MOOCs vs Textbooks for computer science students

[Saqib Ali]

https://backdoorgraduteschooladmissions.quora.com/Mastering-lower-division-mathematics-courses-especially-for-computer-science-majors

The above link has a list of free online material to learn a lot of the math required in computer science. I'm already a 4th year undergrad, but I didn't learn much throughout my math courses. I got a C in multivariable calculus and never had to take differential equations. I also got a C in prob/stats. I got an A in an introductory linear algebra course, and I'm taking the second course next semester. To catch up faster, should I use this, or go through textbooks (which would take much longer)?

 

[StoneTemplePython]

Why not start by working through MIT's Math for CS?

https://courses.csail.mit.edu/6.042/spring17/mcs.pdfIf you got a C in multi-variable calc and probability, you likely have some major gaps. I wouldn't worry much about differential equations -- computing is mostly about countable sets so they don't really show up much. (Calc does, though, in probability, and also optimization, and bounding combinatorial structures, etc.)

 

[Buffu]

To catch up faster, should I use this, or go through textbooks (which would take much longer)?

Textbooks will take longer but if don't want to get anymore Cs you should read textbooks in my opinion. Textbooks are always better than anything else on internet.

Luckily the courses in which you got Cs are not very important in computer science, they are somewhat required in CGI and stuff like that.

Can you tell what did you learn in 1st course of LA ?

 

[Saqib Ali]

We learned up to eigen decomposition but didn’t even get into SVD. I want to do data science so I think prob/stats is very important.

 

[Wrichik Basu]

Textbooks are always better than anything else on internet.

True, but sometimes audio-visual teaching is necessary, which is when MOOCs come handy.

 

[Saqib Ali]

What textbooks would you recommend to me in that case?

Textbooks will take longer but if don't want to get anymore Cs you should read textbooks in my opinion. Textbooks are always better than anything else on internet.

Luckily the courses in which you got Cs are not very important in computer science, they are somewhat required in CGI and stuff like that.

Can you tell what did you learn in 1st course of LA ?

What textbooks would you recommend then for Calc -> Multivariable Calc, Diff eq, Lin Algebra, and Prob/stats?

 

[Saqib Ali]

True, but sometimes audio-visual teaching is necessary, which is when MOOCs come handy.

So would you recommend me to use both for learning?

 

[The Bill]

I like Thomas's Calculus and Analytic Geometry 4th edition (1969.) Any edition of Stewart is all right if you want a newer text, but I think Thomas is still fine to learn from.

If you want to go into more depth, you could get Spivak's Calculus for single variable and Vector Calculus by Baxandall and Liebeck for multivariable.

You say you've already done well in linear algebra, so I'm not sure what you're looking for in a recommendation. Anton and Rorres is decent if you want a book with examples of applications. It doesn't go into great depth in any of the applications, but it does fine as a survey. If you want to cover linear algebra with more rigor, you could get Shilov's Linear Algebra, or Axler's Linear Algebra Done Right. I hear Klein's Coding the Matrix: Linear Algebra through Applications to Computer Science is good, but I have no experience with that one.

For solidifying one's foundation in differential equations, I like Ordinary Differential Equations by Tenenbaum and Pollard.

My favorite practical probability and statistics text is Probability and Statistics for Engineers and Scientists by Walpole, Myers, Myers, and Ye. Any edition after the 6th is good. Earlier editions might be fine too, but I have no experience with them.

 

[Buffu]

What textbooks would you recommend to me in that case?

What textbooks would you recommend then for Calc -> Multivariable Calc, Diff eq, Lin Algebra, and Prob/stats?

I think Apostol or Courant will be fine for single/multi variable calculus and DEs but I will prefer Courant as it is less rigorous than Apostol.

For Probability I suggest Probability Theory: The Logic of Science and for statistics I suggest All of Statistics.

I don't know why you need a book for Linear algebra but I suggest Linear algebra done wrong or Linear algebra done right.

 

[Saqib Ali]

I think Apostol or Courant will be fine for single/multi variable calculus and DEs but I will prefer Courant as it is less rigorous than Apostol.

For Probability I suggest Probability Theory: The Logic of Science and for statistics I suggest All of Statistics.

I don't know why you need a book for Linear algebra but I suggest Linear algebra done wrong or Linear algebra done right.

Is Courants all in one book or is it separated?

 

[Buffu]

Is Courants all in one book or is it separated?

There are two book. https://www.amazon.com/dp/4871878384/?tag=pfamazon01-20 and https://www.amazon.com/dp/4871878384/?tag=pfamazon01-20.

 

[Wrichik Basu]

So would you recommend me to use both for learning?

If you have access to authenticate MOOCs, I would recommend to go through them at least once. At least I feel they are helpful in many cases.

 

[vanhees71]

True, but sometimes audio-visual teaching is necessary, which is when MOOCs come handy.

Well, I'd say, why not using both? It's great to have video lectures on the internet available. It's of course true that you have to go through textbooks yourself to really learn the material, and a math or physics textbook should always be read with paper, pencil (and eraser ;-)) at hand to follow the calculations in the text for onelself and also summarizing what you read in the book (and do this by hand, not typing into a computer; it's my personal experience that I remember things better when writing them by hand than by directly typing into the laptop).

After this step, i.e., learning the material from the lectures and the textbook, it's absolutely mandatory to do good problem sets. I think, it's not so important to solve a lot of problems of the same type all the time but to have solved a few number of problems of each type but doing this really yourself and also at the very end solve some more difficult non-standard problems where you need to think about a strategy to find a solution for yourself. Remember, as the ancient Greeks already knew, there's no royal road to mathematics; you have to walk it all for yourself!

Last but not least one should also consider to find some other students and form a learning group, where you can discuss the material and solve problems together.

 

[Buffu]

it's not so important to solve a lot of problems of the same type all the time but to have solved a few number of problems of each type but doing this really yourself and also at the very end solve some more difficult non-standard problems where you need to think about a strategy to find a solution for yourself.

This simple logic evades so many authors and publishers.

 

[Wrichik Basu]

Well, I'd say, why not using both?

Of course, if possible and if time permits, one can use both.