For a paper I'm writing: What's your math background?

[Skrasms]

I'm writing a detailed paper about phase and how to predict/manipulate phase problems with audio. I'm trying to go into as much detail as I can, including the math behind *everything*. The problem is, I don't really know what kind of math backgrounds most people have, but I want to make it accessible to as many people as I can. I'm trying to get some ideas of what areas will need more explanation. Here's a list of some math concepts:

2-Dimensional Graphing
Trigonometry
Vectors
Algebra
Calculus
Phasors (the math kind)
Phase Angles
Frequency Response
Time Shifting
Frequency Scaling
Complex Exponentials

Which of those haven't you seen before? What have you heard of, but never really learned? etc
Don't be concerned if you've never heard of a lot of them, a lot can be simplified into combinations of other concepts for the sake of my paper. I'll also have plenty of audio and illustrative examples of everything.

[8th_note]

The only class I flunked in College was Calculus. I don't know what a math Phasor is unless it has something to do with Star Trek. The rest of the stuff on your list I'm pretty sure I could make sense of.

[Professor]

Oh, I think you'd be safe to figure on explaining all of those terms. There are some folks 'round these parts who were EE majors, but there are probably many more who are musicians that just barely made it through the 'math for poets' class.
As for me specifically, I'm an oddball... and there are few others of us around here. Before going to the conservatory I was a Mech. Eng. major at RPI, and went through Calc I & II among other things while I was there. So I'm pretty comfortable with that. I've also been toying with the idea of a short article on the confusion of "phase" vs. "polarity" so I'd be interested in where you're heading with your paper there too. No, not to steal it, don't worry. I'm thinking more along the lines of a 1-pager in TapeOp or a similar magazine, and I can't tell if you're talking about something for course work, or something aiming for an AES presentation.

-Jeremy

[Skrasms]

I've also been toying with the idea of a short article on the confusion of "phase" vs. "polarity" so I'd be interested in where you're heading with your paper there too. No, not to steal it, don't worry. I'm thinking more along the lines of a 1-pager in TapeOp or a similar magazine, and I can't tell if you're talking about something for course work, or something aiming for an AES presentation.

-Jeremy

Don't let me get in the way of that, I think phase vs. polarity is something that can't be stressed enough lately.

I'm putting this paper together mainly for the writing practice (I'm in my 4th year of EE myself). I've been doing experiments with phase on my own for a couple years now, and I think it would be useful to people to see how comb filtering works, what uniform phase shifts actually do to phase problems, the difference between time shifting and phase shifting, and so on.

Trying to get all the math in without making it impossible to read is the hardest part for me.

[Phiz]

Some relatively famous science author (Roger Penrose? Stephen Hawking? Richard Dawkins?) once said something like, your readership decreases by 25% for each equation you use. I may have the percentage wrong, but you get the idea.

I would try to use a minimal number of equations, unless your goal is to prepare people for the quantative analysis of phase issues. Making the paper accessible to as many people as possible, with the goal of giving them a working knowledge of the concepts, would be better served with lots of diagrams and examples.

And to actually answer your question, I am experienced with all the concepts listed.

[Skrasms]

Right now I have it split so that it's going to be a paper full of diagrams and examples, and a separate math reference section. That way a person can understand the results of the math without needing to wade through it, but it will still be available if they're interested.

[;ivlunsdystf]

Calculus, intro physics 2 semesters, plus the trigonometry and whatnot ... but I will not read papers on acoustics because they bore me (personal preference) which is perhaps why my recordings sound like they were made in somebody's sinuses...

[Knights Who Say Neve]

Oh, I think you'd be safe to figure on explaining all of those terms. There are some folks 'round these parts who were EE majors, but there are probably many more who are musicians that just barely made it through the 'math for poets' class.

-Jeremy

How did you do in your "Poetry for engineers" class? Just barely make it?

[vsr600]

i'm curious as to why you need calculus to explain phase problems in audio. I understand the other stuff, especially complex exponents (cause that number next to the i in the exponent is the phase) but why calculus?
I'm a physics grad student getting a phd in acoustics (or at least trying to), i can help with your research probably if you need it....

[Professor]

How did you do in your "Poetry for engineers" class? Just barely make it?

Yea, though I did make the attempt
it seems my meager mind
could only fathom prose...

-sigh-

yet still I try
I wish
I hope


-J

[AGCurry]

I made it through three semesters of calculus in college, with As and Bs. I had to take them for my major in Computer Science, although the only thing I've actually used calculus for is in figuring out algorithm efficiencies, which is something I've never seen done in "real life."

Generally I don't pay much attention to math in documents unless I have to.

[JASIII]

I did terrible in algebra I in high school. Got "C"s in intermediate algebra in college. all the rest of the things on that list I don't know one thing about.

[MoreSpaceEcho]

i am pretty good at rudimentary everyday math, calculating tips and stuff like that. but as soon as there are letters involved in the equation my brain shuts right down.

i don't find this hinders my work though. as a drummer i only need to count to 4. and really, you can cheat and just count to 2 twice as often.

[Professor]

Trying to get all the math in without making it impossible to read is the hardest part for me.

Funny thing is, this is really where a class like "poetry for engineers" would be a good idea. One of the hard things most technical folks encounter is how to share their knowledge and ideas to a non-technical audience. And that's not just in the engineering & scientific fields either. I've had music teachers who had dug themselves so deeply into theory and the technical language of music that they could barely communicate their ideas to music majors who were not at a high enough level. And it's probably no surprise those were the folks tasked with freshman theory class.
Technical writing is a challenge, but it's also something worth working on doing well. I was lucky enough to receive a book as part of an award my senior year in high school (as it happens it was a math award) entitled 'Up the Infinite Corridor' written by a past president of the MIT. I can't remember now if he addressed technical writing/speaking and jargon directly or if it was just something I picked up from the style of the book, but it really helped me early on to see some of the pitfalls there. And when I arrived at RPI and began encountering the teachers who could really communicate vs. those who were incomprehensible, it showed me where I wanted to land regardless of what career field I might happen to arrive in.
What will be tough for you is gauging your audience. If you're writing with the intent to publish in the AES or IEEE journals, then you have to maintain a level authority and technical detail just to make sure they consider the work scholarly in nature. But then it's nice when the article is approachable enough for those who would most directly benefit from the concepts to absorb them without being confused or put off by proofs & equations. It sounds like you'll have the text and the charts & graphs, and then follow those with the more heavy tech stuff, and I think that sounds like a great approach. And I look forward to reading it.

-Jeremy

[Skrasms]

i'm curious as to why you need calculus to explain phase problems in audio.

I was originally considering it for the sake of explaining Fourier Transforms and Frequency response, but now I think that's going a little too far with detail.