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I agree with your points so much.

I am a applied Maths student (currently) and when looking for internships I noticed 80% of them are for CS related stuff. Imagine being me ( 19 years old ), offered a 15K/year job in my first year in university. My best job up until then was cleaning the floor at a mall. I have studied insane amount of mathematics all my life ( proofs after proofs ), how much longer do I need to wait until I am able to something of value in society ?

Compared that to the amazing 14 weeks internship I did at a startup churning out frontend javascript. Those 14 weeks were the best weeks of my life, I never felt more confident and of value. My depression vanished overnight, I found a new aim in life, I treated coding the same way nations treat nuclear weapons.

I learnt more things of value in those 14 weeks then I did in the previous 19 years, I didn't need to set up an alarm clock to wake up in the morning. There was no hand holding, because I was getting paid. I spent the rest of my waking hour churing code with no need for external motivation.

I got really angry at society for misleading me for such a long time because of how easy it was for me to do something useful, finally. I see my friends struggling with the same problems and feel so much of young ppl's time is wasted, In my mind its a crime.

I think as always mathematicians fail to grasp the human side of the argument, why are they complaining about lack of interest in statistics ? its their own fault this problem exists. There is no Neil Degrasse Tyson for statistics, there is no mark zuckerberg for stats, you don't need to hire a PR department. Just show us the wonderful magic that you speak of and we are smart enough to figure out why we should dedicate our lives to your cause.

This is why if some statistical axiom/theory doesn't have a CS applied part I became really skeptical of doing that course.

>I think as always mathematicians fail to grasp the human side of the argument, why are they complaining about lack of interest in statistics ? its their own fault this problem exists. There is no Neil Degrasse Tyson for statistics, there is no mark zuckerberg for stats, you don't need to hire a PR department. Just show us the wonderful magic that you speak of and we are smart enough to figure out why we should dedicate our lives to your cause.

It doesn't help that textbooks and course materials in mathematics sometimes appear to be designed for working mathematicians more than for students, with a lot of outright hostility towards the very concept of students learning maths.

(I acknowledge that this comes from Math professors hating the time they spend teaching STEM weed-out courses, but I still think that overall, Mathematics is much worse than even theoretical computer science at avoiding things like Notation Proliferation Syndrome and Greek Letter Syndrome that make it artificially hard to learn.

Explain the rigor, yes, but also explain the meaning and the concepts such that a decent learner should understand them well enough to reconstruct the rigorous parts on-the-fly as he or she needs.)

While it must be a factor, I don't think weariness from teaching intro courses is the main reason we don't see better math books.

I think it is genuinely difficult to write engaging texts that are sufficiently rigorous and retrain teachers in the methods that go along with them and drum up support among administrative types.

Not that it's impossible, but it is very challenging.

Agreed but also easier said than done

Yeah, I use this book. Its the most clear book I have ever read for 1-2 year applied Mathematics.

http://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/...

Theoretical Computer Science is great in my opinion.

Many mathematics ppl complain about external factors, I agree there may be many external factors but there are also a bucketload of problems with mathematics itself that the are in a position to solve.

I am convinced that you cannot do applied mathematics without computers. An anecdotal example: I have been solving differential equations since I was 15 and only when I tried creating mathematical models for self-driving cars for my CS assignments did I realize that I have no clue what I understood. I spent 5 years just manipulating algebra which python can do with one line of code in Sympy.

I suspect money is a big motivation behind all the hand-wringing by statisticians. It is about jobs, grants, prestige. I don't blame them; people want these things. I defintively see a competition between computer scientists and statisticians for the mantle of date scientists. When the current bubble bursts and the hype dies down, one side could have won and the world could be very different, or not. What do I know?

I am a little torn between realistic business demand of paying least money to get jobs done and thorough mastery and understanding of theories. Look at biostatistics; there master graduates become data analysts and process data. They know the nomenclature and can understand instructions from more advanced statisticians. The majority of practitioners don't know proofs and they carry off their tasks reasonably well. I would call all but very select few statisticians applied statitisticans and the world is fine with that. I am not sure machine learning industry will not turn out like this, although I am not looking forward to that day.

I would just note that numerical optimization is a big deal in machine learning while I know of no statistical department strong in it. The popularity of SVM owes a load of gratitude to pracitical breakthrough in dynamic optimization. But if one elevates to the level of functional approximation then statistics is similar to almost all engineering fields. In fact, I suspect statisticians have more common with engineers than scientists. I bet Eric Cantor didn't care that polling results had margins of errors but that he lost his House seat due in part to overconfidence coming from unreliable statistics. Real world applicability, not theoretical nicety.

> I am not sure machine learning industry will not turn out like this

I am certain it will. The machine learning field is already rife with best practices, general-use algorithms, software solutions and tutorials.

>As for R/Python/Matlab/etc., I will let the zealots argue what's best. To me, they are like statistics and machine learning: similar with different emphasis.

Having tried working with Matlab and having extensive experience with Python, my verdict is: Haskell or Ocaml.

Ok, but seriously, once I understand just fine what algorithm I'm implementing, doing numerical computation in these all-dynamic languages is atrocious. I could have saved hours of runtime if I'd been allowed and able to just write the damned algorithms in a statically-typed language that compiles to machine code, on top of saving myself debugging time.

>When big tech companies are offering a Stanford graduate with only a few summers of programming internships under the belt for 150k/year

Aren't most of these offers in a part of CA where the cost of living is just as ridiculous as the salary? Therefore making the salary not ridiculous at all.

I work in the DC area, and veteran programmers normally can't get anywhere close to that unless its a contract job with no benefits and shitty working conditions. Even still, it will likely be about 30k less than that.

All-in compensation for a top student out of a top college (think Stanford, MIT, Berkeley) in SV can be $200k.

But keep in mind that the high cost of living really only applies to certain areas (albeit desirable ones like SF, Palo Alto, even Mountain View). There are tons of affordable locations if you are willing to have a 30 minute commute and are willing to accept sketchier environments (Berkeley, Oakland, other East Bay locations, East Palo Alto, etc.).

Berkeley is sketchy now?

The cheaper parts of Berkeley are sketchy, yes.

"top student out of a top college" doesn't exactly describe a lot of individuals (10? 15?), which makes that compensation value an extreme outlier.

Allow me to revise that to "top student at a decent school." (School is actually less important). I would say it describes >200 people every year (take the top 5-10% of Stanford, Harvard, Berkeley, MIT, CMU, Princeton, UPenn, UT Austin, Caltech, a couple others, and then maybe the top 2-5% at UCLA, UCSD, CU-Boulder, dozens more schools.

That is precisely a significant reason why I left DC - the pay is tied heavily to years of experience, and getting something like $150k is difficult, albeit not impossible, to do there.

I'm not sure if I buy that a Stanford graduate would necessarily net $150k starting at most companies (certainly possible at big companies, but I am skeptical - one software engineer told me that at one tech giant, he was offered $160k as a senior engineer, and was told that was about the max they could offer any software engineer then. He was a lead developer for a major group for this company, and this was with proven productivity) - I certainly wouldn't hire one at that price currently unless they are absolutely stellar, and I work in downtown Palo Alto for a pretty healthy startup. At that base salary, they'd be making around my salary, with far less productivity and likely even less potential.

$120k is more in the ballpark one might make typically , and even then I'd want a strong mind that is open to teaching/mentoring & investing in developing himself/herself.

> 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?

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.

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

I am a big fan of 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.

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.

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.

"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.

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.

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.