11–20 of 69 posts
"Many students struggle with the idea of recursion..." I still remember one of the worst bugs I'd ever introduced (in terms of pain to me). I was maybe 2-3 years out of my bachelors, and I thought recursion was so nifty that I'd use it where ever I could. I was coding C++, at the time. And, I got the dreaded 2am call after all of the production servers went down hard. Like terminate and corrupt data hard. Lesson lear…
It's also interesting to consider the chapter headings in Concrete Mathematics (Graham, Knuth, Patashnik), a text designed with students of CS and programming in mind:
Recurrent Problems
Summation
Integer Functions
Number Theory
Binomial Coefficients
Special Numbers
Generating Functions
Discrete Probability
Asymptotics"Many students struggle with the idea of recursion..." I still remember one of the worst bugs I'd ever introduced (in terms of pain to me). I was maybe 2-3 years out of my bachelors, and I thought recursion was so nifty that I'd use it where ever I could. I was coding C++, at the time. And, I got the dreaded 2am call after all of the production servers went down hard. Like terminate and corrupt data hard. Lesson lear…
I'd include combinatorics under 'useful' too - although the basics are usually covered in statistics courses. Odd that the list mentions differential equations but not basic calculus, which I'd think is more fundamental. It's also interesting to consider the chapter headings in Concrete Mathematics (Graham, Knuth, Patashnik), a text designed with students of CS and programming in mind: Recurrent Problems Summation In…
This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
> Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all over the place, It's still interesting to think about which branches of math are actually applicable to programming itself. People…
- You write a recursive program the same way you write an inductive proof
- Abstract algebra and category theory are likely relevant, especially for metaprogramming. My math education hasn't included this, so I can't say much more.
- Linear algebra is just ridiculously important
- Statistics for machine learning. Also for figuring out how to combine data in a meaningful way. There are also a lot of people asking statistical questions directly, and writing programs is how you get those kinds of answers in a reasonable timeframe.
This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
> Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all over the place, It's still interesting to think about which branches of math are actually applicable to programming itself. People…
- Linear algebra used in graphics and game programming
For a lot of programming understanding user interaction and human psychology is much more important than mathematics.
I never liked these kinds of lists. The people who ask the question always seem to be under- or overwhelmed by the answer (programmers don't need any math?! theoretical computer scientists need all math?!). And the people who answer are almost always skewed toward whatever it is they do. Even the top-voted response to the OP is obviously biased toward the logic flavor of computer science, with awkwardly scattered rec…
However, you should keep in mind that these lists are intended as an answer to "What Math should we teach freshmen undergrads?", not an answer to "What Math do all the CS-people need to know?". The latter is naturally a very small subset of Math, the 'logicish' type.
I do STRONGLY agree with you that we should help students figure out the areas that they find interesting, and let them know what kind of Math is useful for each.
This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
> Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all over the place, It's still interesting to think about which branches of math are actually applicable to programming itself. People…
I think it's amazing that programming can leverage and express so many mathematical facts - from implementing a binary tree that is enforced to always be balanced by the type system in Haskell, to using linear types to safely use and free OS resources in ATS.