# Questions tagged [education]

Referring to matters of learning/teaching computational science

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### How is the final result calculated in RK-Dopri(4,5)?

I have found a toy implementation of RK-Dopri(4,5), written in Python. I am concerned however, about line 118: y = y + h * (b1*K1+b3*K3+b4*K4+b5*K5+b6*K6) Has the ...
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### What is a dense ODE system? What is a sparse ODE system?

Can you provide a jargon-free (as much as possible) explanation of what is meant by "dense ODE systems", and "sparse ODE systems"? Some hints I have gotten from Googling: dense ...
227 views

### Evaluation of slope at iteration ith - Newton-Raphson method

I'd like to know how Ansys computes the slope (=stiffness matrix) at point x1 in figure. I'm studying the way in which Ansys uses the Newton-Raphson method when there are nonlinearities. In the slide ...
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### References in Scientific Computation for a Computer Science Undergrad? [duplicate]

TLDR: What references and pre-requisites are necessary for a Computer Science Undergraduate to get ready for a Masters and Career in Scientific Computation / Computational X For a Computer Science ...
312 views

### Easily understandable argument that normal Runge–Kutta methods cannot be generalised to SDEs?

A naïve approach to solving stochastic differential equations (SDEs) would be: take a regular multi-step Runge–Kutta method, use a sufficiently fine discretisation of the underlying Wiener process, ...
124 views

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### Scientific computing vs numerical analysis

I'm a double major in computer science and mathematics. I love both subjects. I'm thinking in taking a graduate career, perhaps in scientific computing. What's the real difference between scientific ...
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### Mathematical error when attempting to represent step function using fourier series

I am attempting to work through a very simple problem. Determine the Fourier series expansion for the following heat PDE problem with ICS and BCS: $$u_{t} = \alpha^2u_{xx}$$  u(0, t) = u(L, t) =...
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### Do you spend time reading pure math books as a graduate student on computational math

I am going to start my first year of a research-oriented master program on inverse problem. From what I know, unlike pure math students, applied math students usually don't spend the first year ...
108 views

### Practices to convert computer algorithms to matheamtical notations [closed]

First, an example: Given an image (2D array) to write down a mathematical notation for the function of pixelation, for example. Fig. 0: The pixelated version (right) of the given 2D array (left) ...
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### Is there a reference-level implementation of BLAS in C/C++?

The netlib BLAS implementation is an excellent reference, being mostly un-optimized and well documented (e.g. zgemm). However, it is in Fortran 77, making it somewhat inaccessible to those with a ...
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### simple MHD simulation code for (self) education and play with

I would like some super simple computational code for solving magnetohydrodynamics problems. High accuracy nor performance is not my concern. I wan't it just to visually explore qualitative behavior ...
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### Do I need to learn C?

I am a PhD student in Scientific Computing and over the past few months, I spent a good amount of time learning Python and C++ the right way. I feel that I have learnt C++ well and I can use Python to ...
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### Is computational science recommended as part of the typical undergraduate curriculum every computer science department should teach?

Computational science remains uncommon in many computer science departments, particularly in universities without an engineering school. Is it not considered part of the standard computer science ...
206 views

### Difference between Computational science and Computational X (X = some natural science or discipline)

Where is the divide between a computational scientist and a computational X (X = some natural science or discipline)? What questions could someone ask themself to decide which is the best route for ...
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### Recommendation for a python book for data processing

I've been doing FORTRAN programming for 10 years and I've started using python for a few years now, mostly for data processing. I've been lucky enough to work with people that are knowledgeable ...
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### Does Computational Science involve programming?

I read about computational science on Wikipedia, but my understanding is not very clear. Does computational science involve programming? How different is computational science from computational ...
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### How are collisions detected in simulations?

I want to understand how does the simulation identifies and models when two bodies are colliding with each other. For example car crash simulation. The car moves towards the wall or another crash. ...
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### Priorities for learning computational methods, when should I write my own code vs. using libraries as a beginning graduate student?

I am beginning my graduate studies in engineering and will be working on computational science projects. I noticed that there has been some discussion about the advantages and disadvantages of ...
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### Universities known for computational physics

I am very interested in computational physics and it is great lot of fun studying these topics. Since I am planning to go one semester abroad, I was wondering what universities are known for ...
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### How can we evaluate performance of students in computational science courses?

As someone who has to teach courses in computational science, I am confronted with the age-old question: how do I evaluate the ability of the students to learn a subject that depends on applications ...
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### Power series approximation for any function such as $-e^{x^{2}}$ in some easily-accessed open-source software?

My comrades repeatedly encourages monotonous problems where the issue is the same: chain-rule and some basic arithmetic. Is there some computational way to derive power series approximations? Suppose ...
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### What core skills should every computational scientist have? [closed]

Every scientist needs to know a bit about statistics: what correlation means, what a confidence interval is, and so on. Similarly, every scientist ought to know a bit about computing: the question is, ...
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### Is there any open-source or easy-to-access software that can simplify algebraic expressions like $x^{2}+2x+3, x=\sqrt{2}t-1$?

I always calculate things by hand, but now my comrades are getting nasty and making a lot of repetitive exercises involving just plugging things in like the expression above. I am particularly ...
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### How effective is the 'tendrils of knowledge' approach to Comp. Sci?

I was reading this on Math SE. The basic question is : Assume that someone wishes to study something advanced; one way to do this would be to start off from basics and build up. But the "bigger ...
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### Is it preferable to concentrate on studying math or computation?

Concurrent to my research on Krylov Subspace Methods, I have the option of exploring mathematics behind HPC a step ahead or the theory of computation (hardware, OS, compilers etc.). Currently, I know ...
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### Introductions to hp-FEM

do you know good introductions into or surveys $hp$-adaptive finite elements? In particular I do not know how the heuristics for choosing spatial refinement or increased polynomial degree are ...