proginthebox

Selecting an approachable problem is also a skill that more experienced people have and often the younger people don't. Some problems are just not ready to be tackled because the field hasn't developed for it yet. It is a risk factor between choosing your own problem and floundering through the quagmire or getting help in choosing a problem you have confidence in solving in some years.

While I appreciate your brother's personal choice, to each their own after all. There is quite a lot of merit in your PhD advisor helping you in choosing a problem. That being said, good advisors provide students with an array of good problems out of which the student can choose one they are the most passionate about. This is what happened with me, I was provided with around 7 different choices to make. In the end, I chose 2 of them even though I wanted to chose 3 more but couldn't because of lack of time.

If you want to understand algorithms, you need a computer science curriculum, not a mathematical curriculum.

Also, unfortunately, its not the recommended order to learn them in.

I see. Well, you have a point, but the OP did specifically ask for a plan like that Susan Fowler's blog post. And I am an applied mathematician working mostly on computational physics and I can attest to the requirements I mentioned.

But your advice has a point, just going through books mindlessly is not motivation enough/ can lead to wandering. And it is always good to have specific tasks at hand. Like, solving a particular ordinary differential equations numerically.

This is terrible advice. Apart from the last sentence. A better advice would be to specify which subject to learn.

For example, (since I don't really have much time)

1. Topology (book by Munkres)

2. Real Analysis and Measure Theory (book series by Stein Shakarchi)

3. Algebra (book by Aluffi)

4. Linear Algebra (book by Friedberg Insel)

5. Measure Theoretic Probability (book by Cinlar)

6. Differential Geometry (book Smooth Manifolds by Lee)

7. Numerical Analysis (book by Quarteroni)

8. Set Theory and Propositional Logic (books by Goldrei)

This is what one will mainly learn in a strong undergrad/grad math program. Once this is done, then there are different tracks to follow.

With proper use of constexpr, templates and types, you can make C++ at least as fast as C code without giving up on readability.

In short, the two fields just look similar, but are actually extremely different fields.

Physical simulations need to preserve entropy, maximum principle, energy conservation and other kinds of conservation, preservation of consistent states, convergence in case of finer mesh.

There are multiple equations which model different forms of fluid: 1. Incompressible Euler (For liquid) 2. Compressible Euler (For non-viscous gases) 3. Navier Stokes Equations (For viscous liquids)

There are multiple solver methods: 1. Finite Difference 2. Finite Element 3. Discontiguous Galerkin Finite Element 4. Finite Volume Method

There are multiple equation methods: 1. equation splitting is just one of the many methods possible.

Just because the equation is unique does not mean that the solution is unique. Single equation provably have multiple and even infinite solution for the same initial condition. Computer graphics fluid simulation does not care (with a good reason) about this and hence, often their simulations even though they look kind of nice, are often incorrect since they do not demonstrate various physical characteristics that must be preserved.

In contrast, the qualitative/quantitative constraint in physical simulations are very strict. You need to know a lot of theoretical math to even understand if you are even computing the correct solution.

Liberalism is always against an axis. As such, there are two different factors in liberalism, Social and Economic. The so-called liberals in America Liberals are socially liberal but economically conservative. While American conservatives are economically liberal but socially conservative.

In Europe, the wired broadbands are cheap and fast. In India, there is no hope for cheap and fast wired broadband due to poor planning. Hence the craze for 4G. Also, the rates are marginal. For a long time, the rates induced loss for companies.

Just because someone can use a software does not mean they can/will pay for it. In other words, you'll can only earn money if your customers are rich.

Such systems also most likely are not vulnerable to Meltdown/Spectre.

What I've observed in Europe is that there are huge amount of small companies instead of one big one. While big and powerful companies might be important on global scale. I suspect that on a more local scale, it is the large number of small companies which are more beneficial.

how do you integrate neovim clipboard with system one? I use KDE/X11 although I do not think that should be relevant.