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But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geome

But statistics and probability is really just integration. It's either that or stamp collection. And optimization is really just differentiation (+ some geometry). I'd say the problem is too little calculus and not too much.

tel 12y ago
Don't know why you're being downvoted. This is totally true.
- peterfirefly 12y ago
  Most of my downvotes so far, both here and on reddit, have been earned by writing things that are true but unpopular. The weird thing is that I can't predict which things are going to be sufficiently unpopular amongst people impolite enough to downvote instead of coming up with a good counterargument (or even better: fact). I had /never/ expected something like this to get a single downvote (and I was down at -3).
profinger 12y ago
I agree as well. Not sure why you're being downvoted. Maybe I don't know enough about linear algebra to judge but everything ML that I've ever worked in was spoken in calculus..
Dudelander 12y ago
Totally agree, calculus is a prerequisite for understanding statistics, unless you're just plugging in numbers for an A-B test - and you don't really need a class to do that. Linear Algebra is very useful too, but it's not really fair to say one is more valuable than another. It just depends on what kinds of applications you end up working on. Universities should just teach both.
- peterfirefly 12y ago
  Many interesting things require a combination of more than one area of math. I don't understand how you can do much within robotics or vision without using all three of calculus, linear algebra, and statistics :)
  - varelse 12y ago
    I'll go even further and state that without an understanding of calculus, linear algebra, and statistics, an engineer or even a data scientist is little more than a glorified script kiddy.
romaniv 12y ago
Statistic teaches you application and helps to develop correct intuition. Can's speak for everyone, but my college algebra courses were 100% abstract stuff detached from reality. All professors had the attitude that once you learn the theory you could apply it to anything. Problem is, it's hard to remember theory if you don't map to something tangible, and it's hard to apply it to reality when you're just used to crunching equations.
- tel 12y ago
  Statistics is, classically, more developed in the realm of "applied math" than "pure math" while linear algebra is, again classically, more a "pure math" discipline. The difference in rhetoric you cite falls out of this exactly. In practice, both have wonderful presence in math both applied and pure. Linear algebra is one form of abstract algebra which is easily one of the most important mathematical disciplines. It's also the characterization and method of manipulating large arrays of numbers in interesting and practical ways. Statistics is the mechanism of interpreting live data under knowledge of uncertainty toward generalization. It's also probably well characterized as a particularly well-behavior substudy of measure theory... the pure mathematical notion of generalized "substance"
- romaniv 12y ago
  my college algebra courses Sorry, I meant my college calculus courses, although incidentally the statement applies to both. I think colleges would be much better off teaching introductory math as "applied". I got significantly more out of statistics, because that class taught us how to spot problems where that branch of mathematics is applicable. I really liked how Udacity used real-life orbit calculations from various space missions as assignments. It gives the whole thing some context.

tel 12y ago

Don't know why you're being downvoted. This is totally true.

peterfirefly 12y ago
Most of my downvotes so far, both here and on reddit, have been earned by writing things that are true but unpopular. The weird thing is that I can't predict which things are going to be sufficiently unpopular amongst people impolite enough to downvote instead of coming up with a good counterargument (or even better: fact). I had /never/ expected something like this to get a single downvote (and I was down at -3).

profinger 12y ago

I agree as well. Not sure why you're being downvoted. Maybe I don't know enough about linear algebra to judge but everything ML that I've ever worked in was spoken in calculus..

Dudelander 12y ago

Totally agree, calculus is a prerequisite for understanding statistics, unless you're just plugging in numbers for an A-B test - and you don't really need a class to do that. Linear Algebra is very useful too, but it's not really fair to say one is more valuable than another. It just depends on what kinds of applications you end up working on. Universities should just teach both.

peterfirefly 12y ago
Many interesting things require a combination of more than one area of math. I don't understand how you can do much within robotics or vision without using all three of calculus, linear algebra, and statistics :)
- varelse 12y ago
  I'll go even further and state that without an understanding of calculus, linear algebra, and statistics, an engineer or even a data scientist is little more than a glorified script kiddy.

romaniv 12y ago

Statistic teaches you application and helps to develop correct intuition. Can's speak for everyone, but my college algebra courses were 100% abstract stuff detached from reality. All professors had the attitude that once you learn the theory you could apply it to anything. Problem is, it's hard to remember theory if you don't map to something tangible, and it's hard to apply it to reality when you're just used to crunching equations.

tel 12y ago
Statistics is, classically, more developed in the realm of "applied math" than "pure math" while linear algebra is, again classically, more a "pure math" discipline. The difference in rhetoric you cite falls out of this exactly. In practice, both have wonderful presence in math both applied and pure. Linear algebra is one form of abstract algebra which is easily one of the most important mathematical disciplines. It's also the characterization and method of manipulating large arrays of numbers in interesting and practical ways. Statistics is the mechanism of interpreting live data under knowledge of uncertainty toward generalization. It's also probably well characterized as a particularly well-behavior substudy of measure theory... the pure mathematical notion of generalized "substance"
romaniv 12y ago
my college algebra courses Sorry, I meant my college calculus courses, although incidentally the statement applies to both. I think colleges would be much better off teaching introductory math as "applied". I got significantly more out of statistics, because that class taught us how to spot problems where that branch of mathematics is applicable. I really liked how Udacity used real-life orbit calculations from various space missions as assignments. It gives the whole thing some context.