How to improve math skills?

[Krice]

Finally, if you think programming is about mathematics, you are wrong. It's about abstraction.

This thread is about how to improve math skills, so it's a specific topic only for mathematics. While some things you say is true you should calm down and put your opinions in another thread. And you should probably not forget to take your medication.

[Soulmask]

The thread might be on mathematics, but this subforum is about programming. You said you wanted to improve maths because you needed it for programming. I was exactly answering that. I'm the second person that tries to help you you tell to calm down in a very short span of time. You should probably go on a math forum, and hopefully after reading 20 math books you'll realize you ain't better at programming.

[mushroom patch]

re: the offending formula on wikipedia:

That's indefensibly badly written, especially for a general audience. Use of that carrot notation for "and" is not widespread even in the mathematics literature. It just shouldn't be there. Unfortunately, wikipedia articles on mathematical topics that can be easily grasped by people outside of the research community are plagued with this kind of garbage. It gives the half-educated a sense of accomplishment to write expressions like that.

I was planning to be subtle but the way you insult people while saying incorrect statements is just too much. You imply that the notation for carrot AND is not widespread. Not only it doesn't matter at all, but discreet mathematics use it. Arguing about correct notations is like arguing over the best color. You refer to people outside the math research community has half-educated and laymen while calling a notation garbage. It is you who is trying to give yourself a sense of superiority over futile things, and not only that you're insulting everybody else in the meantime. You are criticizing the method rather than the concrete content. Especially in programming, many different ways can achieve the same thing.

I was planning not to read your posts, but I noticed you quoted me. It's not incorrect to say that actually writing the word "and" is better than "^" in that formula. Wikipedia targets a general audience and the page in question is one that deals with an accessible topic of general interest. It should use transparent notation where it can and in this instance, it obviously can. The purpose of notation is to communicate. Using a notation that is seldom used outside of certain subfields of mathematics the reader most likely isn't familiar with is bad practice when a plain English alternative is available.

I assure you, it gives me no satisfaction to compare myself favorably to random people on the internet. I do not refer to people outside of the mathematics community as half-educated, I refer to the person who chose that notation that way. I could be wrong, but I doubt it. As far as my characterization of wikipedia editors, obviously many of them do good work on mathematics articles, but those who do almost uniformly hold or are working on advanced degrees in mathematics. Unfortunately, many people with a programming background, perhaps yourself included, consider themselves experts on mathematics (and a surprising number of other areas as well) and cry "elitism" when anyone tells them otherwise. Their sheer numbers in "geek" communities tend to drown out other perspectives, but on wikipedia in particular, this dynamic tends to dominate articles that a nonspecialist is likely to understand and approach, to the detriment of the project as a whole.

[Soulmask]

Oh I don't consider myself an expert in math, merely half-educated, as I only had basic engineering math and statistic classes. I'm glad that your last post is much more reasonable than the one I quoted, seems like you're a reasonable person after all. Indeed, discreet mathematics could be called a sub-field, but's it's also one of the fields of mathematics that influenced computer science the most, especially in the early days of computing theory. It uses many symbols, and cluttering formulas with 3-letter notations like AND would make already big formulas too big in the end. Indeed the more "pure" mathematical circles might not use that notation, but in their own subfield they use it exclusively, and would find the use of and in their formulas as otherworldly as you do ^. In my opinion, the use of one character that is included in the default 255 ascii character table and doesn't mean anything else than and is the correct way to to write it, especially for computer science subjects since discreet mathematics is useful for "computer algorithms, programming languages, cryptography, automated theorem proving, and software development."(from wikipedia)

[mushroom patch]

The formula I criticized was not complicated enough to need specialized notation. There may be contexts where using notation denser than "and" to mean "and" is warranted, but this was not one.

[Krice]

You should probably go on a math forum, and hopefully after reading 20 math books you'll realize you ain't better at programming

Well if you want to go that way I will explain you that being quite bad at math myself has made me a worse programmer. It's really simple actually. Even if you try to think programming as "not math" you still need to implement various types of algorithms.. which.. as a word may sound familiar in math context, because it is. My opinion can go as far as to claim that everything in programming is math, most people just don't think it that way. Whatever the case I know for sure that the more I know about math the better I am as a programmer, because it's probably the only area of programming where I need to be better.

[Eudoxus]

maybe "&" would have been a good middle ground between "AND" and "^", and it's perfectly fine in research papers (I've seen all three in many different branches of math).  then again, I think it's cool and helpful that the logical-and and the logical-or symbols look similar to the union and intersection symbols...

[mushroom patch]

. . .

[Krice]

For example I have linear falloff (or is it just an interpolation?) for light sources, but I think it would be better to have more "unrealistic" falloff where the brightest light covers more tiles at the beginning and then drops fast to darkness. I think it's something like cubic falloff (or inverse cubic?). However my lack of math skills makes it quite difficult to understand how to change the linear falloff (in interpolation) to what I need. I've tried to search the internet, but every subject related to falloffs seems to cover only 3D rendering software light falloff settings.

[reaver]

Let's say the light intensity at the light tile is I. Let's say you use linear falloff: for a distance "x", the light reached is I - kx (k is some factor you decide). Of course that's quite intuitive, but the results are un-great.
A much better formula which you can try at your heart's leisure is this:
1/(1 + a*abs(x) + b*x*x)
( Interactive link here -> https://www.desmos.com/calculator/nmnaud1hrw )
where x is your distance, and factors a and b you decide to get the shape right. What it calculates is the attenuation of the light, so you multiply that to "I". This formula approaches the "physically correct" way of calculating light falloff with distance, but it's very tweakable and practically better. Go wild and light the world on fire now.

[Krice]

This formula approaches the "physically correct" way of calculating light falloff with distance

I don't want that. I want the opposite! I know light intensity decreases by the square of the distance, but it's not practical in a tile based lighting routine.

[reaver]

You do want that. You don't want the light intensity to increase with distance, right? Now stop whining and use the bloody formula, and tune it to your heart's desire to make it as unrealistic or realistic as you want. Seriously.

[Krice]

It doesn't work. What you want is the light intensity at a certain area stays the same, otherwise it looks bad if only the light source tile itself has the brightest value which then drops to whatever rate right after that.

[reaver]

Here's a pro-tip: use the same function form, multiply by a value HIGHER than 1 and clamp it to 1 (link below). Voila, you can have the same maximum light on several tiles. There are several ways to do what you want, you are presented with one but you refuse to use a brain cell to see how that works for you and how you can use it to your advantage.

Look here and feel the magic of clamping: https://www.desmos.com/calculator/lopuoqdpms

[reaver]

You can also use this:

https://www.desmos.com/calculator/v3hs2592pp

This is pretty much the smootherstep function (http://en.wikipedia.org/wiki/Smoothstep). It's a typical, nice function to get smoothly from 0 to 1, by determining two edge points ("a" and "b" variables in the graph in the link above). Again, if none of these cover you, I'm at a loss.