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Ask HN: Math for hackers.

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Re: Ask HN: Math for hackers.

#41

Post by hs »

hernan7 wrote: post #35

I'm one of those programmers returning to study math after all these years. (Mostly so I can write some DSP code for my own amusement.) Currently reading a bit about complex numbers, planning on re-learning some trig next. Statistics is in my to-do list too. Kind of unavoidable if you want to work on machine learning.

complex math is beautiful and it does relate to trig nicely (sum of exponentials)

but i'm not sure if complex is useful in stats. in all my stats courses i didn't see any complex, maybe simply because all observations are of real number (height, age, stock price, etc)

oh wait, maybe in the stochastic (cyclostationary process, etc) ... my memory betrays me. oh well, dsp is fun ;)

Re: Ask HN: Math for hackers.

#42

Post by ErrantX »

philfreo wrote: post #29
bonsaitree wrote: post #18

I'd recommend using this book as a rough guide: http://tinyurl.com/nfe3gv Don't let the title fool you. It's really a guide to advanced applied mathematics. I'd also suggest the material be supplimented with a good bit of statistics. In my experience, statistical reasoning (particularly as it applies to noise, perturbation, and system reliability) tends to be weakness with hackers.

using tinyurl to hide your amazon referral url... nice

none ref link for those inclined to make a purchase

http://www.amazon.com/Road-Reality-Complete-Guide-Universe/d...

Re: Ask HN: Math for hackers.

#43

Post by tlrobinson »

Beanblabber wrote: post #4

This would be absolutely awesome. I'm 14 and going into 9th grade. I'm taking algebra 2 / trig next year but I hate how they teach it so I use the internet to teach me. This would be a really cool idea, I'd definitely use it.

Read this: http://www.maa.org/devlin/LockhartsLament.pdf

Now.

Re: Ask HN: Math for hackers.

#44

Post by jerf »

scott_s wrote: post #38
jerf wrote: post #34

Earlier quoted context omitted.

I think you may forget what is taught as "trig" in school. Yes, knowing what sin, cos, and tan are is important. No, wasting weeks on pointless identities and digging into the minutia of lines and triangles well beyond what you will ever need, even in the course of getting a degree in mathematics , is not a sensible use of time. The only reason it is done is "that is how things are done". When people argue about the…

I used a lot of trig in my physics classes - yes, including identities. You may be falling into the trap that because it wasn't useful to you, then it's useful to no one.

And you may be falling into the trap that because it's useful to you, it's useful to lots of people. Again, it's not about "is it valuable", it's about opportunity costs! While you're fiddling with trig you're not learning other more useful things.

Let it be learned when it's actually useful. If you use it in physics, fine, learn it there, when you have context. Not in some abstracted "trig" course.

To be honest, I'm not sure I believe you anyhow. I took a lot of physics, as much as anyone not majoring in it will take, and I did not make heavy use of trig identities, nor did anybody else, nor do I recall a huge number of problems where they would have come in useful, and what problems they might have been useful in were textbook problems anyhow. (In the real world, inclined planes are not all at 30 and 45 degrees.) I think you might just be saying that to score rhetorical points.

Re: Ask HN: Math for hackers.

#45

Post by kqr2 »

smanek wrote: post #5

As a really high level overview of math, I like The Princeton Companion to Mathematics (or the ~1/4 I've made my way through so far). It's a bit too abstract though - it covers an immense amount of material so they have to be - but I still feel like something is missing. My 'overview of math' is probably The Road to Reality (which is ostensibly about Physics, but really spends just as much time talking about math) -…

I'm working my way through the Princeton Companion to Mathematics too.

I like it because each topic is written in small digestable chunks by different authors. The change in writing style and view points keeps it refreshing.

Although it's a bit high level, it gives you a taste for a lot of different areas in mathematics -- kind of a mathematical buffet.

Re: Ask HN: Math for hackers.

#46

Post by yummyfajitas »

jerf wrote: post #34
yummyfajitas wrote: post #25

Earlier quoted context omitted.

I disagree with you on trig. Trig is the study of straight lines and what you can do with them. The important part of calculus is the fact that you can approximate curves by straight lines [1]. A folk theorem in applied math is that 90% of the time, an approximation by straight lines is good enough (another 9% of the time, you'll need a parabola). You can drop some of the petty stuff (x,y,(180-x-y) triangles), but do…

I think you may forget what is taught as "trig" in school. Yes, knowing what sin, cos, and tan are is important. No, wasting weeks on pointless identities and digging into the minutia of lines and triangles well beyond what you will ever need, even in the course of getting a degree in mathematics , is not a sensible use of time. The only reason it is done is "that is how things are done". When people argue about the…

I freely admit I have no idea what goes into a trig class. I dropped out before trig was taught.

You are probably right: when I teach calculus, there does seem to be an assumption that students know way too much petty nonsense. But some basics are necessary, even if the computer knows how to compute sin and cos. Students must understand angles and straight lines.

As for tradeoffs, I completely agree. I just think the value of basic trig is ridiculously high.

Re: Ask HN: Math for hackers.

#47

Post by scott_s »

jerf wrote: post #44
scott_s wrote: post #38

Earlier quoted context omitted.

I used a lot of trig in my physics classes - yes, including identities. You may be falling into the trap that because it wasn't useful to you, then it's useful to no one.

And you may be falling into the trap that because it's useful to you, it's useful to lots of people. Again, it's not about "is it valuable", it's about opportunity costs ! While you're fiddling with trig you're not learning other more useful things. Let it be learned when it's actually useful . If you use it in physics, fine, learn it there, when you have context. Not in some abstracted "trig" course. To be honest, I…

But what are the more useful things? That depends heavily on what, exactly, you go into. For many people, most of the math they took is never used. But that's not known at the high school level, so a high school education tries to serve as a foundation for further learning. You're assuming discrete math would be more useful to more students than trig. I doubt this is true.

If I had to learn trig my freshmen and sophomore year of college, when I was taking my introductory physics classes, I never would have kept up with the physics. My course assumed a solid foundation in trig and calculus.

I distinctly remember having to use various properties of triangles to solve many of my introductory mechanics problems.

Re: Ask HN: Math for hackers.

#48

Post by SapphireSun »

seanc wrote: post #21
mtomczak wrote: post #17

Earlier quoted context omitted.

Here is the thing I wish someone had told me my freshman year of high school. If you're interested in computer science, study topics in discrete mathematics, real algebra (the algebra where you compute with symbols instead of numbers, look into "rings", "groups", and "fields"), and some statistics. And if you have to scale back on something to make room, scale back on trigonometry. Discrete is a subset of math that w…

Aw, but triangles and circles are such a huge part of everyday life, one should understand them well for that reason alone. From as practical as hammering wood together to as abstract as noticing the sine curves of the seasons. And without Pythagorous, you can't grok Euler's Identity, which would be a real shame. Finally, trig is the gateway to Euclidian Geometry, which is the first taste of realish math most people…

Don't forget that trig pops up everywhere in more advanced math as well. Fourier/Laplace transforms anyone?

Re: Ask HN: Math for hackers.

#49

Post by RiderOfGiraffes »

jodrellblank wrote: post #39

It will also be on a wiki-like system so you can contribute later if you want, although not at first while I get it running. Don't. There is already Wikipedia and Wolfram Mathworld. I have no interest in another system where math geeks compete to put the biggest knowledge dumps and most obscure references into a great big technopeacock tail. You know all that stuff about usability and simplification that Apple/Micros…

The intention is explicitly to provide a commentry, overview and connections between topics. It would not be good use of anyone's time to duplicate a lot of work that's already out there.

Specifically, I'll be looking to create skims of topics with insight, then point to deeper treatments elsewhere, then provide some examples for people to get their teeth into to confirm their understanding. It's the links, and the dependencies, that I'll be covering.

Thanks for this comment - it's resonated with my thoughts. Being wiki-like, though, I think can be made to work. There will be controls.

Work to be done on that aspect, which is why it won't simply be a wiki from the start.

Re: Ask HN: Math for hackers.

#50

Post by menloparkbum »

mtomczak wrote: post #17
Beanblabber wrote: post #4

This would be absolutely awesome. I'm 14 and going into 9th grade. I'm taking algebra 2 / trig next year but I hate how they teach it so I use the internet to teach me. This would be a really cool idea, I'd definitely use it.

Here is the thing I wish someone had told me my freshman year of high school. If you're interested in computer science, study topics in discrete mathematics, real algebra (the algebra where you compute with symbols instead of numbers, look into "rings", "groups", and "fields"), and some statistics. And if you have to scale back on something to make room, scale back on trigonometry. Discrete is a subset of math that w…

Trig class in grade school (or high school) sucks, in a major way.

However, I worked as a math tutor for 4 years in college. I tutored both college students and in an after school program for east african immigrants.

What I observed in that experience was that people with good trig backgrounds did very well with the mechanical formula manipulation stuff in Calc. They were mostly having issues with proof structure, etc.

The students who had a sketchy trig background had problems with proof structure and also had a lot of issues simply doing mechanical symbol manipulation problems.

I majored in math and focused on abstract algebra. I don't think rings, groups and fields are very useful to general programming or even computer science. I actually have the exact opposite opinion on the matter. Unless you're going into crypto algorithm research you don't need to know that stuff, you just use a pre-existing library. On the other hand, trig establishes a foundation for stuff like robotics, DSP, computer graphics, computational physics and so forth. Almost anything falling into the traditional "applied math" bin requires you to have gotten trig down cold at some point.

However, arguing this is sort of a moot point because I can't think of any elementary or secondary school math sequence where you just skip over trig and take group theory instead. Trig is usually required somewhere along the way and abstract algebra is usually not available in high school unless you're going to a specialized math and science school. Indeed, it's usually not even available in college unless you're a math major.

If you have a sketchy trig background and need more practice and inspiration, I recommend:

Trigonometric Delights by Eli Maor, for inspiration.

Trigonometry Refresher by A. Albert Klaf for practice problems

Advanced Trigonometry by C.V. Durell and A.Robson for examples of advanced applications

Statistics is very important and totally overlooked by most hackers and even math majors (including myself.) If you have the opportunity to take a good stats class in high school or university, do so. I do not have any good recommendations on self study, but it seems like books on things like Biostatistics often lay the basics out more clearly than general stats textbooks.

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