relevant topics by consulting these books' bibliographies.

General chemistry, organic chemistry/synthesis: I liked Linus Pauling's General Chemistry more than whatever my school gave us for general chemistry. I liked this undergraduate organic chemistry book, though I should say that I have little exposure to other organic chemistry books, and I found Protective Groups in Organic Synthesis to be very informative and useful. Unfortunately, I didn't have time to take instrumental/analytical/inorganic/physical chemistry and so have no idea what to recommend there.

Biochemistry: Lehninger is the standard text, though it's rather expensive. I have limited exposure here.

Mathematics: When I was younger (i.e. before having learned calculus), I found the four-volume The World of Mathematics great for introducing me to a lot of new concepts and branches of mathematics and for inspiring interest; I would strongly recommend this collection to anyone interested in mathematics and especially to people considering choosing to major in math as an undergrad. I found the trio of Spivak's Calculus (which Amazon says is now unfortunately out of print), Stewart's Calculus (standard text), and Kline's Calculus: An Intuitive and Physical Approach to be a good combination of rigor, practical application, and physical intuition, respectively, for calculus. My school used Marsden and Hoffman's Elementary Classical Analysis for introductory analysis (which is the field that develops and proves the calculus taught in high school), but I liked Rudin's Principles of Mathematical Analysis (nicknamed "Baby Rudin") better. I haven't worked my way though Munkres' Topology yet, but it's great so far and is often recommended as a standard beginning toplogy text. I haven't found books on differential equations or on linear algebra that I've really liked. I randomly came across Quine's Set Theory and its Logic, which I thought was an excellent introduction to set theory. Russell and Whitehead's Principia Mathematica is a very famous text, but I haven't gotten hold of a copy yet. Lang's Algebra is an excellent abstract algebra textbook, though it's rather sophisticated and I've gotten through only a small portion of it as I don't plan on getting a PhD in that subject.

Computer Science: For artificial intelligence and related areas, Russell and Norvig's Artificial Intelligence: A Modern Approach's text is a standard and good text, and I also liked Introduction to Information Retrieval (which is available online by chapter and entirely). For processor design, I found Computer Organization and Design to be a good introduction. I don't have any recommendations for specific programming languages as I find self-teaching to be most important there, nor do I know of any data structures books that I found to be memorable (not that I've really looked, given the wealth of information online). Knuth's The Art of Computer Programming is considered to be a gold standard text for algorithms, but I haven't secured a copy yet.

Physics: For basic undergraduate physics (mechanics, e&m, and a smattering of other subjects), I liked Fundamentals of Physics. I liked Rindler's Essential Relativity and Messiah's Quantum Mechanics much better than whatever books my school used. I appreciated the exposition and style of Rindler's text. I understand that some of the later chapters of Messiah's text are now obsolete, but the rest of the book is good enough for you to not need to reference many other books. I have little exposure to books on other areas of physics and am sure that there are many others in this subreddit that can give excellent recommendations.

Other: I liked Early Theories of the Universe to be good light historical reading. I also think that everyone should read Kuhn's The Structure of Scientific Revolutions.

Okay. The book ''Calculus'' by Michael Spivak link is an introduction to Calculus, but using precise/rigorous notions that do away with the vague and imprecise infinitesimals. This should be what you want.

If you want something a bit more hardcore, but self-contained, I can recommend that you look at Rudin's The Principles of Mathematical Analysis, which should be in any library.

Calculus done rigorously usually goes under the name of Analysis/ Real Analysis, there should be tons of books in any math library on this subject if you feel uncomfortable with the two above.

I used calculus throughout the SAT, and especially on the Math Level 2 exam. It makes many problems much quicker, and also less complicated so you're not as prone to fuck-up.

Also, I don't believe that the SAT expects people to know the law of cosines and the sine rule, but if you do, you can blow past the trig in a few seconds.

Of course, the ACT is an easier test, so I think everyone should just take that. Well, stastically they compare scores and find that ACT scores are equivalent to some SAT score, but I almost maxed out on the ACT, and wasn't all too close to that on the SAT. And I didn't study for the ACT at all, whereas I did for the SAT.

Of course (yet again), standardized test are a load of bullshit so don't take any of it too seriously.

Edit:

Also, I think that calculus shouldn't be taught in high school. AP Calculus is trimmed down stupid shit for stupid kids who want to be able to use their calculators without understanding.

Spivak calculus is where it's at: http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098896

Everything is rigorous, everything is proved, and he introduces many interesting things like the gamma function (for finding non-integer factorials).

You might look at Michael Spivak's Calculus ( http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098896 ). In the preface to the second edition, Spivak writes:

>I have often been told that the title of this book should really be something like "Introduction to Analysis", because the book is usually used in courses where the students have already learned the mechanical aspects of calculus--such courses are standard in Europe.

The book starts by developing the real and complex number systems and later goes into proofs that pi is irrational, e is transcendental, etc.

Please note that I'm not a math major and have only just started working through the Spivak book myself, so I'm far from an authority on the subject. But it's the book I stumbled onto when I was looking for a similarly non-numeric perspective on calculus and basic analysis and so far I've been pleased with it.

I've only used it briefly but Spivak's Calculus is pretty popular around here.

Calculus
Spivak
http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098896

You can find Michael Spivak's Calculus, which everyone tells me ought to be titled "Introduction to Analysis" on libgen.