If you don't find any official degree online you can always stick to a bootcamp course that is similar to Harvard Math 55. It has had several forms. The most interesting ones being either Halmos + Rudin (plus many aids such as Gelbaum & Olmsted) or just Hubbard & Hubbard. Either way you will get a very solid introduction to mathematics that covers algebra and analysis, in a really rigorous way.
However, being a computer scientist I think a different approach to mathematics can be more enjoyable and also much more useful for many theoretical and practical developments that are yet to come. The downside is that materials are a lot less cohesive (any other references appreciated!). I'm talking about an approach with a focus on the foundations of mathematics, emphasizing logic, category theory and type theory.
I've read parts of Halmos + Rudin, and I think that they would be a fast track to higher level pure math, but I've known people who've gone down such path and end up being able to prove Fubini's theorem using measure theory without understanding what it means.
The ideal approach for a self learner, which would simulate the university experience, would be doing as many problems in Schaum's outlines for math subjects and supplementing the info with textbooks/online resources.
I'm not a big Apple fan. I've bought some of their laptops after the transition to Intel, but slowly switched away when macOS became less of a priority.
That said, I think Apple is sitting on top of another blockbuster, similar to the iPhone in terms of impact, if they know how to play it well. I'm referring to the Apple Watch equipped with a non-invasive glucose sensor.
I realize that they have a bit of a regulatory battle to fight before releasing it. But the potential is immense. It will change how people eat, not just diabetics. It's pretty well established science now that if we reduce the area under the glucose curve (read minimize glucose spikes), we will age more slowly and we will reduce metabolic disease enormously.
> I've bought some of their laptops after the transition to Intel, but slowly switched away when macOS became less of a priority
I recall at one of his last keynotes Jobs pointed out that compared to what the iPhone and iPad were bringing in the Mac/macOS division was small by comparison but compared to computer companies like HP or Dell that Apple was shipping more units of higher quality products to fiercely loyal users/fans (this observation preceded announcements of new/upgraded computers iirc). I realize Apple has an obsession with Ferrari-like cool, slick looks to their laptops but I think a blue-collar, enterprise-aimed laptop that says "I'm a serious developer/business person, I will lug an 8 pound laptop if it gives me lots of RAM, lots of processing power, and an all day batter, even if it's not sexy but gets the job done more reliably than anything else in existence" would be a wildly popular product. In short: something like a Lenovo P series (with 8 cores, up to 128GB RAM and a full, QUALITY keyboard without the BS touchbar) but running macOS. Hell, steal the advertising memes that Ford and Chevy use for selling their trucks: an industrial-grade laptop workstation for the knowledge workers who make the knowledge economy work.
> I'm referring to the Apple Watch equipped with a non-invasive glucose sensor.
As someone who has dated someone that is diabetic and now works with someone who is diabetic--someone who likes to sit at the cutting edge of technology and is even using hacked equipment to improve his experience--I don't think we have that technology yet.
We don’t, the latest commercial technology consists of disposable sensors that require a probe to penetrate the skin. Whoever brings something non-invasive (and reusable) to market will be raking it in whether they’re apple or not.
Could you provide a source on the last claim? I am generally quite skeptic whenever I hear anything in food science as being represented as well-established.
Sure. This recent Nature Reviews Genetics paper should describe the basic associations between DNA methylation and glucose levels, as well as point you towards more specific literature:
Bagsvaerd is great. I was living in the Lyngby-Naerum-Birkeroed-Farum area for many years, working in formal methods. I hope to be back soon! Are you still in the area?
Thanks, I'll make sure to read that. Generally I am greatly frustrated about how little I know about 'physical things'. Like all my effort has always been poured into philosophy, mathematics, economics, and computer science, never leaving any time to appreciate physics, chemistry and engineering. Just the title of that paper has three words I don't know what mean!
I moved to Copenhagen, but I guess that qualifies as the area :P
> We hate to ground your technological hopes, but Valencell, which licenses sensor technology to Samsung, Sony and the rest, says that noninvasive glucose tracking is impossible.
Not that I necessarily believe the quote, but I've seen no sign yet that it's likely to happen any time soon.
If you are willing to take total control of your mobile environment, Android can give you very good privacy. Arguably better than Apple.
Simply buy a Pixel (or any other device that supports AOSP). Build your own AOSP image (which is quite easy). And you are ready to go. Use applications from F-Droid only.
Admittedly it's not as straightforward as running your favorite Linux distro, and there are some caveats, but it's quite close.
Both of those apply to iPhones as well. The only difference is that on iOS, you cannot turn off AGPS location collection, while on Android, not only can you turn it off, it's opt in.
This 100%. It will also make your web experience a lot better because so much of the javascript out there just does things you don't want anyway, such as loading ads and displaying popups.
If you are a web developer or are familiar with web terminology like origins, domains, frames, XHR, etc on the web, and are willing to put in some time learning how to use it (15 mins for a seasoned web dev, maybe 30-60 mins otherwise) get uMatrix (https://github.com/gorhill/uMatrix). It will change your life! If not, use ScriptBlock on Chrome or NoScript on Firefox. Block all scripts (and if using uMatrix, cookies, XHR, and frames) by default and whitelist as you go for sites you trust (or want to use bad enough to potentially open yourself up for tracking).
> so much of the javascript out there just does things you don't want
JavaScript developers should ask themselves if they want JS to become the popup of the 2010s: initially well-intentioned, shamelessly abused, universally loathed, and ultimately killed.
I think the point is not that the core domain can't fingerprint you, it is that 3rd party JavaScript is blocked by default, which makes those domains less likely to track you. Not impossible, just less likely. For example there is almost never any reason to allow Google Analytics JS.
Agreed. If you take the default uMatrix setup, change javascript to be disabled, then just whitelist as you go, you'll pass most of those tests and be pretty tracker-resistant.
My suspicion is that fingerprinting by the core domain will actually get worse since your browser behaves so differently from stock browsers (which is after all the point of uMatrix :-) ). The majority of trackers tho will be third party (such as Google analytics). Very few sites roll their own trackers because it's hard to get right, and some great ones like GA is free. For those that do, I'm not too worried anyway, but that's certainly just a personal thing.
I've been blocking JS for the last 6 months or so and I've found it to be a greatly improved experience overall. I can enable at the click of a button JS for a website that fails to load properly but the majority of sites I view are fine without this. It was refreshing to learn that not as many websites as I suspected are JS abominations!
My experience exactly. Everyone said "don't do it, most sites need js!" but it isn't true. SPAs are certainly out there, but not nearly as common as you'd think (I most thank SEO for that since only recently would Google crawl a client-side rendered page). Will it be a seamless experience? No, definitely not, but I agree, overall it's an improvement.
I do have Firefox set to noscript. When things don't display, I copy the URL to Chrome where I don't have it so locked down. But I've been dismayed to see over the last year that a lot of sites that used to be usable no longer are.
I don't. The only one I know is using Tor Browser without any customization, without even changing the windows size, because it makes you look like every other Tor Browser user.
However, it comes with a fairly long list of downsides: less secure than Chrome, less secure than even Firefox it's based on because it's not updated as often and quickly, and you MITM yourself by default, and it's slow, it doesn't block ads... The price to pay is steep.
It's fast enough to be my main browser and plays e.g. YouTube at lower resolutions fine. I chose to install ublock origin, makes me stand out more from other users but I'm on Linux which is now revealed directly in the useragent string so I decided it wasn't a concern for me as I'm already not in the larger group of Windows users.
I love working remotely from a home office in some sunny spots of the Mediterranean. If you choose well, you can find cheap places with great weather all year round, quality food and very good services (including healthcare).
For me nothing beats a quiet home office as I need to do really deep work in probability & logic.
In addition to what has already been said, the last time i used btrfs in this manner the protocol had issues with some extended attributes which happened to manifest in issues on binaries which lets them gain additional capabilities[0] for example. Most notably this made iputils ping[1] utility unusable after branching of a previously made snapshot for further usage. This appears not to be a too common thing in other distributions but in arch the ping utility uses CAP_NET_RAWIO capability in order to avoid the need to use setuid which appears to be more common elsewhere. None the less i think that is something one would want to know the consequences of as i am sure there are quite a few more binaries with extended capabilities set in the extended attributes of its file or use them in another manner like security labels for SELinux. I just rechecked if this is still the case and found this patch[2] but i am not sure this has already landed.
For my usage, I have BTRFS on my backup host, but not on all (or even any) of the machines I want to back up. They're variously macOS, Windows, Linux ext4, FreeBSD, and OpenBSD.
Go for the btrbk tool - automates snapshots, and sends / receives them incrementally via SSH to a Server, with pretty fine-grained retention settings. Awesome.
I have also had episodes of extreme eye dryness. Furthermore, I got floaters whose onset matches my tinnitus onset. Additionally I have very mild sporadic joint pain. I'm HLA-B27+.
Altogether, this is quite obvious evidence for autoimmune arthritis or some related autoimmunity. I know this because I do autoimmune genetics research in a top lab. I've gone to a few doctors and they never even suggested the possibility of me suffering from autoimmune disease, which is scary.
I'm in the process of being diagnosed only because I explicitly decided to go to a rheumatologist myself. The rheumatologist facepalmed when he heard the whole story.
I suspect a significant proportion of tinnitus phenotypes are mild autoimmune ones.
I've heard from my doctor and from other patients about cases where some steroids helped or even resolved tinnitus completely. I'm currently investigating this option.
In my case, years before my tinnitus onset, I started having a lot of discomfort on my right ear (my tinnitus is mostly one-sided, just like my floaters).
Firstly, my right ear started getting clogged with wax really frequently. Then, I developed extreme sensitivity to cold. So, cold air would give me acute ear pain.
Immediately before and after my tinnitus onset I had mild vertigo quite frequently.
Ever since I developed tinnitus, my ear feels full and clogged.
The Human Leukocyte Antigen complex is a protein complex that immune cells use to determine self from non-self cells. There are many many many possible alleles, some of which are thought to be defective and contribute to auto-immune disorders. The most notorious (for medical students studying for standardized tests) is HLA-B27.
However, being a computer scientist I think a different approach to mathematics can be more enjoyable and also much more useful for many theoretical and practical developments that are yet to come. The downside is that materials are a lot less cohesive (any other references appreciated!). I'm talking about an approach with a focus on the foundations of mathematics, emphasizing logic, category theory and type theory.
Some links:
http://www.paultaylor.eu/~pt/prafm/
https://ncatlab.org/nlab/show/computational+trinitarianism
https://softwarefoundations.cis.upenn.edu/
http://adam.chlipala.net/frap/
http://concrete-semantics.org/