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Ask HN: Math for hackers.

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Re: Ask HN: Math for hackers.

#21

Post by seanc »

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…

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 get in High School...

Re: Ask HN: Math for hackers.

#23

Post by dfj225 »

nihilocrat wrote: post #8

During college, I must admit that I would kind of space out whenever math discussion entered a CS class, and would regain my attention once the professor said "and here's how that looks in code" because I would end up thinking of the math the same way I thought of code anyways. It would be neat if you expressed some of the concepts in source code examples in some sufficiently high-level and clean-syntax language of y…

I think the math/cs book by Aho and Ullman does a good job of introducing basic math concepts backed up with plenty of code and examples. Plus: it is available online for free.

http://infolab.stanford.edu/~ullman/focs.html

Re: Ask HN: Math for hackers.

#24

Post by wfarr »

4180122 wrote: post #10

Basic linear algebra is extremely important in conjuncture with rudimentary matrix manipulation. I am always astounded by the number of college graduates who can't perform simple matrix multiplications, cross-products, dot-products, L-U factorization, etc without references. Without these basics, it becomes increasing difficult to grasp more advanced subjects such as (non)linear optimization, calculating computation…

Additionally, touch on a few other really useful methods for approximating solutions and decompositions, namely: partial pivoting, Householder reflections, Givens rotations, and of course, the Power Method.

Additionally, SVD.

We covered these pretty thoroughly in the Calculus 3 for Computer Science class here at Georgia Tech, and they're relatively easy to learn and are fairly useful.

Re: Ask HN: Math for hackers.

#25

Post by yummyfajitas »

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…

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 don't skip the basics.

I'd also suggest skipping rings/fields since most of the algebra important to CS involves structures weaker than groups (semigroups and monoids). Also add graphs/combinatorics to your list.

[1] This fundamental fact is briefly mentioned in a subsection called "differentials", and otherwise ignored by textbooks.

Re: Ask HN: Math for hackers.

#26

Post by jimbokun »

4180122 wrote: post #10

Basic linear algebra is extremely important in conjuncture with rudimentary matrix manipulation. I am always astounded by the number of college graduates who can't perform simple matrix multiplications, cross-products, dot-products, L-U factorization, etc without references. Without these basics, it becomes increasing difficult to grasp more advanced subjects such as (non)linear optimization, calculating computation…

Never having taken a Linear Algebra course, this is the math I've been working the hardest at learning, and absolutely agree it is indispensable for understanding many things (in my case, machine learning). Anything that makes this easier to learn or remember I welcome with open arms.

Re: Ask HN: Math for hackers.

#27

Post by tokenadult »

Oddly enough, I will start with "Adding Fractions" and basic algebra (expanding, factoring and simplifying)

It's not odd at all to start with adding fractions. I've seen multiple questions on Usenet over the years from programmers about how to write a generalized routine for adding fractions. Many people don't learn the simple algorithm for that

http://math.berkeley.edu/~wu/fractions2.pdf

http://math.berkeley.edu/~wu/AE3.pdf

http://math.berkeley.edu/~wu/EMI2a.pdf

and it is good to look at the common site of all the links I've just posted for more links with tips on teaching the most fundamental math concepts.

Re: Ask HN: Math for hackers.

#29

Post by philfreo »

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

Re: Ask HN: Math for hackers.

#30

Post by profquail »

Instead of starting your own, why not contribute to Wikibooks? It's already an established site with a fair number of users, but there are several sections (especially technical areas) that are incomplete or haven't been updated in years. Plus, everyone else would be able to start contributing NOW.

http://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf

http://en.wikibooks.org/wiki/Wikibooks:Computer_science_book...

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