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> The biggest problem with both statistics and machine learning education, I would say, is their lack of emphasis on mathematical foundations. Any recommendati

> The biggest problem with both statistics and machine learning education, I would say, is their lack of emphasis on mathematical foundations. Any recommendations for someone who'd like to pick up sound (if modest) foundations?

GFK_of_xmaspast 12y ago
Hogg & Craig used to be one of the standard texts.
jamii 12y ago
I am a big fan of http://www.amazon.com/Probability-Computing-Randomized-Algorithms-Probabilistic/dp/0521835402/ref=sr_1_1?ie=UTF8&qid=1409098878&sr=8-1&keywords=probability+and+computing http://www.amazon.com/Probability-Computing-Randomized-Algor... . Every time it teaches a new chunk of theory it motivates and grounds it in some algorithmic application.
sampo 12y ago
A college-level textbook in linear algebra, another in calculus (must include vector calculus), and one in probability? For linear algebra and calculus, at least, Coursera also offers courses.
kiyoto 12y ago
Yes. For example, to follow CS229's lecture notes, the following material should suffice. - Linear Algebra Done Right by Sheldon Axler - Linear Algebra by Steven Levandosky - Linear Algebra and Multivariable Calculus, and Manifolds by Ted Shifrin (you probably do not need the manifolds part) Also, as paradoxical as it may sound, CS229 lecture notes themselves. The key here is to verify the details painstakingly. In math, we joke that whenever a book says something is "trivial" or "easy to verify" or "clear to show", it is a substantial exercise in disguise.
- skybrian 12y ago
  Yes, the whole "trivial exercise" thing is in itself a big problem with how mathematics is taught. Someone who's struggling just to understand the text could probably really use a worked-out example.
  - dceddia 12y ago
    "Left as an exercise to the reader," the bane of my existence as a college student. I especially remember the Sipser book doing this. He'd show a super-simple example, like proving 2+2=4, and then the next thing would be actually interesting and would be left as an exercise. Awesome.
  - brational 12y ago
    That's the wrong interpretation. In math, a 'trivial' or 'clearly' is supposed to indicate that a certain detail is important to understanding the subject. And if it isn't clear or trivial then the reader is expected to delve deeper before moving on. The "big problem" is that math is taught in a restricted time scale - a semester, just like all other standard courses. In reality it might take someone many weeks or months to pick up a certain piece of measure theory or hilbert spaces. Math builds upon itself and when it is rushed there is a lack of connection and then ultimately failure to understand. This is why MOOCs are a great boon for many, as they allow more freedom to self-dictate the pace.
    - skybrian 12y ago
      If that's what it really means then a perfectly good way to say it is: "To test your understanding, make sure you can do this exercise before continuing." I suspect many mathematicians like being intimidating.

GFK_of_xmaspast 12y ago

Hogg & Craig used to be one of the standard texts.

jamii 12y ago

I am a big fan of http://www.amazon.com/Probability-Computing-Randomized-Algorithms-Probabilistic/dp/0521835402/ref=sr_1_1?ie=UTF8&qid=1409098878&sr=8-1&keywords=probability+and+computing http://www.amazon.com/Probability-Computing-Randomized-Algor... . Every time it teaches a new chunk of theory it motivates and grounds it in some algorithmic application.

sampo 12y ago

A college-level textbook in linear algebra, another in calculus (must include vector calculus), and one in probability? For linear algebra and calculus, at least, Coursera also offers courses.

kiyoto 12y ago

Yes. For example, to follow CS229's lecture notes, the following material should suffice. - Linear Algebra Done Right by Sheldon Axler - Linear Algebra by Steven Levandosky - Linear Algebra and Multivariable Calculus, and Manifolds by Ted Shifrin (you probably do not need the manifolds part) Also, as paradoxical as it may sound, CS229 lecture notes themselves. The key here is to verify the details painstakingly. In math, we joke that whenever a book says something is "trivial" or "easy to verify" or "clear to show", it is a substantial exercise in disguise.

skybrian 12y ago
Yes, the whole "trivial exercise" thing is in itself a big problem with how mathematics is taught. Someone who's struggling just to understand the text could probably really use a worked-out example.
- dceddia 12y ago
  "Left as an exercise to the reader," the bane of my existence as a college student. I especially remember the Sipser book doing this. He'd show a super-simple example, like proving 2+2=4, and then the next thing would be actually interesting and would be left as an exercise. Awesome.
- brational 12y ago
  That's the wrong interpretation. In math, a 'trivial' or 'clearly' is supposed to indicate that a certain detail is important to understanding the subject. And if it isn't clear or trivial then the reader is expected to delve deeper before moving on. The "big problem" is that math is taught in a restricted time scale - a semester, just like all other standard courses. In reality it might take someone many weeks or months to pick up a certain piece of measure theory or hilbert spaces. Math builds upon itself and when it is rushed there is a lack of connection and then ultimately failure to understand. This is why MOOCs are a great boon for many, as they allow more freedom to self-dictate the pace.
  - skybrian 12y ago
    If that's what it really means then a perfectly good way to say it is: "To test your understanding, make sure you can do this exercise before continuing." I suspect many mathematicians like being intimidating.