Why do mathematicians and physicist use the words “elementary” and “introduction” for advanced textbooks in the field? Is it to flex intellectual powress?
“Elementary” doesn’t mean “what you learned in elementary school,” although it is publically perceived as such.
Almost universally, in almost every text I’ve read, it means “use tools that are well-known to people with an undergraduate degree in a related field, or simple extensions thereof.” (There are some cheeky counter-examples, such as Weil’s Basic Number Theory, but this is far more rare.)
In the same way you cannot expect someone who has never seen a circuit or understand logic gates to construct a processor, you cannot expect someone without any mathematical maturity (e.g. basic linear algebra and calculus) to use QM in any fashion other than understand the most basic of constructions.
Say I am enrolled in a CS PhD program but want to get hired as a quant. What math courses should I take to get the required background? Would I even be looked at if I had a CS PhD instead of a Math PhD?
Plenty of CS PhDs get hired as quants. Be sure to take as much math as possible. Google around to find which things you should take. If your school offers (graduate if possible) classes in financial modelling take some of those.
Quant jobs are making models of markets (or other financial items), using the best math and tools available. For practical performance these models need implemented, so you'll program. Developing these models is often done in math packages like Mathematica, then once nicely tested, ported to high performance code in C/C++/asm or sometimes even into FPGAs or ASICs.
Quant job are a mix between math and programming. The better you are at both, the more valuable you become. If you're really strong at one compared to the other, you'll drift that way. If you are terrible at either, you'll not get hired.
I agree. If you look at what a mathematician does they sit around and think. You don't have that sort of luxury if you are from a poor family and have to worry about basic survival. In many cases (not all) the people that complete major accomplishment X at young age Y is from an upper middle class to upper class family with lots of life advantages. Not everyone have these advantages early in life and may eventually get to those positions due to their talents, but it may take them longer given their life situations. There are poor but extremely talented underrepresented people out there the world may never know. We tend to celebrate talent from the elite class, not the poor. The elite are given resources they need to succeed, the poor are often overlooked. This can cause a major talent drain from truly exceptional but unknown folks in the world.
Is this a problem only in countries where you have to pay a lot to study? I did not had to pay for my higher education and the people that had a high talent and potentials achieved good results, there was no need to work to make money for studying and if you are good you got positions at University or get jobs at high paying companies.
In countries like the US it starts at birth. Families in rich areas will send their children to elite, selective high schools that cost upward $30,000+. Some of these schools have strong math and science curriculum and are considered direct feeders to elite universities, such as the ivies. These poorer kids could be high IQ'd just like the richer ones, but with less access to resources, may be very behind their richer peers. These richer kids will get into the elite schools, while the poor kids may go to lower end ones or not go to colleges at all. Rich parents can hire their children SAT tutors, ensure their children go to good STEM schools, have various college prep resources for their children, while the poor parents don't know anything about college, sent their children to lesser high schools, and have children that may be just as bright, but essentially ones that have no chance to be admitted to the places they otherwise might have gotten into. College admissions at elite colleges favor children from the elite that had the resources to prepare their children for such pedigree. There are exceptions to the rule, but many poor families face deep struggle. This is regardless of however high IQ'd their children may be.
I agree with all of this, but don't see what it has to do with age. The best 50-year-old mathematicians also heavily tend to come from privileged backgrounds. Privileged upbringing is simply one required component of what it takes to be among the best mathematicians of your generation.
I think this rule is just wrong. Some mathematicians come from privilege, some do not. Even for the ones who do, it's rare that they come from _great_ privilege for the time. They are the children of mayors, not kings -- professors and engineers, not the financial aristocracy.
Now it seems you're moving the goalposts on what counts as privilege. Do you have any quantitatively backed reason to believe Fields medallists are more likely to come from the financial aristocracy than say Abel prize winners?
I don’t have access to a biography of all the Field’s medalists. I am simply pointing out that there is a wide distribution of financial privilege in a list of famous mathematicians that I did not choose. I would argue this is unexceptional, but I point it out because I have trouble with the hypothesis that one must come from privilege to get anywhere in math. If anything I should be asking for the quantitative proof of the hypothesis.
>Maybe I'm just easily impressed but the idea of a 17 year old who skipped three grades and is already a third-year university student..
Not saying this applies to Tang. But would you be equally impressed by a 17 year old from an upper middle class family whose parents recognized their gifts and used their influence to assist them in skipping 3 grades and enrolling in college early vs 17 year old from lower income family who is equally bright as the former kid, but graduates at 21 and receives no recognition for it due to an unheard of advisor at a low ranked school? On paper you'd be more amazed by the former, while the latter is equally as bright but is sort of dismissed because of their situation.
Jeremy, thanks for putting this out. I had issues with part 1, v1 with the AWS set up. But I had none of those issues with this course. As a beginner programmer the template provided via Paperspace is just what I needed. I've been waiting for this course to be released for a really long time now, so I am incredibly excited to have successfully set up the environment and am now FINALLY ready to learn. Thank you!
As a beginner I cannot recommend this class in its current form. The first lecture with its setup walk through is outdated and I have trouble understanding how to do a work around.
This is welcomed news, thank you for the update. Can you link to v2? On the site I just see part 1, v1 with the AWS set up. This is the beginner unfriendly/outdated one I am referring to, and I don't see the updated version you're referring to.
I just checked the course forum, and Jeremy asked us not to share on high traffic sites until theyve finished the new website. I think it'll be out within a week or so, so check the fast.ai site for updates. Should be soon!
NLTK tutorials are interesting for the absolute basics in Python, e.g. http://www.nltk.org/book/ch01.html. The field has moved into advanced Bayesian and neural methods, but NLTK still has a use in pre-processing and thinking about how to work with text. The first thing to recognize, I think, is to realize how hard many of the language tasks are that people do trivially.
How does one get hired to be a researcher at google? What job title or level would this be? How does being a researcher differ from being a regular SDE? What background are they looking for here? Do these people write code on a daily basis?
As a follow up: I want to pursue a math degree study. What course titles and textbooks starting at the calculus level do you guys recommend? I want enough math chomps to then go onto a PhD in ML.
Linear Algebra (which is what you really need): Gilbert Strang - Linear Algebra and its applications
These two are all you need, with which you'll get a solid base. Then you're good to go on your own. These two combined are about 4 semesters worth of work. But if you really focus, I think you can get them done in a little less than 6 months.
If you want a 'just what I need' approach, Khan Academy.
For self-study, you don't necessarily need to follow the usual progression of math classes that start at calculus. It's more important to get comfortable with linear algebra than calculus, especially the way a lot of intro calculus courses focus on calculating integrals and derivatives. Maybe it's not the best message, but the worst grades in my math degree were in the intro calculus classes.
I don't remember what intro linear algebra books I used, but my college uses this: https://www.math.ucdavis.edu/~linear/ (I took the class before this free textbook was developed).
