#80 overallEvergreen
18.01 Single Variable Calculus
MIT OpenCourseWare
5 recommenders · 6 threads · recommended in 6 years, 2013–2022 · score 5.5
MIT OpenCourseWare's single-variable calculus course (18.01, with an SC version from Fall 2010 linked) covering limits, derivatives, integrals and their applications, delivered as free lecture videos and notes.
Commenters point to it as a free, university-level calculus course to learn from on their own, often alongside a textbook and problem sets.
Recommendations by year
20062026
Don't read books, take classes instead - Khan Academy, MIT 18.01, 18.02, 18.06, Harvard Stat100 etc.
Take university classes - it's the same material, you just won't get any academic credits. MIT Opencourseware has Single Variable Calculus (18.01), Multivariable Calculus (18.02) and Linear Algebra (18.06). That's plenty of material to get started with. Watch the lectures, follow along with the textbook, do the exercises.
If you're concerned that you don't have some of the prerequisites like high school algebra or trigonometry, Khan Academy have a pre-calculus course - start there.
I switched to data science from an unrelated field and had to do a lot self-study like this to catch up on my math.
I know that you've decided to take a gap year but my advice for next steps is actually to take undergraduate courses in single variable calculus, multivariable calculus, linear algebra and probability theory. All four of these are available online for free (course names: MIT 18.01, 18.02, 18.06, Harvard Stat110).
Start small. I would look at Stat 110 from Harvard, Strang's OCW lectures, and the intro calculus MIT course.
When you're done with that, it'll be easy to see where you want to go next.
Have you mastered algebra and trig? If not, do it. Khan Academy is great for this. Watch the videos and do lots and lots of problems. In learning math, there is no substitute for working through lots of problems.
After this, I suggest learning some discrete math and proof techniques. The book How To Prove It is great. It will teach you logic, set theory, how to write proofs, and how to invent proofs. Learning this first will help you actually understand calculus when you study it next.
For calculus, MIT's OCW course is really good. Pick up a standard book like Stewart, do a lot of problems, and try to understand the proofs of all the theorems. Or if you'd really like a challenge and some more theory, pick up Spivak's book.
I learnt only a bit of discrete math in my CS undergraduate degree, I had calculus and linear algebra but barely passed it by memorizing how to solve concrete problems and by having merciful professors - I was already working full time and had 4 or 5 courses going on, I just didn't manage to find enough time to study properly. If you have bigger gaps in your math knowledge and can't go to an university you just have to start at a lower level, there is a wide selection of "intro to higher mathematics" books meant for people like that, and if that level is still too high you might need to review high school math, e.g. Serge Lang has a good "Basic Mathematics" review book, or you can use Khan Academy videos etc. I myself had to review a lot of high school math when I was starting.
MIT OCW has excellent courses for discrete math, calculus and linear algebra and in some cases videos from the recitations are included.
http://ocw.mit.edu/courses/mathematics/18-01sc-single-variab...
I also stressed a few times already I don't think it is "the same kind of experience". But as long as you make an effort you will make progress and not everyone can manage to fit a university degree in their schedule.
First I would recommend Cal Newport's blog about using time wisely. http://calnewport.com/blog/2008/11/25/case-study-how-i-got-t... Plenty more great info in the archive: http://calnewport.com/blog/archive/ Obviously the best way would be to go through your school's course syllabus for whatever classes you want to take and look at the material you will be doing, but these are good for a general preparedness:
Axler - Precalculus 2nd version http://precalculus.axler.net/ He works through every odd exercise solution, in full. Also gives you a good intro to sets and series, summation notation, binomial theorem, all this will come up later in discrete math. He assumes the reader knows nothing about Trig as well.
Gilbert Strang's videos "Highlights of Calculus" https://ocw.mit.edu/resources/res-18-005-highlights-of-calcu... just to get an overview of what calculus really is since I assume your university will throw you into an applied single variable class first year. MIT Open Courseware has their calculus (18.01/18.02) course lectures up if you want to watch them too to get an idea of what you'll run into.
"Elements of Mathematics: From Euclid to Gödel" gives quite a good explanation of Mathematics as a whole, like why we learn elementary math the way we do and how it applies to more advanced concepts, explains Rings/Fields and has a really good introduction to Logic. I wish this book existed 5 years ago when I started http://press.princeton.edu/titles/10697.html
"An Introduction to Mathematical Reasoning" by Eccles is short and excellent. You can also download the lecture notes here from CMU's course on proofs http://math.cmu.edu/~svasey/concepts-summer-1-2014/ and try some of the homework if you want but you probably won't see any of this until second year judging by most university calendars and recommended program course list I've seen.
CLRS https://en.wikipedia.org/wiki/Introduction_to_Algorithms which has a great first chapter "Foundations" that compliments Knuth's 'Mathematical Preliminaries' chapter in TAOCP vol 1. Knuth's book you can really drill yourself in these concepts though with the many, many exercises writing proofs. The skills I learned doing these exercises paid in full years later when I started more advanced math and even at work.