cabinpark
The credit card thing is also true too. Cash is king here and I routinely see people with hundreds of Euros of cash like it is nothing. I always see people paying for groceries with 100 Euro notes. Furthermore, I know Germans are much more concerned with personal security and privacy that there is also going to be a push back about having to share personal information with an American company.
Also I live in Frankfurt, and, to be honest, I have no idea why people even use taxis. To get from the Hauptbahnhof to practically anywhere in the city is only a < 20 minute U-Bahn ride. Also, the public transportation in Europe tends to be insanely good and efficient so a ride-sharing app will also have to compete with this as well.
Unfortunately I see too many people in my job (academia) who don't exercise despite the huge potential benefits to their productivity and life. So this makes me wonder: what is it about exercise that turns people off? Is it a communication issue? Is it the lack of confidence? Lack of knowledge? It seems that there are constant pushes in the media to be more healthy and exercise but it never seems to stick.
Why does my doorknob need to be connected to the internet? Does my fork need to be connected to the internet as well? How about my shelf? Or my towel?
And if they are connected to the internet, who is collecting that data? Is it secure? What will it be used for?
I hate when theorists take some abstract crazy idea and then say the universe has 10 or 11 dimensions when they have no basis for saying that.
But yet, there isn't a crisis in physics at all since these theorists are so far removed from reality, I don't really care what they think. They don't really tell use anything useful or interesting so I tend to ignore them. Instead, I focus on things we do know exist but cannot explain, say astrophysical jets, pulsars, or supernovas. We know they exist and we can see them, yet we understand them very little. We have models that are getting better and better over time, but they all exist within the current understanding of physics. This is where physics really is. Whatever garbage the theorists put up on the arxiv can be ignored with little loss.
Instead, those of us "in the trenches" can continue our work trying to explain observed phenomena with our current theories. There is no need to add in extra dimensions or cohomology. Maybe, when we've done really understanding our current theories can we talk to those theorists again.
Incidentally, since I started my PhD in physics doing numerical relativity, my views on science have changed completely. I used to be interested in stuff like string theory, but actually sitting down and trying to do it left me feeling empty inside. Now that I work in an area that is very closely related to observations, I feel like I am actually learning something about the universe. It's hard to explain philosophically, but I really believe in experiments as the guiding principle of science. In my case, we see pulsars (2500+ of them) and we have yet to provide a full explanation of their nature. To me there is something more real and scientific about this then trying to explain multiverse theory but I don't know the words to describe it.
Saying that, there is one book I like called Quantum Processes Systems, and Information by Schumacher (who coined the term qubit) and Westmoreland since it is an introductory text and has a good discussion of the basics of quantum computing. It does, however, assume you are a physics student with a good understanding of linear algebra.
I am reminded of the following story I experienced in my first year chemistry class. The class was being taught by the head of undergraduate studies for science and he asked us (a room of 500 students) how many people wanted to become chemists and maybe 20 or so people put up their hand. How many people want to become physicists? Maybe 30 or so put up their hand. How many people want to become doctors? A good 400 people put up their hand. He then said "only 20 of you will make it to med school, I hope you have a back-up plan."
The problem is that we only hear about the success stories not the vast amount of people who fail. That isn't to say don't follow your dreams, but be realistic about them and have other options available when things don't go your way.
Additionally, I wonder if he is doing this on person to make a point about drug pricing in the USA.
This doesn't surprise me since bouldering problems, as discussed here, are puzzles, akin to programming puzzles, where the solution is often some clever trick that, once known, makes a problem easy.
And no FFTs are the only transformations I am aware of. I've never heard of anyone using other transformations in a general numerical context, outside of specialized problems.
I highly recommend Spectral Methods in MATLAB by Trefethen (who someone mentions above) for a very good tutorial. You can freely ignore the MATLAB part and use whatever programming language you want, as long as you have an FFT routine.
The problem I've found with assignments though is that people copy and cheat. Many times someone will do very well on assignments and then do absolutely terrible on midterms and finals. It's very frustrating. I remember one course where everyone did nearly perfect on the assignments and yet the final and midterm followed the standard bell curve.
One application I really like is in machine learning: the eigenface algorithm.
And as for TAing, have you ever TA'd? You definitely get a feeling but I can count numerous times when I've stood in front of the tutorial class and asked if there are any questions only to get no response back. I think it's a symptom of first years. I've TA'd calculus as well and I get similar responses. It's very frustrating sometimes.
As someone who has used linear algebra almost every day in some form over the last decade, it's hard to get a perspective of what aspects are challenging to the beginner. And since I TA courses that involve linear algebra, it is good to know where the problems are.
But if you claim to violate the conversation of momentum, everyone is going to be skeptical and not believe it. We have hundreds of years of experiments and observations that support the law and have looked in many places from small to large and not seen violations. This is what makes people not believe it and thus physicists are going to assume you are wrong and not physics. It's not so much a negative concern, but more of a practical one. But should it be tested in a rigorous manner and reproduced, then physicists will believe it. It's just it hasn't and thus we are going to stick with the established very well understood and tested theory. Like are you sure you have properly counted all the initial momentum? Are you 100% you are not introducing energy to the system? The possible explanations is long and a good experiment will eliminate as many of these as possible.
As an example, look at the OPERA experiment which found to have superluminal signals. New physics? Nope, just a faulty piece of equipment. BICEP showing gravitational waves? Nope, just poor data interpretation and neglecting interstellar dust. So if you want to claim new physics, be damned sure you have ironclad proof.
Also because we know how much material is released in a mrger and how much material there is in our galaxy, we can work out how frequent neutron star mergers are and these results agree with other independent estimates of frequency of merger.
My Master's degree was entirely paid for and I actually made money. I wrote a thesis that contained original research and published a paper with my supervisor on the research. This is awesome. It's a 'PhD-lite'. It showed me how to do research and whether or not I would want to continue on with a PhD.
It's a fun recreational mathematics thing, but unfortunately I've never come across a problem where I need to solve Fibonacci insanely quickly. However I still keep my hopes up!
But, as others have said in this thread, there are drawbacks, which have been addressed. But that's true of anything anywhere.
So overall I highly recommend Germany for studies. Plus German is just a cool language to know as well.
The huge amount of libraries for Python, C, C++, and Fortran make them the obvious choice.
Plus functional programming paradigms aren't always the best to do scientific programming. It can be done, but it's really not the right tool for the job, in most cases.
I'm not. Consider all of physics. Physics is written down in terms of differential equations. You need calculus to get these equations. In terms of graphics, for example, are you magically creating only static images that never change in time? How do you think people came up with the algorithms to do things like refraction or reflection? These all involve calculus. Calculus is the most important tool in applying mathematics to the real world. It is how we derive the models for pretty much everything I can think of. Any time you want to model something where anything changes, that is calculus. Any time you want to find an optimal solutions, that is calculus. I can't think of a single area of applied mathematics that doesn't use calculus in some form. Even mathematics in general, calculus is used in some form pretty much everywhere in some form, except maybe in the foundations of mathematics like set theory or logic.
Solving them, on the other hand, is a different problem. This is where linear algebra is important. When solving an ODE or PDE, when I discretise it, all I am doing is re-writing it as a giant linear algebra problem. Quantum mechanics, for example, is dedicated to finding the eigenvalues and eigenvectors of the Hamiltonian. Linear algebra provides the tools to solve the problems posed by calculus. But it isn't always required.
In fact, if you look at the history of linear algebra, it only really became wide-spread when quantum mechanics was developing since there is a deep connection between linear algebra and quantum mechanics. Heisenberg had never heard of a matrix before despite discovering Heisenberg matrix mechanics. He was told by Max Born that what he had been doing is actually this thing mathematicians called "matrices". Now linear algebra is a required course for physicists (incidentally, linear algebra was the first lecture I ever attended at university).
So I would argue that learning calculus is the most important thing someone should know mathematically, since it is the tool we use to build models. The second most is linear algebra since it provides us the tools to solve these problems. But in my mind, knowing how to derive these models is a lot more important than being able to solve them. That and linear algebra doesn't give you any insight into why we are solving the problem that way, it is just a tool to solve the problem.
Also in Calculus 1,2,3 and so on, you learn increasingly more complicated techniques of calculus to solve more problems. But when you start numerically solving them, linear algebra doesn't care. It doesn't care if your equation came from the Einstein field equations or Newton's second law. It's all the same to it. So in a sense, I can teach you everything you'll need to know about linear algebra in a single course but the same is not true of calculus, which requires multiple courses.