What every computer science major should know (2011)

I'm not sure this is relevant to computer science, but as a mechanical engineer, I've used differential equations and topology quite a bit in my coding.

Topology has its important role in CAD and CAE softwares (particularly when dealing with manifold/non manifold objects) where it's important to understand the relation that various geometric entites have with one another (whether you're coding a tool or using one). There is also a good amount of research currently being done on automatic CAD model simplification for analysis (FEM/CFD) based on geometric simplification (various methods exist ranging from topology to fourier analysis [1]). Meshing theory also relies quite a bit on topology. [2] (but I don't think anyone denies the importance of topology in CS though)

As for differential equations and calculus, they are heavily used in FEM [3] and CFD [4] and there is therefore a need to numerically evaluate these equations in a efficient manner. They are also heavily used in controls (for instance, in a quadcopter PID controller [5]). So I'm guessing in that case, differential equations are used to describe something you're then modelling in your code through numerical integration. Numerical methods however rely both on understanding calculus and differential equations as a given numerical scheme may be more adapted to a particular type of DE than others [6][7][8][9] (sorry, couldn't find a comparaison of these schemes on a single link so I'm citing a few).

Signals processing and statistical analysis may also be used in conjunction with differential equations such as in turbulence modeling in CFD. RANS (Reynolds Averaged Navier-Stokes) equations essentially average the NS equations over time in order to locate areas of various turbulence strength [10]. LES (Large Eddy Simulation) filter small eddies out of the NS equations in order to be left with only the large eddies thus requiring less computational power [11] (the filtered eddies are modeled separately for the sake of energy balance).

Finally, I would argue that calculus is also used in optimization codes and neural networks with gradient based descents [12][13]

I hope I didn't go off topic with this post, all I was trying to say is that in some fields of computer science, you do have to come up with algorithms evaluating differential equations using numerical methods, and an understanding of calculus and DE is a definitely plus. I'm sure finance has its share of DE to model requiring their understanding.

[1] http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=7D3... or http://www.sciencedirect.com/science/article/pii/S0010448508...

[2] http://www.ann.jussieu.fr/frey/papers/meshing/Le%20K.H.,%20F...

[3] http://fenicsproject.org/documentation/tutorial/fundamentals...

[4] http://en.wikipedia.org/wiki/Finite_volume_method

[5] https://ghowen.me/build-your-own-quadcopter-autopilot/#toc4

[6] http://en.wikipedia.org/wiki/Lax%E2%80%93Friedrichs_method

[7] http://en.wikipedia.org/wiki/MUSCL_scheme

[8] http://en.wikipedia.org/wiki/Upwind_scheme

[9] http://en.wikipedia.org/wiki/QUICK_scheme

[10] http://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%...

[11] http://en.wikipedia.org/wiki/Large_eddy_simulation

[12] http://en.wikipedia.org/wiki/Gradient_descent

[13] http://karpathy.github.io/neuralnets/

EDIT: added a paragraph on turbulence modeling

EDIT 2: Optimization methods can be used to find optimal solutions to differential equations [A]. I talked about gradient descent earlier, but there's also the simplex method [B] that makes heavy use of linear algebra and topology to navigate in a solution space in order to optimize a solution.

[A] http://en.wikipedia.org/wiki/Mathematical_optimization#Appli...

[B] http://en.wikipedia.org/wiki/Simplex_algorithm

This is the reason language wars are looked down upon on HN - someones going to feel offended. Its pointless. But be reminded that ad hominem is not welcome here either. You are welcome to add to the discussion, in case you are knowledgeable in the subject. You have not done much to factually counter any arguments brought up so far, and in case your goal is to persuade anyone of your contrary position, you have done that goal a disservice.

> I've tried to answer this question as the conjunction of four concerns:

> ∙ What should every student know to get a good job?

> ∙ What should every student know to maintain lifelong employment?

> ∙ What should every student know to enter graduate school?

> ∙ What should every student know to benefit society?

I'm having difficulty articulating why, but I can't help feeling that this approach goes against the idea of education as a good in its own right; that the things that every computer science major should know are those things that are fundamental to the field, defined without reference to e.g. whether it'll get you a good job.

My degree is history, and it would be difficult to provide any sensible answers to those questions for that subject, except perhaps #3. There is an argument that studying the humanities provides transferable skills in critical thinking, which I would dispute; apart from the importance of questioning and evaluating sources, and a large pool of counter-examples for many arguments of the form "people have always done X", most of my (limited) abilities in critical thinking derive from my amateur digressions into science and logical fallacies. The only quantifiable benefit to society I can identify is the nuggets of interesting information I can sometimes throw into discussions and comment threads (my favourite being "Gandhi wasn't a pacifist and the British were bombed out of India", which I don't get to use often enough).

But a society without students of history (or French literature, or ancient Japanese ceramics) would be poorer; so would one without computer scientists, even if the field had no practical applications. Human knowledge advances best with a broad and deep body of ideas to bounce off each other. (No, I can't provide a concrete defence of that statement.)

The things every computer science major should know are those things that, if he or she did not know them, would make it ridiculous to call him or her a computer science major. Ditto for every other formal field of study.

That's a very solid book that deals with things not just restricted to 3D programming. It covers vectors, matrices and linear transformations, which are useful in other areas of Computer Science.

Although an excellent book that covers these things is The Manga Guide to Linear Algebra, by O'Reilley.

Most problems out there are probably solved in an excel sheet at present. No need for machine learning.