> As usual, there was a lot of cleaning up going on, and there notably, a good chunk of this year’s Google Summer of Code project to clean out the issues reported by Coverity Scan is already in.
Yup, they're working on coreboot support. If you're in Europe Tuxedo Linux is also working on coreboot, and the Purism laptops ship with it out of the box.
I'm optimistic about the OLinuXino boards from Olimex. They're certified open source hardware by OSHWA, with all the bootloader code, schematics, and even CAD files on Github. I think the Mali firmware is the last holdout, but with the new Lima and Panfrost drivers landing in Linux we may soon have replacements for that too.
I'd even recommend Aegis [1]. Also open source with encrypted backups, but has better crypto than andOTP (both devs talk a bit about it here [2]). Plus, it can do imports from other OTP apps for easy migration.
Thanks for this, I really like the discourse between these two in the second link. The andOTP author is open about their crypto being sub-optimal and giving the Aegis dev a thumbs up, reason enough for me to give Aegis a shot to replace it. Perhaps they'll join forces going forward and we all win. :)
I personally agree with the philosophy of the author: I think all software should be free, and in the perfect world, I would license everything I do under the GPL. However, not everyone in the open source world has this philosophy. A lot of people prefer more permissive licenses like Apache and MIT, and using the GPL excludes these people and projects from using the code - by its viral nature, any single usage of the GPL would force the entire project to be under the GPL as well. Cooperation is the greatest strength of the FOSS world, and so I'm willing to compromise a bit to make that possible. As such, I personally prefer the MPL - it is a weak copyleft license that enforces all modifications to the source code itself are released back (important for me), but unlike the GPL is not viral and will not spread outside its own source files to other projects (important for others). This way I can keep the project and all modifications to it free, but also allow it to be used by others who don't share that point of view.
I made a similar switch to Lineage about a year ago, and it's also been absolutely great. No regrets whatsoever. Also, AFAIK you can root your phone to fool play store checks, using something like Magisk if that's important enough.
> The success of Riemann’s project is strong evidence that the whole numbers – which we think of as static, unchanging quantities – are really some kind of shadow or projection of the Hegelian integers. The Zeta function reveals more because it represents whole numbers as what they actually are, that is dynamic contradictions of being and nothing.
> But, in addition, the Zeta function represents the whole numbers as a sublated unity, where the entities internally relate via the exchange of a conserved substance. And this whole moves and changes with time. This is quite unlike the vision offered by set theory.
The way modelling normally works is you have a certain phenomenon (falling rocks, fish populations, market booms-and-busts) that you attempt to describe numerically, and then create a mathematical model to make conclusions about the phenomenon. Here we have the opposite: the author takes the phenomenon (the Hegelian contradiction) and uses the model to make conclusions about mathematics!
Hello! I am a fourth year undergraduate in pure mathematics, and have taken many of the classes in your list (especially in the first and third categories), so I'll try to give some advice.
First of all, what you're about to do is an very large endeavor - mathematics is a difficult subject, and learning math will take great persistence and self-motivation, especially if you are self-learning. However, it is also extremely rewarding - mathematics is a beautiful subject, and learning math has easily been one of the most enjoyable things I have ever done.
For the next point, if you want to go deep into math, then you will have learn how to prove things. The heart of math is not at all computation, but ideas, and to know that ideas are true, we need proofs. All of pure mathematics is based on rigorous formal reasoning and proofs, and sadly, most high schools and even universities never touch this part of math. If you have never seen proofs before, I would first recommend reading the book How to Prove It: A Structured Approach by Daniel J. Velleman, which goes through basic set theory, logic, and various proof techniques. Most importantly, it will give exercises for you to practice. Let me say this now: it is impossible to learn math without doing exercises. Again, this will take some work, and the beginning may be a bit slow, but as I said above, it is extremely rewarding - there are few things so satisfying as finding a beautiful, clean, or elegant proof. I hope you will enjoy this as much as I have.
Now then, let's dive into the courses and textbooks. I'm going to model this after what I did in my degree. Many of these topics require earlier ones as prerequisites, so I'm going to organize them into several layers. Some of the textbook recommendations may be a bit difficult, since in many of my classes the professors taught out of their own notes and left textbooks only as references, but I'll do my best. In your "first year", so to speak, there are three main things to learn:
- Single variable calculus, differential and integral. You likely know calculus already, but again, we are now taking the proof based road! The canonical text for this topic is Calculus by Michael Spivak. It's what I used in my first year, and most importantly, comes with a solution manual :)
- Linear algebra. As others have noted, linear algebra is absolutely crucial for many other subjects. I personally learned from Algebra by Michael Artin, but have heard very good things about Linear Algebra Done Right by Sheldon Axler, so I'd probably start there.
- Graph Theory and Combinatorics. These are I think are somewhat more accessible than the others (perhaps at least more intuitive), so I might actually recommend trying these first. For the basics, try A Walk Through Combinatorics by Miklos Bona.
By the way, whenever I need to find a textbook on a subject, I just Google "best (subject) textbook", and try to find the Math Stack Exchange post where someone has asked this question. (Eg. here's [0] the one for graph theory, which is where I got the combinatorics book.)
Now, this post is already getting long enough, so I'll post this for now and follow up the rest in another comment.
Hey that's me! :)