Khaltazar wrote:

namealreadytaken wrote:

Khaltazar wrote:

I feel like for sure ... Linear Algebra should not be required to become a computer science major.

Linear Algebra is used in computer games. How do you rotate an object? How do you make things move? It all comes down to Matrix transformations. Linear Algebra is also used in designing Artificial Intelligence (along with statistics), and an important mathematical tool in

the area of computer security. Linear Algebra makes it easier to solve certain problems, and the problem is more intuitive.

Linear Algebra is also used extensively in engineering, when solving systems of equations, and also has important applications in game theory.

I know it has it's purposes, but not everyone wants to get into fields like game programming or theory, etc.

If you want to understand politics (elections and congress voting on bills) you need to know the basics of

**game theory**. Maybe not a full course, but a couple hour coverage is pretty useful. I live in a democracy that has a lot of problems that are easily understood with game theory. If everyone knew game theory, we would probably fix congress already.

A basic grasp of the concepts of

**linear algebra** is great for reasoning about, and explaining common things. Spaces (a nice explanation here:

https://www.youtube.com/watch?v=q6iqI2GIllI&feature=youtu.be) for example are a great concept for reasoning about just about any collection of things with properties, or sets of choices. Orthogonality (

https://en.wikipedia.org/wiki/Orthogonality#Statistics.2C_econometrics.2C_and_economics ) is another fantastic tool for tool for reasoning. Again, you only really need the concept which should take more than an hour and it can change how you thing about things for the rest of your life. I think of most things in these terms: knowing them really changed my life in ways that were not obvious for years. (On the topic of fixing congress, we need some organizational of legislation on unrelated parts of the issues space to reduce the scope of problems like brinkmanship that are easily explained by game theory. See, applicable!)

The subset of

**calculus **thats really useful to just about everyone can also be covered in probably 10 minutes or less if done well (I explained calculus to someone about to drop out of highschool just fine in a couple minutes: he found it a neat and simple concept), but likely a bit more for it to really stick. All calculus is is working with rates of change. Lots of things change with respect to other things (such as world population, or the number of manga champers published changing over time). The concept of derivatives and integrals are trivial and useful: its only computing them that's hard and there is software to do that for you (but you won't need to compute them anyway usally). (And congress should pass their darn spending laws as rates instead of yearly budgets. That would fix the whole shutdown nonsense and be easier to reason about)

If you have a decent intuition for calculus, you know what it means to get a 5% return per pear on your investment, or that a city is growing 10% per year. For that last one, you know that the city is screwed and its gonna end up a logistic curve or something like it, and you can ponder whats going to cause that... The same thing (and understanding of

**exponential growth**, which falls easily of of calculus) provides great intuition into spread of disease, spread of popular memes and videos, and the increasing power of computers (and now long and if that can continue). (Oh, and it would help you understand the relationships between inflation, saving, and dept easier, including that pesky federal dept)

The first things you learn in

**statistics** about correlation and causality and various types of errors provide a great understanding on on the misleading studies published all the time. Sampling bias and multiple testing issues are probably the most important. Personally (since i'm a bit crazy) I find knowing the central limit theorem super useful for any time you know something about some subset of a group, and are interested in how much more information you need to make accurate inference: I watch 3 random shonen shows. If I want to estimate how good the genera is with double the confidence I need to watch 6 more (double the accuracy requires the square of the sample size approximately assuming some details I'll omit, but given that actual content there, assuming an approximately normal distribution is bullshit for that one).

**TLDR**: I really think most people should spend a few days learning about higher mathematics. The available classes generally suck at this and make you do a ton of useless work to get that little bit of great understanding. The internet is full of great resources though: remember you don't need to be able to do the math, instead you need to be able to apply the concepts to your reasoning. And as a bonus, knowing what those concepts are called enables you to explain things easily in those terms, and lets you look up properties that apply when you need them.