PDE's are not discrete math. CompSci majors are more interested in topics like Combinatorics, Graph Theory etc. PDE's are more interesting to applied mathematicians and physicists.
I doubt my CS professors would be able to solve a PDE..
Beyond the basics, not even many math professors can do that. Math is too vast and people specialize. Strong algebraic geometers are not necessarily strong analysts or algebraists or logicians.
> Agda is a programming language that uses dependent types ... you can actually include values inside a type. For example, the List type constructor can be parameterized by both the type of its contents and the length of the list in question ... . This allows the compiler to check for you to make sure there are no cases where you attempt to call head on a potentially empty list, for example.
> If I can come up with a function of type Foo -> Bar (and Agda says that it’s type correct) that means that I’ve written not only a program, but also a proof by construction that, assuming some premise Foo, the judgment Bar holds.
> Proofs work in concurrent scenarios. You can’t reliably unit test against race conditions, starvation or deadlock. All of these things can be eliminated via formal methods.
> Thanks to Curry-Howard, Agda can also be used as a proof language, as opposed to a programming language. You can construct a proof not just about your program, but anything you like.
I'd pick pure math. Suffering through that makes everything else look sooooo trivial in comparison. Yes that includes the highfalutin' branches of Physics :)
As an outsider, I am trying to learn the basics of computer science. I was recommended this book along with the ones listed below. Do I need to study them all or can I do one r two of them and move on?
Introduction to the Theory of Computation by Sipser.
Programming Language Pragmatics by Michael L Scott.
Compilers: Principles, Techniques, and Tools by Aho et al.
Concepts, Techniques, and Models of Computer Programming by Van Roy.
Intro to Computing Systems by Yale Patt & Sanjay Patel.
Computer Systems: A Programmer's Perspective by Randal Bryant & David O'Hallaron.
How much programming do you do? If you're a non-programmer who wants to write software, there are probably better things to do than read a bunch of CS textbooks.
I've been trying to understand programming for a while now. I know some Python and Clojure, but don't consider that programming knowledge mostly because its just syntax and syntax is just a triviality. So, instead I am trying to gain a better proficiency through programming close to hardware because I heard there are programs(for example, Assembly) that are in one-to-one correspondence with the underlying hardware they are written for. I've been recommended the books(and many more), but I am not sure how to group them thematically. I am not scared of math parts - just there's an huge volume of text to digest for just an intro to "programming done right". I am not in a rush to learn JAVA and go dev somewhere. Thanks.
The books you've listed are all excellent, but are not direct paths to 'better proficiency through programming close to the hardware'. I believe that SICP might be your best bet from among the books you've listed. Work through it first, then decide where to go next. A caveat: SICP spends much of its time approaching computation from a hardware-independent perspective (expressed in the old quip 'Computer Science is no more about computers than astronomy is about telescopes'.) Don Knuth takes almost the opposite approach in 'The Art of Computer Programming', defining a machine language (for an imaginary machine) to be clear about implementation details and time-space tradeoffs. Both perspectives dig much deeper than 'just syntax'.
Think of how CS students are going to approach these. They'll watch lectures, skim the text, and do exercises. Few students would sit down and read these like a fiction novel, and if they do, they follow it with exercises because reading retention was low. So I'd do some google searches with "site:.edu" and find powerpoints and homeworks to follow from courses that use these books.
Add in a algorithms text book (and perhaps a lecture series) and an OS book. And you would probably have something more comprehensive then a lot of undergrad CS degrees.
You mentioned and more about the books recommended to you, what are some of the others?
According to these guys, everything complex is harmful and everything simple is great. I want to start learning Assembly to finally understand the whys of programming on a hardware level. Is Assembly harmful? Any simpler and thus better alts? Or is Assembly a simpler version of some other ugly, threatening monster? Oh, btw, where's the best place to learn it?
We can tailor the point being made to your nit-picking: for starters, how about men who were persecuted for having sex in the privacy of their own house, excluding those who were convicted for deeds that are still considered immoral?
Have one who was prosecuted simply for gay sex. According to the organisation Stonewall, there's thousands more - although obviously, there's not going to be a pre-made list somewhere, you'd have to go over court records.
"In the early 1950s, the police actively enforced laws prohibiting sexual behaviour between men. By the end of 1954, there were 1,069 gay men in prison in England and Wales, with an average age of 37."
"1952 - Sir John Nott-Bower, commissioner of Scotland Yard began to weed out homosexuals from the British Government at the same time as McCarthy was conducting a federal homosexual witch hunt in the US. During the early 50's as many as 1,000 men were locked up in Britain's prisons every year amid a widespread police clampdown on homosexual offences. Undercover officers acting as 'agents provocateurs' would pose as gay men soliciting in public places. The prevailing mood was one of barely concealed paranoia."
It's a well-documented thing. Claiming that the targeted harassment and prosecution of the LGBT community never happened is a very dangerous form of denial. You can find anecdotal stories all over the Internet, and in modern media including mass market films. This is the entire reason we have gay pride. I'll see if I can find a book on the subject.
You seem to be saying that men were not prosecuted merely for being gay men or just for having consensual sex with other adult men in private, and that the men must have been having sex with children[1] or in public.
Thousands of men each year were arrested and locked up. Police were acting as agent provocateurs (thus entrapping these men) so obviously many of those prosecutions involve sexual activity in public -- where that's defined as "being approached by a police officer acting as a gay man and having a conversation with that officer".
You appear to be applying stricter standards of conduct to gay men than to heterosexual people. We can see very many convictions of gay men for gross indecency in public. But this definition of "public" included (until the year 2000) anywhere where a third person may be present - two adult men in one of their homes would have been having sex in public if one of those homes was rented lodgings; this was an additional restriction on gay sex that heterosexual couples didn't face. This extra restriction was included in law in 1968, and overturned in 2000.
Finally, around younger people: laws for heterosexuals had the age of female consent at 16 for heterosexual sex. But for gay men the age of consent was 21. Thus a 25 year old man having sex with a 16 year old woman was fine, but a 25 year old man having sex with a 20 year old man would be arrested and imprisoned.
[1] children need to be protected from sexual predators. Suggesting that gay men are more likely to be sexual predators is not supported by any evidence and is a homophobic slur that needs to end.
I don't know how you can say from anything I wrote that I am applying a stricter standard of conduct to gay men rather than heterosexual couples.
I don't understand how the downvoting/banning system works but I think it might be best if I shut up now.
Any studies being done on sinus related problems? Nasal cavities are hard to reach to deliver medication or to just flush the debris out. Nasal bacteria that fight/feed on mold/fungi?
Silent GERD can be related to sinus problems. Acid irritates the sinus and sometimes the ears. Some think the use of antibiotics brought on their problems so it makes sense to think tending to your gut biome might help.
I have an opposite sort of experience: I can't learn things fast enough if they aren't mathematical in nature. I used to think programming was disgusting because of Python(heard Java is even worse) till I came across Clojure. I immediately appreciated how the latter imitates pure math so well :) Never going back to Python. Once in a math mindset, learning anything imperative is painful.
I doubt my CS professors would be able to solve a PDE..
Beyond the basics, not even many math professors can do that. Math is too vast and people specialize. Strong algebraic geometers are not necessarily strong analysts or algebraists or logicians.