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Math topics useful for computer science/programming

84 points by jackhammer2022 12y ago

j2kun 12y ago
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 recommendations for non-logicish topics that are far more useful for all flavors of computer science ("perhaps even eigenvalues," seriously?!). These lists even ignore the deeper question being asked: how do you figure out what sort of mathematics you need for the things you're interested in? Not all computer scientists (and programmers) like the same things in computer science and programming. It's much more advisable to figure out what you like before you go around trying to learn all the math there is to learn related to CS, and then ask about what math topics are related to that.
- Betelgeuse90 12y ago
  I largely agree with your sentiments. 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.
  - j2kun 12y ago
    But the question is one and the same in this instance: they're asking what should be taught in "the" math class for a CS degree. If that doesn't contain the math that all CS-people need to know, then what should it contain? The OP describes universal algebra and term rewriting, which is what I claim is the logicish type that is not as crucial as, say, linear algebra if you want to find widely applicable mathematics for CS/programming.
    - Betelgeuse90 12y ago
      It may not be crucial for programming, but I'd say it's more crucial than Linear Algebra for finishing the degree at all, since there are CS subjects that you just can't really take unless you learn the logicish stuff. I can't imagine not taking calculus either... How do you comfortably take the logarithm of an inequality without it? This whole idea seems so ridiculously impossible to me...
- nraynaud 12y ago
  I agree, I have had to learn Newton's methode for differential equations (for simulation), I've had to use logic and an automatic prover (for system validation), I've had to do some complexity analysis (for everything), I've had to play with linear applications, matrices and all the stuff around 3D, I've had to dig into geographical projection equations for another job (in GIS). I'm currently toying with computational geometry. I think what is important is some kind of math to understand how those people write (which far from obvious), and then random stuff to learn to switch.
- tptacek 12y ago
  This comment is a little frustrating, because part of the point of linking to the Stack Overflow post is to continue the discussion, which is obviously germane to our site. Why not dig into specifics of how you'd approach the intersection of math and CS?
  - j2kun 12y ago
    It's actually inspired me to write my own article, but that will take time. Meanwhile, I actually write a blog called "Math Intersect Programming." Even though it's more about my specific interests than how a freshman should approach the topics, and I certainly emphasize the mathematical ideas over the engineering challenges, it still gives a good idea of what I would suggest: Orient the learning around applications in CS. Find a problem that requires the mathematics you want to learn, and learn it with the persistent contextual understanding that you are trying to do something more than just tinker with definitions. Do this for one application and repeat as desired. My view is that when this is done, you learn to focus on the things that matter over the things that are used to fill empty space in courses (calculus courses come to mind as a specifically abhorrent example of this). You get better at seeing the forest over the trees. The problem is this avoids the OP's question (and this ensuing discussion about the OP's questions and the purported answers), since you can't organize a single class around it. Another problem is that very few books are written this way, or are only superficially so.
    - apu 12y ago
      I want to chime in and say that I've found your blog wonderful, and since you're too modest to post a link, let me do it: http://jeremykun.com/ http://jeremykun.com/
stiff 12y ago
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 over the place, unlike most things listed it's something that you can expect to encounter almost regardless of what domain you are interested in. I mean, the guy asks what should replace Calculus and then the first answer includes "Asymptotics", "basic limits, sequences and series", so actually calculus. In general I cringe a little every time I hear Computer Science people should focus on "discrete math", because without tools from analysis you can only solve the most trivial discrete problems. And yes, calculus by itself is hardly ever applicable in CS, yet you still have to learn it, tough luck. In general what is not stressed enough I think is that applying math is hard and you need to learn a lot of it before you have enough tools to tackle problems anywhere close to real-world complexity. The top answer also lists random concepts. I am learning probability currently, for applications in machine learning. "Discrete spaces, Bayes theorem and expected values" you can learn in a day, "Markovs, Chebyshev and Chernoff inequalities" are mostly only useful for further theoretical work, so is "the law of large numbers". What will really be useful will depend a lot on the applications, if you are a theoretical computer scientist, mastery of generating functions and transforms will be useful, and it's one of those instances where discrete problems are solved via tools from calculus/analysis. For machine learning you need to know everything about the normal distribution by heart, and this means you have to know everything about the exponential function by heart, so again back to calculus. Notions from information theory are useful, but of course none of the ones he listed. The comment "This is a must for modern programmers." sounds just comic.
- superuser2 12y ago
  > 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 tend to talk about programming and math as very strongly related, and of course there is the obvious relationship that "some computer programs do particular kinds of math" like you're talking about here. But there is no (intuitive) overlap between writing, say, a web application and doing algebraic or calculus computation on paper. However, there are things like: - Set theory underpinning relational databases - Typed lambda calculus underpinning functional programming I'd be interested in other examples like this.
ap22213 12y ago
"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 learned: it's good to know recursion, but it's also good to know maximum stack sizes.
- KRuchan 12y ago
  What problem were you trying to solve with recursion?
- archena 12y ago
  That and tail-call optimisation :)
- jostylr 12y ago
  There's also thunk/trampolining continuation style to convert recursion easily into something that is not stack limited. http://nathansuniversity.com/cont.html http://nathansuniversity.com/cont.html
userbinator 12y ago
In my experience, I've seen a lot of students entering CS not comfortable with even basic arithmetic and algebra, despite it not being mentioned in any of the linked responses. As for calculus, I think its importance is overrated - unless you are specifically doing some numerical computation that requires it.
- Bahamut 12y ago
  Calculus gives you some of the intuition for figuring out a good big O bound for the computing time of an algorithm.
archena 12y ago
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 Integer Functions Number Theory Binomial Coefficients Special Numbers Generating Functions Discrete Probability Asymptotics
- bainsfather 12y ago
  I got Concrete Mathematics a few days ago, after someone recommended it. My background is physics, and I find the "mathematicians' style" to be very awkward to learn from. This book is excellent for me - concrete examples - it is always trying to solve specific problems, so if I don't follow the theory, I can always refer to a concrete example and try to understand that specific case. This the way I learn best/fastest.
deleted 12y ago
[deleted]
weavie 12y ago
Although I did mathematics to degree level, I have used so little of it in my professional career that I have largely forgotten it all now. Any such list is going to depend on what area of programming you want to get into. For a lot of programming understanding user interaction and human psychology is much more important than mathematics.
jostylr 12y ago
Why not teach math + programming together? I didn't seem to see anyone suggest that. Calculus: simplify and iterate to solve a problem (like Newton's Method). Lots of issues to tackle with. Much more useful than learning formulas, but it can also be interesting to show how converting forms can take an unstable problem into a stable one. Combinatorics: Explore the small side of a problem, code up the larger version, explore how far one can get, show methods for dealing with the problem beyond the scope. Graphics, user interface design, etc., are also very big in math. In a course I teach to Enviro Science people, they come in scar(r)ed of math and by the end, they enjoy it. A big trick is getting them to use GeoGebra in an exploratory, visual fashion. It makes the math real. The same approach in code can help make CS students get math while also getting the issues in CS. Anyone who thinks the exponential as 1+ x+ x^2/2 + .... is useful as is for x = 100 needs some actual experience with it. But at the same time, teaching them how to translate e^100 ~~ e^(43ln(10) + .98) ~~ 10^43 (1 + .98 + .98^2/2 + .98^3/6) = 10^43 * 2.62 has its value (compare to e^100 ~~ 2.69 * 10^43) This is the kind of math that is useful. Exploratory math that struggles with mathematical truths and practical implementations. Students should get a sense of the limits of computers, what they can handle and not. And designing a good math interface for these problems can be quite the UI learning experience. There are so many ways to explore math. Stop teaching dry math and start teaching programming math.
- JoeAltmaier 12y ago
  Linear algebra/vector algebra is the single most useful topic for programming I can imagine.
  - ktran03 12y ago
    And yet, so many coders don't know linear algebra.
  - tptacek 12y ago
    Why?
    - JoeAltmaier 12y ago
jules 12y ago
Which area of math isn't useful for computer science/programming? Certainly some areas are more useful than others, but I think rather than looking at areas it matters more how in depth you go in one area. Going super deep into an area is often not a lot more useful than just knowing the basics. Complexity theory is useful, but it's not that practically useful to know deeply about all the complexity classes.
brirush 12y ago
I wrote the original question. I've always been interested in how much math various careers use, but I wrote this question the way I did in a shameless attempt to drive traffic to the site by appealing to the Stackoverflow and reddit communities. Everyone has given me a different answer so far, but that's to be expected, because there are ~1000 subcategories of computer programmers.
- nmrm 12y ago
  > I've always been interested in how much math various careers use > ... there are ~1000 subcategories of computer programmers. I'm curious: what about other careers? Are there fewer categories? Do they all do the same type of math? etc.
alok-g 12y ago
What would be a good writeup for understanding term-rewriting? (My current background level: I understand most of what OP has listed in "actually useful" and "can run into", and "automata theory" from the third list.)
- j2kun 12y ago
  I wouldn't recommend it as being as important as the OP claims, but if you must: http://www21.in.tum.de/~nipkow/TRaAT/ http://www21.in.tum.de/~nipkow/TRaAT/
  - alok-g 12y ago
    Thanks! Could you also recommend something on how symbolic computation works? I have used computer algebra systems like Mathematica for long; would like to understand how it works internally. I currently understand some basics like DPLL, semantic first-order unification, methods of solving specific equation systems like linear systems, numerical differential equations, etc. I am missing at least how the "top-level" of symbolic computation works. For example, from what I currently understand, first-order semantic unification can find "x = Cos[y]" from "Sin[x] = Sin[Cos[y]]", but cannot solve "Sin[x] = Cos[x]" for x, and cannot simplify "[(Sin[x])^2 + (Cos[x])^2] = 1" to True. I am hoping to find something simpler than reading through SymPy source code. :-)
    - nextos 12y ago
      Peter Norvig's PAIP book has a chapter devoted to Student, a computer algebra system. It's very didactic: http://norvig.com/paip/student.lisp http://norvig.com/paip/student.lisp
RogerL 12y ago
I went to an engineering University. Besides having a wide variety of math required (3 semesters of Calc, 1 semester of either stats or probability, 1 semester of either linear algebra or matrices), we also had to take 3 semesters of physics, and 2 of chemistry. Most of us (those not just looking for a piece of paper) went considerable deeper in at least one area. No, you don't need to understand organic chemistry to write a CRUD app. But, you don't need university to write a CRUD app. I think I received an excellent education that prepared me for about any job out there. And, I've done it. I've done cancer statistics for the NIH. I've worked in avionics and simulation. Well, blah blah, no one cares about my resume, I'll just say I couldn't have done any of it without the education I received. I haven't done financial quant stuff, as an example, but how could I without the math background? Or how could I program a controller in a factory without understanding PID (done that)? How can I get a piece of that neat drone project (done that)? Hey, that computer vision stuff looks interesting, all I need to know is ...derivatives, statistics (done that too). For most of us, university is the last and/or best chance to really understand how the world works. For that you need quite a bit of math and science. Another example. We have a voluntary Arduino robotics workshop going on at work, coupled with 3D printing. Naturally, people are excited, and have all kinds of ideas. But, how do you execute on that if you don't understand how to design an op amp circuit, or filter data with something more sophisticated than a moving average? Robotics spans a number of fields, and to actually produce something more than a gimmick requires a lot of knowledge. Knowledge that you can pretty easily pick up in University, but knowledge you mostly just long for as you have to rush home at 5:30 to pick up the kids and make dinner. I guess this is a cranky rant from an old guy. But I hear about University programs that are nothing more than Java voc ed systems and I despair. $100K in debt to learn something most anyone on here could just pick up on their own. You don't need university for that stuff.
- klibertp 12y ago
  > but how could I without the math background? You could have just learned it as you went. Done that.
deleted 12y ago
[deleted]

j2kun 12y ago

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 recommendations for non-logicish topics that are far more useful for all flavors of computer science ("perhaps even eigenvalues," seriously?!). These lists even ignore the deeper question being asked: how do you figure out what sort of mathematics you need for the things you're interested in? Not all computer scientists (and programmers) like the same things in computer science and programming. It's much more advisable to figure out what you like before you go around trying to learn all the math there is to learn related to CS, and then ask about what math topics are related to that.

Betelgeuse90 12y ago
I largely agree with your sentiments. 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.
- j2kun 12y ago
  But the question is one and the same in this instance: they're asking what should be taught in "the" math class for a CS degree. If that doesn't contain the math that all CS-people need to know, then what should it contain? The OP describes universal algebra and term rewriting, which is what I claim is the logicish type that is not as crucial as, say, linear algebra if you want to find widely applicable mathematics for CS/programming.
  - Betelgeuse90 12y ago
    It may not be crucial for programming, but I'd say it's more crucial than Linear Algebra for finishing the degree at all, since there are CS subjects that you just can't really take unless you learn the logicish stuff. I can't imagine not taking calculus either... How do you comfortably take the logarithm of an inequality without it? This whole idea seems so ridiculously impossible to me...
nraynaud 12y ago
I agree, I have had to learn Newton's methode for differential equations (for simulation), I've had to use logic and an automatic prover (for system validation), I've had to do some complexity analysis (for everything), I've had to play with linear applications, matrices and all the stuff around 3D, I've had to dig into geographical projection equations for another job (in GIS). I'm currently toying with computational geometry. I think what is important is some kind of math to understand how those people write (which far from obvious), and then random stuff to learn to switch.
tptacek 12y ago
This comment is a little frustrating, because part of the point of linking to the Stack Overflow post is to continue the discussion, which is obviously germane to our site. Why not dig into specifics of how you'd approach the intersection of math and CS?
- j2kun 12y ago
  It's actually inspired me to write my own article, but that will take time. Meanwhile, I actually write a blog called "Math Intersect Programming." Even though it's more about my specific interests than how a freshman should approach the topics, and I certainly emphasize the mathematical ideas over the engineering challenges, it still gives a good idea of what I would suggest: Orient the learning around applications in CS. Find a problem that requires the mathematics you want to learn, and learn it with the persistent contextual understanding that you are trying to do something more than just tinker with definitions. Do this for one application and repeat as desired. My view is that when this is done, you learn to focus on the things that matter over the things that are used to fill empty space in courses (calculus courses come to mind as a specifically abhorrent example of this). You get better at seeing the forest over the trees. The problem is this avoids the OP's question (and this ensuing discussion about the OP's questions and the purported answers), since you can't organize a single class around it. Another problem is that very few books are written this way, or are only superficially so.
  - apu 12y ago
    I want to chime in and say that I've found your blog wonderful, and since you're too modest to post a link, let me do it: http://jeremykun.com/ http://jeremykun.com/

stiff 12y ago

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 over the place, unlike most things listed it's something that you can expect to encounter almost regardless of what domain you are interested in. I mean, the guy asks what should replace Calculus and then the first answer includes "Asymptotics", "basic limits, sequences and series", so actually calculus. In general I cringe a little every time I hear Computer Science people should focus on "discrete math", because without tools from analysis you can only solve the most trivial discrete problems. And yes, calculus by itself is hardly ever applicable in CS, yet you still have to learn it, tough luck. In general what is not stressed enough I think is that applying math is hard and you need to learn a lot of it before you have enough tools to tackle problems anywhere close to real-world complexity. The top answer also lists random concepts. I am learning probability currently, for applications in machine learning. "Discrete spaces, Bayes theorem and expected values" you can learn in a day, "Markovs, Chebyshev and Chernoff inequalities" are mostly only useful for further theoretical work, so is "the law of large numbers". What will really be useful will depend a lot on the applications, if you are a theoretical computer scientist, mastery of generating functions and transforms will be useful, and it's one of those instances where discrete problems are solved via tools from calculus/analysis. For machine learning you need to know everything about the normal distribution by heart, and this means you have to know everything about the exponential function by heart, so again back to calculus. Notions from information theory are useful, but of course none of the ones he listed. The comment "This is a must for modern programmers." sounds just comic.

superuser2 12y ago
> 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 tend to talk about programming and math as very strongly related, and of course there is the obvious relationship that "some computer programs do particular kinds of math" like you're talking about here. But there is no (intuitive) overlap between writing, say, a web application and doing algebraic or calculus computation on paper. However, there are things like: - Set theory underpinning relational databases - Typed lambda calculus underpinning functional programming I'd be interested in other examples like this.

ap22213 12y ago

"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 learned: it's good to know recursion, but it's also good to know maximum stack sizes.

KRuchan 12y ago
What problem were you trying to solve with recursion?
archena 12y ago
That and tail-call optimisation :)
jostylr 12y ago
There's also thunk/trampolining continuation style to convert recursion easily into something that is not stack limited. http://nathansuniversity.com/cont.html http://nathansuniversity.com/cont.html

userbinator 12y ago

In my experience, I've seen a lot of students entering CS not comfortable with even basic arithmetic and algebra, despite it not being mentioned in any of the linked responses. As for calculus, I think its importance is overrated - unless you are specifically doing some numerical computation that requires it.

Bahamut 12y ago
Calculus gives you some of the intuition for figuring out a good big O bound for the computing time of an algorithm.

archena 12y ago

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 Integer Functions Number Theory Binomial Coefficients Special Numbers Generating Functions Discrete Probability Asymptotics

bainsfather 12y ago
I got Concrete Mathematics a few days ago, after someone recommended it. My background is physics, and I find the "mathematicians' style" to be very awkward to learn from. This book is excellent for me - concrete examples - it is always trying to solve specific problems, so if I don't follow the theory, I can always refer to a concrete example and try to understand that specific case. This the way I learn best/fastest.

deleted 12y ago

[deleted]

weavie 12y ago

Although I did mathematics to degree level, I have used so little of it in my professional career that I have largely forgotten it all now. Any such list is going to depend on what area of programming you want to get into. For a lot of programming understanding user interaction and human psychology is much more important than mathematics.

jostylr 12y ago

Why not teach math + programming together? I didn't seem to see anyone suggest that. Calculus: simplify and iterate to solve a problem (like Newton's Method). Lots of issues to tackle with. Much more useful than learning formulas, but it can also be interesting to show how converting forms can take an unstable problem into a stable one. Combinatorics: Explore the small side of a problem, code up the larger version, explore how far one can get, show methods for dealing with the problem beyond the scope. Graphics, user interface design, etc., are also very big in math. In a course I teach to Enviro Science people, they come in scar(r)ed of math and by the end, they enjoy it. A big trick is getting them to use GeoGebra in an exploratory, visual fashion. It makes the math real. The same approach in code can help make CS students get math while also getting the issues in CS. Anyone who thinks the exponential as 1+ x+ x^2/2 + .... is useful as is for x = 100 needs some actual experience with it. But at the same time, teaching them how to translate e^100 ~~ e^(43ln(10) + .98) ~~ 10^43 (1 + .98 + .98^2/2 + .98^3/6) = 10^43 * 2.62 has its value (compare to e^100 ~~ 2.69 * 10^43) This is the kind of math that is useful. Exploratory math that struggles with mathematical truths and practical implementations. Students should get a sense of the limits of computers, what they can handle and not. And designing a good math interface for these problems can be quite the UI learning experience. There are so many ways to explore math. Stop teaching dry math and start teaching programming math.

JoeAltmaier 12y ago
Linear algebra/vector algebra is the single most useful topic for programming I can imagine.
- ktran03 12y ago
  And yet, so many coders don't know linear algebra.
- tptacek 12y ago
  Why?
  - JoeAltmaier 12y ago

jules 12y ago

Which area of math isn't useful for computer science/programming? Certainly some areas are more useful than others, but I think rather than looking at areas it matters more how in depth you go in one area. Going super deep into an area is often not a lot more useful than just knowing the basics. Complexity theory is useful, but it's not that practically useful to know deeply about all the complexity classes.

brirush 12y ago

I wrote the original question. I've always been interested in how much math various careers use, but I wrote this question the way I did in a shameless attempt to drive traffic to the site by appealing to the Stackoverflow and reddit communities. Everyone has given me a different answer so far, but that's to be expected, because there are ~1000 subcategories of computer programmers.

nmrm 12y ago
> I've always been interested in how much math various careers use > ... there are ~1000 subcategories of computer programmers. I'm curious: what about other careers? Are there fewer categories? Do they all do the same type of math? etc.

alok-g 12y ago

What would be a good writeup for understanding term-rewriting? (My current background level: I understand most of what OP has listed in "actually useful" and "can run into", and "automata theory" from the third list.)

j2kun 12y ago
I wouldn't recommend it as being as important as the OP claims, but if you must: http://www21.in.tum.de/~nipkow/TRaAT/ http://www21.in.tum.de/~nipkow/TRaAT/
- alok-g 12y ago
  Thanks! Could you also recommend something on how symbolic computation works? I have used computer algebra systems like Mathematica for long; would like to understand how it works internally. I currently understand some basics like DPLL, semantic first-order unification, methods of solving specific equation systems like linear systems, numerical differential equations, etc. I am missing at least how the "top-level" of symbolic computation works. For example, from what I currently understand, first-order semantic unification can find "x = Cos[y]" from "Sin[x] = Sin[Cos[y]]", but cannot solve "Sin[x] = Cos[x]" for x, and cannot simplify "[(Sin[x])^2 + (Cos[x])^2] = 1" to True. I am hoping to find something simpler than reading through SymPy source code. :-)
  - nextos 12y ago
    Peter Norvig's PAIP book has a chapter devoted to Student, a computer algebra system. It's very didactic: http://norvig.com/paip/student.lisp http://norvig.com/paip/student.lisp

RogerL 12y ago

I went to an engineering University. Besides having a wide variety of math required (3 semesters of Calc, 1 semester of either stats or probability, 1 semester of either linear algebra or matrices), we also had to take 3 semesters of physics, and 2 of chemistry. Most of us (those not just looking for a piece of paper) went considerable deeper in at least one area. No, you don't need to understand organic chemistry to write a CRUD app. But, you don't need university to write a CRUD app. I think I received an excellent education that prepared me for about any job out there. And, I've done it. I've done cancer statistics for the NIH. I've worked in avionics and simulation. Well, blah blah, no one cares about my resume, I'll just say I couldn't have done any of it without the education I received. I haven't done financial quant stuff, as an example, but how could I without the math background? Or how could I program a controller in a factory without understanding PID (done that)? How can I get a piece of that neat drone project (done that)? Hey, that computer vision stuff looks interesting, all I need to know is ...derivatives, statistics (done that too). For most of us, university is the last and/or best chance to really understand how the world works. For that you need quite a bit of math and science. Another example. We have a voluntary Arduino robotics workshop going on at work, coupled with 3D printing. Naturally, people are excited, and have all kinds of ideas. But, how do you execute on that if you don't understand how to design an op amp circuit, or filter data with something more sophisticated than a moving average? Robotics spans a number of fields, and to actually produce something more than a gimmick requires a lot of knowledge. Knowledge that you can pretty easily pick up in University, but knowledge you mostly just long for as you have to rush home at 5:30 to pick up the kids and make dinner. I guess this is a cranky rant from an old guy. But I hear about University programs that are nothing more than Java voc ed systems and I despair. $100K in debt to learn something most anyone on here could just pick up on their own. You don't need university for that stuff.

klibertp 12y ago
> but how could I without the math background? You could have just learned it as you went. Done that.

deleted 12y ago

[deleted]