121 karma · joined March 4, 2015
I didn't like either Royden or Rudin. I really like Folland's book "Real analysis: modern techniques and their applications." His Fourier analysis book is also pretty good IMO.
What college your children attend seems to have a big affect on your social status in the US, and the children's social status is definitely hugely affected by what college they attend. Apparently it is much cooler to say you went to USC then the University of Arizona.
Maybe it shouldn't be this way, but I think the parents aren't stupid to be worried about their children's social status in this way.
I rent them both out I pay a management company to handle maintenance. I screen tenants myself, and so far I've been lucky getting tenants who stay for fairly long periods. I clear about 5K/month after maintenance fees, taxes and insurance. Its very little work.
https://your.yale.edu/sites/default/files/rate-agreement.pdf
If I am reading it right, it says that on-campus research has an overhead rate of 67.50 or 69.0 percent depending on the funding source. Ouch! I imagine that the federal government knows that it is subsidizing universities as a whole through this system and intends to do so.
What if the paper is written by Author Z, whose work you are familiar with and whose papers you read anyway. Why not review it?
And so on.
Moreover, the plaintiffs commissioned a study on the effect color blind admissions would have on the racial distribution of Harvard's undergraduate population. It should be taken with a grain of salt, as should the materials offered by the defense, and I suspect it overestimates the effect a bit, but it conforms fairly closely with anecdotal evidence I've seen and so sounds much more plausible to me than the ACLU's take.
It claims the share of black students would shrink from ~15% to ~0.9% and the share of hispanic students from ~15% to ~3%. Meanwhile, the share of white students would shrink slightly from ~37% to ~35%. The proportion of Asian students would roughly double, from ~25% to ~50%.
Again, the specific numbers might be a bit off, but it generally agrees with a lot of anecdotal evidence I've seen --- being black or Hispanic gives one a large advantage, being white is close to neutral, and being Asian is a large disadvantage.
The scandal here is the journal editors deviating from their standard procedures. There are procedures in place for re-evaluating articles which have been published or accepted for publication, and for retracting them if they don't meet proper standards. If the members of editorial boards don't think those procedures are proper, they should work to change them, or, barring that, resign. What they did instead undermines the credibility of the journals. How do we know that usual procedures are followed in other cases when they clearly weren't in this one (assuming the facts are as stated in the post)? Are there articles that are accepted for publication because of external pressure, over the objection of reviewers and editors? Are there other papers which have been disappeared without the expected retraction notices? What a disgrace.
How about the big law firms? I know they don't really hire much outside of the Top 14 law schools, and I wouldn't be surprised if the top few schools provide 40%-50% of their hires.
I think the discussion has to be broader than just tech ... America is looking an awful lot like an oligarchy with a caste system. Especially when you consider the recent articles about Ivy League admissions policies.
And this seems to have accelerated in the last 30-40 years. It seems to me that in the past it was much more common to see very successful and highly placed people from humble backgrounds, with degrees from schools I've never heard of, or good regional schools which aren't the Ivies. Now it is dreadfully monotonous, with a huge percentage of people in leadership roles from Yale, Princeton, Harvard or Stanford and whose parents have similar backgrounds.
The scoring system has been changed several times since 1995 and I have no idea how the current system compares to the pre-1995 system or the recentered test given for some years afterward.
Many, including myself, suspect that one of the motivations for the recentering was to give colleges cover for their admissions decisions. It is pretty hard to turn down students who get 1600s when only 7 or 8 students a year do so. It is easier to "shape" a class without provoking criticism when a large percentage of students score 1500+.
Everything else is lower order.
To give one example, drivers are required to yield to pedestrians in cross walks and to pedestrians approaching crosswalks while pedestrians are only required to "exercise due care," which is a much weaker requirement. If you want to see how weak this requirement really is, look at the case law. In many cases in which the average driver thinks the pedestrian is in the wrong, the law disagrees and would place the lion's share of blame on the driver.
I recently saw a breakdown of where the money for one of the UC campuses comes from. About 50% was from the associated Medical center, about 25% was from federal research grants (many of which had PIs in the medical school and medical center), about 15% from tuition, and 10% from other sources (not broken down further). This wasn't UCSF, either, where I would expect the medical center's budget to dwarf everything else.
I don't think it would be too far fetched to call it a medical center that happens to have school with 30K undergraduates attached. I wonder how the cost of running the chancellor's office there compares with the costs of administration of a medical services company?
Of course, at this point aren't Yale and Harvard basically hedge funds?
These are facts and easily verifiable.
(a_1,a_2), (a_2,a_3), ... (a_{n-1},a_n)
and approximately the area under the graph of the function via sums of the form
\sum_i f(x_i) (a_{i+1} - a_i)
where x_i is a point in the interval (a_i,a_{i+1}).
Lebesgue integrals turn this procedure on its head by partitioning the range of f into disjoint intervals
(a_0,a_1), (a_1, a_2), ... (a_{n-1},a_n)
and approximating the area under the graph of the function via
\sum_i m({x : a_i < f(x}) < a_{i+1}) a_i
where m(E) refers to the "measure" of the set E. That is, for each i, we multiply the "size of the set on which f is mapped to a value near a_i" by a_i and then sum over i.
The principle advantage of the Lebesgue scheme is that f can be very badly behaved and the quantities involved are still well-defined and make sense, whereas the Riemann integral only leads to reasonable approximations if f is somewhat well-behaved (more-or-less continuous). Otherwise, the value of f(x_i) (x_{i+1}-x_i) is not a reasonable approximation of the area under the graph of f "over the interval (x_{i+1}-x_i)".
There are even more general notions of integral. To my knowledge, most are based on observing that an integral is a linear functional on some space which should satisfy certain properties.