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Mathematics for Computer Science (2017) [pdf]

156 points by Schiphol 6y ago

danielscrubs 6y ago
Interesting that they call this “Mathematics for Computer Science”. In my university it was simply computer science and programming was computer engineering.
- Jtsummers 6y ago
  In the US, at least, computer engineering != programming. Computer engineering is more commonly (when you look at the courses) electrical engineering with a digital logic focus with some additional programming courses (often the first 2-4 CS courses). Programming falls squarely within computer science.
  - abhinav22 6y ago
    Same in Australia
  - closeparen 6y ago
    Sometimes business-y programming falls into Software Engineering or Management Information Systems but programming around operating systems, compilers, databases, graphics, etc. is squarely within CS.
  - kinow 6y ago
    Same in Brazil.
fcanesin 6y ago
The home page has a updated 2018 version of the readings: https://courses.csail.mit.edu/6.042/spring18/mcs.pdf https://courses.csail.mit.edu/6.042/spring18/mcs.pdf
throwaway_pdp09 6y ago
I have a background in some computer related mathematics, not once in my entire life has anything but the most trivial of it (basic logic equivalences) been of any use. That's deeply sad.
- irishspring 6y ago
  Just for perspective, math (and some compsci) students (and practitioners) would consider everything in the linked book to be "trivial math". That's because this book is a compilation of surface level sampling from various branches of math. Mathematicians' version of your lamentation would probably look something like "I studied all the ins and outs of measure theory/functional analysis and category theory/algebraic geometry for four years and all I do today is teach engineering students calculus and freshman math majors - elementary real analysis. That's deeply sad". :)
  - throwaway_pdp09 6y ago
    A fair lament, surely. Teaching stuff that has no immediate use displaces stuff that may be. It's not that simple because I think learning maths teaches you a broader, more rigorous way of thinking, but still, maybe maths education needs to look at itself hard.
deleted 6y ago
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deleted 6y ago
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7373737373 6y ago
How can one solve optimization problems like Cookie Clicker or https://qewasd.com https://qewasd.com in practice? Optimizing shortest paths is nice, but what about more complex causal structures, with preconditions, mutually exclusive choices, and varying resources?
- colelyman 6y ago
  A few tools that I use for solving optimization problems in practice are: - MiniZinc, https://www.minizinc.org/ https://www.minizinc.org/ a constrain set programming language that can also optimize an objective - Picat, http://picat-lang.org/ http://picat-lang.org/ a general purpose language that specializes in logic and optimization
hankchinaski 6y ago
does anybody uses this math in their daily job? perhaps in some fancy R&D lab in a few fortune 500?
- mettamage 6y ago
  As a web dev I needed to know some trig to visualize a star shaped diagram. Not that advanced, I know. In HFT firms you need to know some calculus as some of your data are going to be mathematical objects that are squarely in the field of calculus. Game devs need to know about matrices and quaternions. Mostly on how to use it, no proofs necessary. There are some fields and exploit chains where knowing some math to advanced math is necessary for hacking. For example checkout Triton and PIN from Intel and SMT solvers. I needed to instrument a binary program in class and use Triton to make an SMT equation, solve it and crack a password that way. Data scientists need to know statistics but you could argue they aren’t software devs but I bet some of them are both while having data scientist as a title. When performing speed optimization experiments, it is necessary in some cases to know statistics as you’re really finetuning things. Simply hitting run for a few times and observing a 5x to 10x speedup doesn’t fall into this category, as the speedup is obviously visible. I am talking about stuff that you can’t distinguish that easily. In general life, I would say strong knowledge about statistics is helpful. It helped me accurately assess the covid threat where I live. It also taught me to take every small chance out there. If I take enough chances then the likelihood of me hitting one of them becomes very very likely. I played poker as a teenager and have used statistical/chance-based thinking ever since and it helped me to experience more certainty in uncertain situations. I have played enough hands to know what a 1% chance of losing feels like (it feels like paying a fee to win the other 99 times, on average. Except if you’re not paying attention. Then it feels like you shouldn’t have lost and you’re probably going on tilt.). That’s what I know so far.
  - vram22 6y ago
    >In general life, I would say strong knowledge about statistics is helpful. It helped me accurately assess the covid threat where I live. It also taught me to ... and have used statistical/chance-based thinking ever since and it helped me to experience more certainty in uncertain situations. Interesting. Are there any specific books you would recommend for this sort of thinking, or are just basic stats books good enough?
nimish 6y ago
Concrete mathematics by Knuth oren and patashnik is very good as a primer too
fred256 6y ago
The second author, F Thomson Leighton, doesn't just work at Akamai Technologies, he's the co-founder and CEO.
323454 6y ago
I highly recommend reading chapter 9 (number theory) just for the sheer fun of it. Number theory is one of the oldest and yet probably the most surprising branches of mathematics.

156 points by Schiphol 6y ago

Interesting that they call this “Mathematics for Computer Science”. In my university it was simply computer science and programming was computer engineering.

Jtsummers 6y ago
In the US, at least, computer engineering != programming. Computer engineering is more commonly (when you look at the courses) electrical engineering with a digital logic focus with some additional programming courses (often the first 2-4 CS courses). Programming falls squarely within computer science.
- abhinav22 6y ago
  Same in Australia
- closeparen 6y ago
  Sometimes business-y programming falls into Software Engineering or Management Information Systems but programming around operating systems, compilers, databases, graphics, etc. is squarely within CS.
- kinow 6y ago
  Same in Brazil.

fcanesin 6y ago

The home page has a updated 2018 version of the readings: https://courses.csail.mit.edu/6.042/spring18/mcs.pdf https://courses.csail.mit.edu/6.042/spring18/mcs.pdf

throwaway_pdp09 6y ago

I have a background in some computer related mathematics, not once in my entire life has anything but the most trivial of it (basic logic equivalences) been of any use. That's deeply sad.

irishspring 6y ago
Just for perspective, math (and some compsci) students (and practitioners) would consider everything in the linked book to be "trivial math". That's because this book is a compilation of surface level sampling from various branches of math. Mathematicians' version of your lamentation would probably look something like "I studied all the ins and outs of measure theory/functional analysis and category theory/algebraic geometry for four years and all I do today is teach engineering students calculus and freshman math majors - elementary real analysis. That's deeply sad". :)
- throwaway_pdp09 6y ago
  A fair lament, surely. Teaching stuff that has no immediate use displaces stuff that may be. It's not that simple because I think learning maths teaches you a broader, more rigorous way of thinking, but still, maybe maths education needs to look at itself hard.

deleted 6y ago

[deleted]

deleted 6y ago

[deleted]

7373737373 6y ago

How can one solve optimization problems like Cookie Clicker or https://qewasd.com https://qewasd.com in practice? Optimizing shortest paths is nice, but what about more complex causal structures, with preconditions, mutually exclusive choices, and varying resources?

colelyman 6y ago
A few tools that I use for solving optimization problems in practice are: - MiniZinc, https://www.minizinc.org/ https://www.minizinc.org/ a constrain set programming language that can also optimize an objective - Picat, http://picat-lang.org/ http://picat-lang.org/ a general purpose language that specializes in logic and optimization

hankchinaski 6y ago

does anybody uses this math in their daily job? perhaps in some fancy R&D lab in a few fortune 500?

mettamage 6y ago
As a web dev I needed to know some trig to visualize a star shaped diagram. Not that advanced, I know. In HFT firms you need to know some calculus as some of your data are going to be mathematical objects that are squarely in the field of calculus. Game devs need to know about matrices and quaternions. Mostly on how to use it, no proofs necessary. There are some fields and exploit chains where knowing some math to advanced math is necessary for hacking. For example checkout Triton and PIN from Intel and SMT solvers. I needed to instrument a binary program in class and use Triton to make an SMT equation, solve it and crack a password that way. Data scientists need to know statistics but you could argue they aren’t software devs but I bet some of them are both while having data scientist as a title. When performing speed optimization experiments, it is necessary in some cases to know statistics as you’re really finetuning things. Simply hitting run for a few times and observing a 5x to 10x speedup doesn’t fall into this category, as the speedup is obviously visible. I am talking about stuff that you can’t distinguish that easily. In general life, I would say strong knowledge about statistics is helpful. It helped me accurately assess the covid threat where I live. It also taught me to take every small chance out there. If I take enough chances then the likelihood of me hitting one of them becomes very very likely. I played poker as a teenager and have used statistical/chance-based thinking ever since and it helped me to experience more certainty in uncertain situations. I have played enough hands to know what a 1% chance of losing feels like (it feels like paying a fee to win the other 99 times, on average. Except if you’re not paying attention. Then it feels like you shouldn’t have lost and you’re probably going on tilt.). That’s what I know so far.
- vram22 6y ago
  >In general life, I would say strong knowledge about statistics is helpful. It helped me accurately assess the covid threat where I live. It also taught me to ... and have used statistical/chance-based thinking ever since and it helped me to experience more certainty in uncertain situations. Interesting. Are there any specific books you would recommend for this sort of thinking, or are just basic stats books good enough?

nimish 6y ago

Concrete mathematics by Knuth oren and patashnik is very good as a primer too

fred256 6y ago

The second author, F Thomson Leighton, doesn't just work at Akamai Technologies, he's the co-founder and CEO.

323454 6y ago

I highly recommend reading chapter 9 (number theory) just for the sheer fun of it. Number theory is one of the oldest and yet probably the most surprising branches of mathematics.