7 ms·

Mathematics for Computer Science - Lecture Notes

176 points by iamanet 16y ago

jlmendezbonini 16y ago
Good find. Note that the Fall2005 offering includes solutions to the assignments and in-class problems while Spring2005, the one linked, does not. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2005/lecture-notes/ http://ocw.mit.edu/courses/electrical-engineering-and-comput...
justlearning 16y ago
are there any lecture videos available for this course?
- iamanet 16y ago
  Nope ;-) I even searched for related math books by these course instructors but no luck.
SandB0x 16y ago
This is useful, but pretty standard undergrad material. There are more interesting OCW courses, such as Street Fighting Mathematics: This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) http://ocw.mit.edu/courses/mathematics/18-098-street-fighting-mathematics-january-iap-2008/readings/ http://ocw.mit.edu/courses/mathematics/18-098-street-fightin...
- edge17 16y ago
  cool, are there any vids for this course?
  - iamanet 16y ago
    Nope there are no videos but the notes are simple to understand since they are very clearly explained.
- arethuza 16y ago
  "singing logarithms" - just like Anathem!
- viae 16y ago
  Note that the course's textbook, which is also called Street Fighting Mathematics, is available via Creative Commons Noncommercial Share Alike: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=12156 http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&#38... Its a link on the left side under the picture.
- mathgladiator 16y ago
  Simple put: awesome this reminds me of when I took partial differential equations where the instructor said: "this shit is really hard, so we are going to learn to guess the solution so we can even have a chance at getting close to the solution".
amichail 16y ago
Mathematics gets way more attention than it deserves in computing -- particularly with today's sophisticated libraries/frameworks. Just because a topic can be challenging doesn't automatically make it worthwhile. This is a trap that many people fall into.
- endtime 16y ago
  I think the more common trap, into which you appear to have fallen, is thinking that computer science and software engineering are the same thing.
  - bediger 16y ago
    The other common trap to fall into: thinking that all programming problems are solved. All you have to do is code the "business logic". A corollary of this is that it's impossible to speed up "business logic" at all. You have to drop from Java (typically) directly into assembly language.
    - amichail 16y ago
      Not all programming problems have been solved, but your time is not unlimited either. You need to spend your time on what really matters for your development.
      - jgg 16y ago
        Who are you to say that this doesn't matter for someone's development? This thread reads like you're trying to convince yourself that you don't need to understand this stuff.
        amichail 16y ago
        I've taken quite a lot of university math courses. Not much is helpful for what I do in my development. In fact, not even the algorithms courses I've taken are all that helpful since most of the hard stuff is already done for you in libraries/frameworks.
codewall 16y ago
I have always been intimidated by college level math and secretly wished I was smarter to not just understand, but to enjoy it as so many people seemingly do. I tried but failed to attain that level of proficiency multiple times. The mistake I was making was that I was trying to read lectures/blogs/books recommended by random people who knew nothing about me. It doesn't work. The thing is: math is big. It's HUGE, it's a whole world with something for everyone, and not everything in there excites me. I discovered this by accident by picking an easy and fun book about cryptography called (I think it was called The Code) - it was fascinating, it took me to wikipedia and I started to explore this world following my own interests And then it clicked: suddenly even "boring" aspects of math showed me their exciting sides.
- d0m 16y ago
  Yeah, somewhat a really good teacher helps students to like what they need to learn.. that make a huge difference. When you want to learn it because you like that, everything become easy.
- raju 16y ago
  Is the book you were referring to "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography" by Simon Singh? Amazon link - http://amzn.to/dlNAeO http://amzn.to/dlNAeO It's on my reading shelf right now, but I have not gotten around to reading it. I think your comment just might make that happen. Thanks for the recommendation
  - oscardelben 16y ago
    I've read that book although I admit I did not take the final challenges. Still I found that to be a very interesting book, very well written where you can actually learn something useful.
- iamanet 16y ago
  What you say is very true. I guess the whole idea of this course was to equip students with the necessary Math skills to comprehend courses like Algorithms and data structures especially the CLRS's 'Introduction to Algorithms' book. At the least these notes helped me comprehend that book ;-)
jgg 16y ago
This is stuff that's usually taught in a course called "Discrete Mathematics". As far as textbooks go for this type of material, which do you all like? I own Rosen's famous book ( https://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073229725 https://www.amazon.com/Discrete-Mathematics-Applications-Ken... ), but it's the "James Stewart's Calculus" of Discrete Mathematics books. I purchased some really old books too, but I haven't yet found one that I like a lot (I settled for a Dover text that's mostly passable). For the specific topic of set theory, though, I haven't found one I like better than Paul Halmos: https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Mathematics/dp/0387900926 https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math... If I could only find a number theory text that I like as much.
spektom 16y ago
Do the page "The ZFC Axioms" contain errors? I can't understand the following proposition: ∃y∀z(∃w(z ∈ w ∧ w ∈ x) ⇒ z ∈ y) Shouldn't it be: ∃y∀z(∃w(z ∈ w ∧ w ∈ y) ⇒ z ∈ y)

176 points by iamanet 16y ago

Good find. Note that the Fall2005 offering includes solutions to the assignments and in-class problems while Spring2005, the one linked, does not. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2005/lecture-notes/ http://ocw.mit.edu/courses/electrical-engineering-and-comput...

justlearning 16y ago

are there any lecture videos available for this course?

iamanet 16y ago
Nope ;-) I even searched for related math books by these course instructors but no luck.

SandB0x 16y ago

This is useful, but pretty standard undergrad material. There are more interesting OCW courses, such as Street Fighting Mathematics: This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) http://ocw.mit.edu/courses/mathematics/18-098-street-fighting-mathematics-january-iap-2008/readings/ http://ocw.mit.edu/courses/mathematics/18-098-street-fightin...

edge17 16y ago
cool, are there any vids for this course?
- iamanet 16y ago
  Nope there are no videos but the notes are simple to understand since they are very clearly explained.
arethuza 16y ago
"singing logarithms" - just like Anathem!
viae 16y ago
Note that the course's textbook, which is also called Street Fighting Mathematics, is available via Creative Commons Noncommercial Share Alike: http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=12156 http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&#38... Its a link on the left side under the picture.
mathgladiator 16y ago
Simple put: awesome this reminds me of when I took partial differential equations where the instructor said: "this shit is really hard, so we are going to learn to guess the solution so we can even have a chance at getting close to the solution".

amichail 16y ago

Mathematics gets way more attention than it deserves in computing -- particularly with today's sophisticated libraries/frameworks. Just because a topic can be challenging doesn't automatically make it worthwhile. This is a trap that many people fall into.

endtime 16y ago
I think the more common trap, into which you appear to have fallen, is thinking that computer science and software engineering are the same thing.
- bediger 16y ago
  The other common trap to fall into: thinking that all programming problems are solved. All you have to do is code the "business logic". A corollary of this is that it's impossible to speed up "business logic" at all. You have to drop from Java (typically) directly into assembly language.
  - amichail 16y ago
    Not all programming problems have been solved, but your time is not unlimited either. You need to spend your time on what really matters for your development.
    - jgg 16y ago
      Who are you to say that this doesn't matter for someone's development? This thread reads like you're trying to convince yourself that you don't need to understand this stuff.
      - amichail 16y ago
        I've taken quite a lot of university math courses. Not much is helpful for what I do in my development. In fact, not even the algorithms courses I've taken are all that helpful since most of the hard stuff is already done for you in libraries/frameworks.

codewall 16y ago

I have always been intimidated by college level math and secretly wished I was smarter to not just understand, but to enjoy it as so many people seemingly do. I tried but failed to attain that level of proficiency multiple times. The mistake I was making was that I was trying to read lectures/blogs/books recommended by random people who knew nothing about me. It doesn't work. The thing is: math is big. It's HUGE, it's a whole world with something for everyone, and not everything in there excites me. I discovered this by accident by picking an easy and fun book about cryptography called (I think it was called The Code) - it was fascinating, it took me to wikipedia and I started to explore this world following my own interests And then it clicked: suddenly even "boring" aspects of math showed me their exciting sides.

d0m 16y ago
Yeah, somewhat a really good teacher helps students to like what they need to learn.. that make a huge difference. When you want to learn it because you like that, everything become easy.
raju 16y ago
Is the book you were referring to "The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography" by Simon Singh? Amazon link - http://amzn.to/dlNAeO http://amzn.to/dlNAeO It's on my reading shelf right now, but I have not gotten around to reading it. I think your comment just might make that happen. Thanks for the recommendation
- oscardelben 16y ago
  I've read that book although I admit I did not take the final challenges. Still I found that to be a very interesting book, very well written where you can actually learn something useful.
iamanet 16y ago
What you say is very true. I guess the whole idea of this course was to equip students with the necessary Math skills to comprehend courses like Algorithms and data structures especially the CLRS's 'Introduction to Algorithms' book. At the least these notes helped me comprehend that book ;-)

jgg 16y ago

This is stuff that's usually taught in a course called "Discrete Mathematics". As far as textbooks go for this type of material, which do you all like? I own Rosen's famous book ( https://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073229725 https://www.amazon.com/Discrete-Mathematics-Applications-Ken... ), but it's the "James Stewart's Calculus" of Discrete Mathematics books. I purchased some really old books too, but I haven't yet found one that I like a lot (I settled for a Dover text that's mostly passable). For the specific topic of set theory, though, I haven't found one I like better than Paul Halmos: https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Mathematics/dp/0387900926 https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math... If I could only find a number theory text that I like as much.

spektom 16y ago

Do the page "The ZFC Axioms" contain errors? I can't understand the following proposition: ∃y∀z(∃w(z ∈ w ∧ w ∈ x) ⇒ z ∈ y) Shouldn't it be: ∃y∀z(∃w(z ∈ w ∧ w ∈ y) ⇒ z ∈ y)