8 ms·

Mathematics I Use (2012)

248 points by pmarin 9y ago

deleted 9y ago
[deleted]
richardwhiuk 9y ago
[2012]
OskarS 9y ago
I feel like you have to know a little bit about a lot of things. Like, yeah, you have to have a basic understanding of SOME graph theory when programming computers, but you don't really need anything too advanced. Yes, I guess you need to understand SOME category theory to be able to use advanced typing systems effectively, but it's a very surface level understanding of a very deep field. Same thing with most of the other fields mentioned. One thing that wasn't mentioned: if you're doing any kind of graphics programming, you use a huge amount of basic linear algebra every day. Vectors, matrices, dot/cross products, affine transforms, spaces and subspaces, that kind of thing. If you're doing more advanced stuff, a working knowledge of how to solve large linear systems (i.e. things like Gauss-Seidel/Jacobi methods) and the physics of light transmission is also useful. If you're doing physics simulations, obviously you need a working familiarity with calculus. Again, though, all of these things are massively deep fields that people dedicate their lives to understanding, but as a programmer you just need to skim the surface, generally speaking.
- jcadam 9y ago
  I agree. Writing spacecraft simulation software you use a lot of 3D math as well: matrix math, euler angles, quaternions, etc (being thrown into writing a simulation model for an attitude determination and control system with no prior exposure to orbital mechanics was great fun). Didn't have to become an expert (we had PhDs on staff for that), but had to gain an understanding of the basic concepts in order to get the job done. I've also worked on some signal analysis stuff -- had to learn about FFTs and basic filtering (band-pass filters, etc.) -- it's all math. But had books and the internet to look up those algorithms. I have several books on my bookshelf for these things, including an old copy of "Numerical Recipes in C" :)
  - totallynotadev 9y ago
    If I may ask, how does one get "thrown into writing a simulation model for an attitude determination and control system with no prior exposure to orbital mechanics"? I always wanted to write software that deals in some way with spacecraft, but always thought one needs to have some physics degree for that.
    - jcadam 9y ago
      Right place, right time. My career path has been a little weird. I got into the aerospace industry because after leaving the Army in 2006, I had a 4-year old CS degree and no work experience - but I did have a clearance, so I was able to land an entry-level SW job with a small aerospace company working on 3D visualization stuff. After a couple of years with that employer, I was hired on with a huge aerospace company working on a large satellite program. As to the how, consider that if finding good software engineers is hard (debatable), finding them with clearances is even harder (definitely true). The interviews for defense and aerospace jobs are easy compared to your standard technical interview at Netflix, Google, et al. They really don't want to risk screening folks out for trifling things like "competence" when they have billets to fill (because they're selling man-hours of labor to the govt, even a mediocre engineer can be profitable). But you should also know, that while working on a large satellite program may sound cool, the maddeningly slow and byzantine bureaucratic development processes (I'm currently on a waterfall-driven project) inherit in such programs will suck every last ounce of joy out of your working life. So, there's that...
- ivanhoe 9y ago
  IMHO you need just enough to be comfortable using math as a tool applied to your particular every-day practical situations, but you don't need to go into the academical depths like e.g. a scientist would have to. And you also need to have at least some faint idea what are the available options, so that, if needed, you know what to google for.
- professor_plum 9y ago
  Yeah, I'll never tell someone not to learn something for the sheer enjoyment. But this article is downright pretentious. It gussies up a lot of simple day-to-day tasks with off-putting terms and would not be helpful to a beginner.
- chillee 9y ago
  I'm not sure that's true. I think it's pretty tough for somebody who doesn't understand a field to assert that understanding the field deeper is not necessary. You'll see many non-programmers assert that it's not necessary to get trained programmers to do a certain task (say, automation). However, they don't understand all the software engineering considerations and issues that you'll run into if you don't have a programming background. It's only when you truly understand a field that you can see when that field is applicable to the task at hand.
  - mrybczyn 9y ago
    When you say "field", do you mean algebraic field, or professional "field".
    - tomsmeding 9y ago
      I suppose "professional field" here, even though the other interpretation seems more fun.
- hinkley 9y ago
  And yet I’m constantly surprised by people knowing nothing of set theory. Occasionally someone who doesn’t know logic (evidenced by nasty, over-complicated Boolean logic) Or my current favorite: a very senior and very optimistic person who apparently doesn’t believe in decidability, the halting problem, or NP completeness.
  - andrewflnr 9y ago
    Like, they think computers are just invincible problem solvers, or can't even really comprehend the question? I can't grok what it means to not believe in NP completeness.
    - hinkley 9y ago
      That developers can do anything if we stop complaining and get to work. No, in fact we've proven there are a lot of things we can't do, and oceans of things that are theoretically possible but completely impractical to do (another class of people mistake intractable for impossible, but for small enough N sometimes it is both possible and worthwhile).
  - wolfgke 9y ago
    > Or my current favorite: a very senior and very optimistic person who apparently doesn’t believe in decidability, the halting problem, or NP completeness. Undecidability and the halting problem is usually analysed for Turing machines (I am aware that there also exists literature on these problems for other types of automata). The problem is: It is impossible to build a Turing machine. Every computer that has been built up to know is just some kind of finite state machine. So the halting problem is perfectly (in a mathematical sense) deciable for real computer programs. The problem is: We have no idea how to do this in general in a timespan that is suitable for practical purposes.
- Tobba_ 9y ago
  The secret to linear algebra is homogenous coordinates together the exterior algebra. plus matrices sprinkled in. If you use those for everything all your problems simply disappear.
jfv 9y ago
I think if you're a programmer wondering what math will help you in your career, which is the question this article is trying to answer, this article is misleading. Most working programmers won't have to know any math beyond arithmetic. For instance, "Also, how does one distribute a large computation across globally distributed data centers? You have to understand some physics to do this well: at Internet scale, the speed of light starts to be a bottleneck. Heat dissipation, density of electrical current draw per unit area, etc, are all real world considerations that go into what programmers do" Come on, let's be real. In grade school we learned that light goes around the earth 8 times a second. That means 1/16 of a second (63ms) to go around to the other side of the world. That doesn't set a useful lower bound since this is the ballpark of latency within a country anyway. You're just going to ping between the two servers and measure the latency. That being said, programming could in theory require any kind of math. If you're doing machine learning, you'll need to understand statistics. If you're doing graphics programming, you'll need to understand trigonometry, linear algebra, etc. If you're writing software for the medical industry you'll presumably have to understand a little bit about how that industry works, but I wouldn't suggest programmers go learn that just for the sake of improving their "general" programming skills. Here's a more realistic take: 1) Learn math as necessary for a field you're interested in 2) Know binary and hexadecimal representations of numbers. 3) If you're going to use a lower-level language, understand how signed/unsigned arithmetic works, boolean algebra, and some basics of the floating point representation (in a nutshell, don't assume that computations are exact, so don't rely on equality (==)). 4) Understand time and space complexity. For most programmers, this is going to be simple: don't nest too many for-loops. I'm guessing 90% of programmers will never have to construct an algorithm whose complexity involves a logarithmic function, except for maybe binary search. Even then, most programmers will rely on libraries to do those things. 5) Be able to do back of the envelope calculations, and understand that order of magnitude is more important than exact numbers. Try to do them in your head so you can quickly evaluate possibilities. 6) Increasingly, statistics and machine learning are becoming important for programmers to know. Learn some basic statistics and it will make you much more desirable. Play around with R or Octave or numpy and don't make the mistake of applying too much statistics without thinking, unless you're in the marketing department.
- jerf 9y ago
norrius 9y ago
For whatever reason, the link does not work for me. Google's cache doesn't seem to provide a copy, so here's one from the Wayback Machine: https://web.archive.org/web/20180420113021/http://pub.gajendra.net/2012/10/mathematics_i_use https://web.archive.org/web/20180420113021/http://pub.gajend... To the topic, I think this quote from the article is very important to note here: “Of course, I do not do all of this every day, but I have done all of it at one time or another and most of it regularly.” It is nice to have an idea of how you write a parser for a language, but I do not believe the author advocates for being able to write one of the top of your head. Same with most other points.
- deleted 9y ago
  [deleted]
thanatropism 9y ago
This is a very well written post, in the sense that much of what he mentions is central to programming. But there's also a Zadeh's principle to mathematics -- when you have measure theory suddenly everything is a change of measure. And I mean, this is great. "Diversity in tech" should be more like "people who are into analysis, topology" versus "people who are into algebra and cat theory" etc. There are many different ways to skin problem spaces into mental models and coding styles.
maroonblazer 9y ago
As someone who has spent most of his adult life recovering from a math phobia (due largely to poor teachers in middle and high school) and enjoys programming as a hobby, had I read this article when I was exploring whether or not I had the aptitude/background for programming this would have turned me off entirely. I agree with the others that this article seems to overstate the requirements.
- norealidea 9y ago
  So, are you still afraid of math?
  - maroonblazer 9y ago
    No. Post-college, I didn't need it for my job and I discovered programming - at least at the level that I was enjoying it - was as much, if not more, about logic and breaking problems into pieces. Despite that my lack of math ability felt increasingly like an albatross around my neck. In the same way that one might feel they're missing out by not studying history. It was only after coming across a quote from Charles Darwin where he mentioned that one of his regrets was that he didn't study math more thoroughly. And that because of that there were entire "conversations" he was missing out on. For some reason I found that both liberating and motivating. "Me and Charles Darwin, we're not so different you and I." ;-)
kriro 9y ago
I you find yourself wondering how math heavy programming is before diving in...just start programming and ignore the math. You'll get by just fine. There's libraries for everything. Yes int theory you need to know some math to know when to use what but we live in an age where you can search for things like "I want to do X, tell me how" for most programming problems and get a reasonable high level "practical" answer of use library/function X and btw. here's the docs. That being said (basic) logic, applied probability theory (no and some vector and matrix stuff are probably the most useful (for ML/DL). The more into algorithms you get, the more mathy it gets. Most programmers do this rarely in their day to day life unless they are rather specialized. tl;dr: Don't worry about math, start writing code right now. It's fun. The rest will come once you get interested in certain things.
motohagiography 9y ago
I would say almost half the performance problems I have seen developers and devops managers run into over the last 5-6 years could have been avoided with a bit of front loaded queueing theory. When you are doing microservice orchestrations, using an enterprise service bus or a pubsub, or doing multiple asynchronous operations, small delays multiply through the system. Spending a day to model your solution as a queue will give you some ballpark tolerances for lag, queue size, and in particular, RTT through the service. Doing microservice architectures takes a lot of the logic of the problems solved decades ago on the network layer and reinstantiates them at application service layers without those solutions. Request TTL, state, queue flushing, retransmission, shortest path, service availability, 'ping', 'traceroute', etc. If one service crashes, and requests start piling up, you need to clear that queue, and oftentimes your solution isn't built to clear that queue while more requests are coming in and your cache overflows because "keeping state is a next order complexity problem that wasn't specified in the user story." There is an assumption you can just horizontally scale your way out, which has significant compute and administrative costs. I suspect AWS makes a lot of its money as a direct result of those assumptions. Not saying someone needs to be doing new proofs, but some forethought using a handwavy abstraction might provide some insight into the needs of the system under load.
- hackermailman 9y ago
  There's a good book for this if anybody is interested http://www.cs.cmu.edu/~harchol/PerformanceModeling/book.html http://www.cs.cmu.edu/~harchol/PerformanceModeling/book.html
  - Jtsummers 9y ago
    If you have access to Safari Books Online, it may be in your collection there as well. http://techbus.safaribooksonline.com/book/electrical-engineering/computer-engineering/9781139610834 http://techbus.safaribooksonline.com/book/electrical-enginee...
  - mlboss 9y ago
    Cool reference. Lot of mathematical requirements are same as Probabilistic Machine Learning.
glancast 9y ago
You don't need much mathematical knowledge to _merely_ be productive, but his points are valid. 1) The more math I learn, the more I realize how much I'm already doing it (via poor heuristics) without realizing it. 2) Mathematical training comes with many tools I would never think to Google without prior introduction. For instance, I sometimes use Karnaugh maps to simplify complex boolean logic. I'm sure there are many areas where I re-invent the wheel, miss simpler solutions, and generally produce less quality because I'm ignorant of the surrounding mathematical context.
- Ari_Ugwu 9y ago
  This. I believe we are ripe for another leap in math education, or at least computer science education. A new approach to teaching that in a generation will make current methods looks like rhetorical algebra. I think this is a great example: https://github.com/Jam3/math-as-code https://github.com/Jam3/math-as-code That page is a sort of rosetta stone for me after years of learning to code while also struggling with math notation. I find a similar fog lifts when I look at set theory through the lens of SQL and relation databases. It amazes me that we still can't clearly demonstrate to children why math is important and instantly and universally instill a love and curiosity. Instead we have unforgiving educational models that are "well, you either get it or you don't." It angers me to think of all the potentially _effective_ programmers who get their dreams squashed because they can't pass Calculus II (or other prereq.), and thus are literally not allowed to enroll in a programming course. I didn't know about Karnaugh Maps but I use truth tables constantly in the design phase of tasks. Thank you very much for this. If you've found other tools like this please share. Not really related but for requirements I find gap and SWOT analysis to be vital tools as well as weighted pairwise comparisons. Throw in some UML diagrams and I start feeling good about things. These things impress far more people than they should. </rant>
mooneater 9y ago
A good programmer may use many of these types of math without even knowing the formal names. Sometimes knowing the formalism helps a lot, sometimes it doesn't add much. Some people overly obsess with formalisms and some people are overly adverse to them. I do find people who need to over-formalize everything to be annoyingly pedantic.
vignesh_m 9y ago
I'm very skeptical about the applicability of group theory to computer science - outside of the usual applications to counting/combinatorics and crypto/number theory.

248 points by pmarin 9y ago

deleted 9y ago

[deleted]

richardwhiuk 9y ago

[2012]

OskarS 9y ago

I feel like you have to know a little bit about a lot of things. Like, yeah, you have to have a basic understanding of SOME graph theory when programming computers, but you don't really need anything too advanced. Yes, I guess you need to understand SOME category theory to be able to use advanced typing systems effectively, but it's a very surface level understanding of a very deep field. Same thing with most of the other fields mentioned. One thing that wasn't mentioned: if you're doing any kind of graphics programming, you use a huge amount of basic linear algebra every day. Vectors, matrices, dot/cross products, affine transforms, spaces and subspaces, that kind of thing. If you're doing more advanced stuff, a working knowledge of how to solve large linear systems (i.e. things like Gauss-Seidel/Jacobi methods) and the physics of light transmission is also useful. If you're doing physics simulations, obviously you need a working familiarity with calculus. Again, though, all of these things are massively deep fields that people dedicate their lives to understanding, but as a programmer you just need to skim the surface, generally speaking.

jcadam 9y ago
I agree. Writing spacecraft simulation software you use a lot of 3D math as well: matrix math, euler angles, quaternions, etc (being thrown into writing a simulation model for an attitude determination and control system with no prior exposure to orbital mechanics was great fun). Didn't have to become an expert (we had PhDs on staff for that), but had to gain an understanding of the basic concepts in order to get the job done. I've also worked on some signal analysis stuff -- had to learn about FFTs and basic filtering (band-pass filters, etc.) -- it's all math. But had books and the internet to look up those algorithms. I have several books on my bookshelf for these things, including an old copy of "Numerical Recipes in C" :)
- totallynotadev 9y ago
  If I may ask, how does one get "thrown into writing a simulation model for an attitude determination and control system with no prior exposure to orbital mechanics"? I always wanted to write software that deals in some way with spacecraft, but always thought one needs to have some physics degree for that.
  - jcadam 9y ago
    Right place, right time. My career path has been a little weird. I got into the aerospace industry because after leaving the Army in 2006, I had a 4-year old CS degree and no work experience - but I did have a clearance, so I was able to land an entry-level SW job with a small aerospace company working on 3D visualization stuff. After a couple of years with that employer, I was hired on with a huge aerospace company working on a large satellite program. As to the how, consider that if finding good software engineers is hard (debatable), finding them with clearances is even harder (definitely true). The interviews for defense and aerospace jobs are easy compared to your standard technical interview at Netflix, Google, et al. They really don't want to risk screening folks out for trifling things like "competence" when they have billets to fill (because they're selling man-hours of labor to the govt, even a mediocre engineer can be profitable). But you should also know, that while working on a large satellite program may sound cool, the maddeningly slow and byzantine bureaucratic development processes (I'm currently on a waterfall-driven project) inherit in such programs will suck every last ounce of joy out of your working life. So, there's that...
ivanhoe 9y ago
IMHO you need just enough to be comfortable using math as a tool applied to your particular every-day practical situations, but you don't need to go into the academical depths like e.g. a scientist would have to. And you also need to have at least some faint idea what are the available options, so that, if needed, you know what to google for.
professor_plum 9y ago
Yeah, I'll never tell someone not to learn something for the sheer enjoyment. But this article is downright pretentious. It gussies up a lot of simple day-to-day tasks with off-putting terms and would not be helpful to a beginner.
chillee 9y ago
I'm not sure that's true. I think it's pretty tough for somebody who doesn't understand a field to assert that understanding the field deeper is not necessary. You'll see many non-programmers assert that it's not necessary to get trained programmers to do a certain task (say, automation). However, they don't understand all the software engineering considerations and issues that you'll run into if you don't have a programming background. It's only when you truly understand a field that you can see when that field is applicable to the task at hand.
- mrybczyn 9y ago
  When you say "field", do you mean algebraic field, or professional "field".
  - tomsmeding 9y ago
    I suppose "professional field" here, even though the other interpretation seems more fun.
hinkley 9y ago
And yet I’m constantly surprised by people knowing nothing of set theory. Occasionally someone who doesn’t know logic (evidenced by nasty, over-complicated Boolean logic) Or my current favorite: a very senior and very optimistic person who apparently doesn’t believe in decidability, the halting problem, or NP completeness.
- andrewflnr 9y ago
  Like, they think computers are just invincible problem solvers, or can't even really comprehend the question? I can't grok what it means to not believe in NP completeness.
  - hinkley 9y ago
    That developers can do anything if we stop complaining and get to work. No, in fact we've proven there are a lot of things we can't do, and oceans of things that are theoretically possible but completely impractical to do (another class of people mistake intractable for impossible, but for small enough N sometimes it is both possible and worthwhile).
- wolfgke 9y ago
  > Or my current favorite: a very senior and very optimistic person who apparently doesn’t believe in decidability, the halting problem, or NP completeness. Undecidability and the halting problem is usually analysed for Turing machines (I am aware that there also exists literature on these problems for other types of automata). The problem is: It is impossible to build a Turing machine. Every computer that has been built up to know is just some kind of finite state machine. So the halting problem is perfectly (in a mathematical sense) deciable for real computer programs. The problem is: We have no idea how to do this in general in a timespan that is suitable for practical purposes.
Tobba_ 9y ago
The secret to linear algebra is homogenous coordinates together the exterior algebra. plus matrices sprinkled in. If you use those for everything all your problems simply disappear.

jfv 9y ago

I think if you're a programmer wondering what math will help you in your career, which is the question this article is trying to answer, this article is misleading. Most working programmers won't have to know any math beyond arithmetic. For instance, "Also, how does one distribute a large computation across globally distributed data centers? You have to understand some physics to do this well: at Internet scale, the speed of light starts to be a bottleneck. Heat dissipation, density of electrical current draw per unit area, etc, are all real world considerations that go into what programmers do" Come on, let's be real. In grade school we learned that light goes around the earth 8 times a second. That means 1/16 of a second (63ms) to go around to the other side of the world. That doesn't set a useful lower bound since this is the ballpark of latency within a country anyway. You're just going to ping between the two servers and measure the latency. That being said, programming could in theory require any kind of math. If you're doing machine learning, you'll need to understand statistics. If you're doing graphics programming, you'll need to understand trigonometry, linear algebra, etc. If you're writing software for the medical industry you'll presumably have to understand a little bit about how that industry works, but I wouldn't suggest programmers go learn that just for the sake of improving their "general" programming skills. Here's a more realistic take: 1) Learn math as necessary for a field you're interested in 2) Know binary and hexadecimal representations of numbers. 3) If you're going to use a lower-level language, understand how signed/unsigned arithmetic works, boolean algebra, and some basics of the floating point representation (in a nutshell, don't assume that computations are exact, so don't rely on equality (==)). 4) Understand time and space complexity. For most programmers, this is going to be simple: don't nest too many for-loops. I'm guessing 90% of programmers will never have to construct an algorithm whose complexity involves a logarithmic function, except for maybe binary search. Even then, most programmers will rely on libraries to do those things. 5) Be able to do back of the envelope calculations, and understand that order of magnitude is more important than exact numbers. Try to do them in your head so you can quickly evaluate possibilities. 6) Increasingly, statistics and machine learning are becoming important for programmers to know. Learn some basic statistics and it will make you much more desirable. Play around with R or Octave or numpy and don't make the mistake of applying too much statistics without thinking, unless you're in the marketing department.

jerf 9y ago

norrius 9y ago

For whatever reason, the link does not work for me. Google's cache doesn't seem to provide a copy, so here's one from the Wayback Machine: https://web.archive.org/web/20180420113021/http://pub.gajendra.net/2012/10/mathematics_i_use https://web.archive.org/web/20180420113021/http://pub.gajend... To the topic, I think this quote from the article is very important to note here: “Of course, I do not do all of this every day, but I have done all of it at one time or another and most of it regularly.” It is nice to have an idea of how you write a parser for a language, but I do not believe the author advocates for being able to write one of the top of your head. Same with most other points.

deleted 9y ago
[deleted]

thanatropism 9y ago

This is a very well written post, in the sense that much of what he mentions is central to programming. But there's also a Zadeh's principle to mathematics -- when you have measure theory suddenly everything is a change of measure. And I mean, this is great. "Diversity in tech" should be more like "people who are into analysis, topology" versus "people who are into algebra and cat theory" etc. There are many different ways to skin problem spaces into mental models and coding styles.

maroonblazer 9y ago

As someone who has spent most of his adult life recovering from a math phobia (due largely to poor teachers in middle and high school) and enjoys programming as a hobby, had I read this article when I was exploring whether or not I had the aptitude/background for programming this would have turned me off entirely. I agree with the others that this article seems to overstate the requirements.

norealidea 9y ago
So, are you still afraid of math?
- maroonblazer 9y ago
  No. Post-college, I didn't need it for my job and I discovered programming - at least at the level that I was enjoying it - was as much, if not more, about logic and breaking problems into pieces. Despite that my lack of math ability felt increasingly like an albatross around my neck. In the same way that one might feel they're missing out by not studying history. It was only after coming across a quote from Charles Darwin where he mentioned that one of his regrets was that he didn't study math more thoroughly. And that because of that there were entire "conversations" he was missing out on. For some reason I found that both liberating and motivating. "Me and Charles Darwin, we're not so different you and I." ;-)

kriro 9y ago

I you find yourself wondering how math heavy programming is before diving in...just start programming and ignore the math. You'll get by just fine. There's libraries for everything. Yes int theory you need to know some math to know when to use what but we live in an age where you can search for things like "I want to do X, tell me how" for most programming problems and get a reasonable high level "practical" answer of use library/function X and btw. here's the docs. That being said (basic) logic, applied probability theory (no and some vector and matrix stuff are probably the most useful (for ML/DL). The more into algorithms you get, the more mathy it gets. Most programmers do this rarely in their day to day life unless they are rather specialized. tl;dr: Don't worry about math, start writing code right now. It's fun. The rest will come once you get interested in certain things.

motohagiography 9y ago

I would say almost half the performance problems I have seen developers and devops managers run into over the last 5-6 years could have been avoided with a bit of front loaded queueing theory. When you are doing microservice orchestrations, using an enterprise service bus or a pubsub, or doing multiple asynchronous operations, small delays multiply through the system. Spending a day to model your solution as a queue will give you some ballpark tolerances for lag, queue size, and in particular, RTT through the service. Doing microservice architectures takes a lot of the logic of the problems solved decades ago on the network layer and reinstantiates them at application service layers without those solutions. Request TTL, state, queue flushing, retransmission, shortest path, service availability, 'ping', 'traceroute', etc. If one service crashes, and requests start piling up, you need to clear that queue, and oftentimes your solution isn't built to clear that queue while more requests are coming in and your cache overflows because "keeping state is a next order complexity problem that wasn't specified in the user story." There is an assumption you can just horizontally scale your way out, which has significant compute and administrative costs. I suspect AWS makes a lot of its money as a direct result of those assumptions. Not saying someone needs to be doing new proofs, but some forethought using a handwavy abstraction might provide some insight into the needs of the system under load.

hackermailman 9y ago
There's a good book for this if anybody is interested http://www.cs.cmu.edu/~harchol/PerformanceModeling/book.html http://www.cs.cmu.edu/~harchol/PerformanceModeling/book.html
- Jtsummers 9y ago
  If you have access to Safari Books Online, it may be in your collection there as well. http://techbus.safaribooksonline.com/book/electrical-engineering/computer-engineering/9781139610834 http://techbus.safaribooksonline.com/book/electrical-enginee...
- mlboss 9y ago
  Cool reference. Lot of mathematical requirements are same as Probabilistic Machine Learning.

glancast 9y ago

You don't need much mathematical knowledge to _merely_ be productive, but his points are valid. 1) The more math I learn, the more I realize how much I'm already doing it (via poor heuristics) without realizing it. 2) Mathematical training comes with many tools I would never think to Google without prior introduction. For instance, I sometimes use Karnaugh maps to simplify complex boolean logic. I'm sure there are many areas where I re-invent the wheel, miss simpler solutions, and generally produce less quality because I'm ignorant of the surrounding mathematical context.

Ari_Ugwu 9y ago
This. I believe we are ripe for another leap in math education, or at least computer science education. A new approach to teaching that in a generation will make current methods looks like rhetorical algebra. I think this is a great example: https://github.com/Jam3/math-as-code https://github.com/Jam3/math-as-code That page is a sort of rosetta stone for me after years of learning to code while also struggling with math notation. I find a similar fog lifts when I look at set theory through the lens of SQL and relation databases. It amazes me that we still can't clearly demonstrate to children why math is important and instantly and universally instill a love and curiosity. Instead we have unforgiving educational models that are "well, you either get it or you don't." It angers me to think of all the potentially _effective_ programmers who get their dreams squashed because they can't pass Calculus II (or other prereq.), and thus are literally not allowed to enroll in a programming course. I didn't know about Karnaugh Maps but I use truth tables constantly in the design phase of tasks. Thank you very much for this. If you've found other tools like this please share. Not really related but for requirements I find gap and SWOT analysis to be vital tools as well as weighted pairwise comparisons. Throw in some UML diagrams and I start feeling good about things. These things impress far more people than they should. </rant>

mooneater 9y ago

A good programmer may use many of these types of math without even knowing the formal names. Sometimes knowing the formalism helps a lot, sometimes it doesn't add much. Some people overly obsess with formalisms and some people are overly adverse to them. I do find people who need to over-formalize everything to be annoyingly pedantic.

vignesh_m 9y ago

I'm very skeptical about the applicability of group theory to computer science - outside of the usual applications to counting/combinatorics and crypto/number theory.