[QUOTE=JohnnyMo1;50860284] Algebra: Chapter 0 [/QUOTE]
How's that book? If you don't mind me asking.
[QUOTE=Lucasz;50877746]How's that book? If you don't mind me asking.[/QUOTE]
Very good, imo. Category focused, tons of exercises, and his writing style is pretty funny.
[editline]13th August 2016[/editline]
I think it's becoming a very popular second algebra text these days.
[QUOTE=x2yzh9;50876398]This is going to be a tough one..And for good reason. Disclaimer: I don't even have a high school diploma. I have a GED and have passed a college course or two, I've just done a lot of independent study over my life and self-stimulation.
Alright, so from my PoV what your trying to say in lehmans terms: Is that while these 3 axis all have a distinct velocity corresponding equivalently so with eachother, what you're trying to do is eliminate 2 of the axis and correspondingly extend/boost the one dimension you have left, to a certain point in space-time.
I'm not sure if geodesic is the right term but what your trying to convey is a one dimensional segment through space, correct? Well, keep in line, space and time are connected-There's no denying that. So conversely, there will be an equal reaction to your elimination of the 2 dimensions with their respective velocities before hand. Now, when you extend that one dimension, this stretches that reaction, along with, I assume, other things. This has to do with Question #1:converting the spatial event into a polar opposite system which time will not apply to it. There is a fallacy and a truth in that, with respect to duality.
And that's that you basically have to circumvent the loop here. The only possible way that I personally could think of to do that is to say that when your doing this, you are in fact re-inventing the wheel. And that my friend is not a bad thing. There's an assumption that relativity is absolute because it is absolute, it's just no one can perceive it as Einstein had been able to perceive it. That's why we can't disprove it nor prove it any more so. He understood all these concepts like we know how to connect two and two, and I suppose he withheld those techniques of understanding for good reason! That's my personal opinion but I really hope I have helped because I feel like this has gone on to a rambling conjecture. Uh, let me know if you'd like any more input![/QUOTE]
May I ask what your source for self-studying special relativity was?
[QUOTE=JohnnyMo1;50877762]Very good, imo. Category focused, tons of exercises, and his writing style is pretty funny.
[editline]13th August 2016[/editline]
I think it's becoming a very popular second algebra text these days.[/QUOTE]
Sweet, I'll add it to my reading list. Thank you
So, I was thinking long time ago about partially applied derivative operators, and today I discovered theory does indeed exists!
There is function y=x jumping between derivative and anti-derivative
[IMG]https://upload.wikimedia.org/wikipedia/commons/a/ac/Fractional_Derivative_of_Basic_Power_Function_%282014%29.gif[/IMG]
It's called Fractional derivative.. theory is quite complex tbh.
Is it possible to define a fractional derivative as a limit?
Dunno, you ask me too much, but there are limits involved as far as I have seen, but also gamma function.
Look up "fractional calculus", it's quite advanced, and has some weird applications with signals/waves.
[QUOTE=JohnnyMo1;50877580]Sorry, I think I have to be a little harsh here for a second: that was all ramble.[/QUOTE]
..Yes, indeed it was. I'll come back when I have what I was trying to say a little more thought out and uh, understandable.
[url]https://www.coursera.org/learn/complex-analysis[/url]
Complex analysis course starting soon. Also, it's one of the good ones where you can audit and do everything completely free. You don't need to pay to submit assignments or anything, just if you want the verified certificate.
Cool, thanks for posting this. I enrolled, seems interesting.
Has anyone here ever read Concrete Mathematics: A Foundation for Computer Science (2nd Edition)?
I am thinking about reading it since I am a big fan of Discrete Mathematics, but I am not that advanced in it.
How advanced do I need to be in mathematics in order to understand this book?
I became interested in Discrete Mathematics after taking a course at university.
I have also taken two calculus courses and one probability and statistics for engineers and scientists course, although I was pretty bad at probability and statistics, to be honest.
The Discrete Mathematics course was one of the most fun courses I have taken at university, so far.
Just start reading and if you do not understand something, look it up on internet, understand it and move on.
Expect to read 1 to 2 pages a day at first before you become familiar with it.
[QUOTE=Fourier;50921081]Just start reading and if you do not understand something, look it up on internet, understand it and move on.
Expect to read 1 to 2 pages a day at first before you become familiar with it.[/QUOTE]Oh, I'll probably do that.
I've got several CS books that I'd like to read before this one, though, but I'm definitely going to read it.
Thanks for the advice! :smile:
You can also skip pages if you feel like it, but you might not understand something later.
snip, solved it.
Learning Fourier Analysis were hard, specially when you have less then four weeks to learn the entire course.
But the worse part is now waiting for the result and not sure if you did good enough... its killing me.
What do you guys think about how people who have more trouble learning mathematics should handle it? In my uni, I am with a bunch of engineering students in the same classes so as you may expect, mathematics is an extremly important subject, and it is taught not at all superficially. The difficulty plus the pressure is clearly taking a toll on my friends and girlfriend, and the semester is unforgiving.
I don't have much trouble due to do nothing but study for like a solid year, I don't think that will last much longer though. Given that, I try to help as much as I can, but I don't see what is going wrong for some of them, they just study so much and I try to explain to the best of my abilities to help them and they still don't get good or satisfactory results. And that clearly affects some of them.
I don't know, I'd like to discuss what happens to the people that have real trouble learning maths, mainly because they may have a bad base back on school. I'm convinced that anyone can achieve the level they aim for with enough focused work, but, how much is enough?
[QUOTE=Bradyns;50535754]Not sure if I posted it here a few years ago - but there is a problem that I still haven't solved and it runs through my head every now and again.
It went something like,
There is a series of circles; the first circle touches the x-axis, y-axis, and the function y = e^(-x), the rest of them subsequently touch the previous circle as well as the x-axis, and y = e^(-x).
What is the sum of the area of those circles?
Example, but the circles continue on:
[t]http://i.imgur.com/66QsCtf.png[/t]
The area under the curve is 1, so the sum of the areas of the circles should be less than that. The whole problem gives me a headache.[/QUOTE]
This is so late that it's not even funny, but I thought I'd check up on this thread since I hadn't read it in a while. I'm fairly certain that for this problem, we can abuse the fact that e^-x happens to be the pdf of an exponential distribution with parameter lambda equal to one. This is important because the exponential pdf is memoryless. This problem is tied to the function e^-x, because that's the only memoryless continuous function. I'm not even sure you can solve this with anything else but another exponential pdf.
So to put the properties of memorylessness into geometric terms for our use here, if we consider any point along the positive x axis, s, and consider the function to the right of it, this is our original function from [0, inf], but scaled down by a factor of e^s. So say we have the radius of our first circle, R, and its area, A. The area of the second circle is going to be the same as our first circle by that same factor.
[IMG]http://imgur.com/e2Cy4XX.png[/IMG]
And inductively, it's not hard to see that
[IMG]http://imgur.com/IynG17S.png[/IMG]
Where we have A_0 = A
So the sum of our circle sizes becomes
[IMG]http://imgur.com/3lb361Y.png[/IMG]
Now, interestingly enough, the denominator of that equation is the actual area that our original circle is encased in. It's the area under the curve on the domain [0, 2R].
At this point, it's annoying. I think I found R after doing a little bit of work, but it came as the root of r = e^(2r) or something. I'm not sure if you'd want to minimize the distance between e^-x and the origin, or try to maximize the ratio presented above. I also tried
setting the upper portion of the circle equal to e^-x at some point, and setting their first derivatives equal, but it became an annoying system of equations.
Been a while since this thread saw any action, so here's a little boost: Tom Leinster's [I]Basic Category Theory[/I] was released free on arXiv not long ago.
[url]https://arxiv.org/abs/1612.09375[/url]
I'm working through it in preparation for algebraic topology this semester and it seems quite nice. Some naive set theory seems to be the only real prerequisite so far, with a fair amount of algebra and topology as well if you want to get the most out of all the examples, of which there are quite a few.
Got through the first chapter today. Seeing that group and semigroup actions and representations can be seen as functors from one-object categories, with equivariant maps corresponding to natural transformations between functors was really illuminating.
What's the best way to practice math outside of school? I really want to get better at it and I never really paid any attention during math class in school and because I'm majoring in Computer Science I want to genuinely get a grasp on it and not "just get by" my math classes.
[QUOTE=Exigent;51673889]What's the best way to practice math outside of school? I really want to get better at it and I never really paid any attention during math class in school and because I'm majoring in Computer Science I want to genuinely get a grasp on it and not "just get by" my math classes.[/QUOTE]
I set small goals like read a section or two if they're under 10 pages or so, and just make sure I do a little every day. Consistency is key.
[QUOTE=JohnnyMo1;51673975]I set small goals like read a section or two if they're under 10 pages or so, and just make sure I do a little every day. Consistency is key.[/QUOTE]
So should I just focus on what I'm learning in school then? I'm not even sure exactly how proficient I am in math, is there a general test or something I can take to see how proficient I am?
[QUOTE=Exigent;51674341]So should I just focus on what I'm learning in school then? I'm not even sure exactly how proficient I am in math, is there a general test or something I can take to see how proficient I am?[/QUOTE]
Maybe try [URL="https://projecteuler.net/"] Project Euler?[/URL] I haven't had time to try many of these, but those that I did attempt were lots of fun.
I like reading in [URL="http://www.mit.edu/~evanchen/napkin.html"]The infinite napkin[/URL]. It's by no means comprehensive, but rather a collection of crash courses on different subjects. Might be nice to figure out what you like.
[QUOTE=Exigent;51674341]So should I just focus on what I'm learning in school then? I'm not even sure exactly how proficient I am in math, is there a general test or something I can take to see how proficient I am?[/QUOTE]
What are you learning?
[QUOTE=JohnnyMo1;51675385]What are you learning?[/QUOTE]
I'll be taking Intermediate Algebra but I need to take that, the math above it (I forget the name), pre-calc, calc I, calc II, and Calc III
How do you guys study maths from books? Do you take notes? Do you make summaries? Do you just grab the book and use pen and paper only for excercises?
I read it on the toilet. I don't really study cause, well, I don't feel like it and my PhD is way more practical :v:
When I had to study maths for my physics degree it usually was working my way through each chapter of some maths syllabus: understanding and reproducing each proof with as little memorisation as possible (so really only memorise the non-obvious steps), then (re)make exercises. The end goal was what the exam requested, which was usually proving either something from the syllabus or something related that was similar to proofs in the syllabus. You could in theory memorise the entire course without understanding it and still pass, but that would require a photographic memory. Understanding was key for any regular student to be able to pass the exam.
How would you solve this equation?
[img]http://i.imgur.com/kRbVXRq.png[/img]
This is my attempt at a solution which is wrong.
[img]http://i.imgur.com/l7U3iBs.png[/img]
I've got an assignment and I have an idea that I believe is a viable solution. However, I've not got the faintest idea of how to translate my idea into physical results to show whether it's even feasible. It's a topic on Engineering Mechanisms, so lots of fun stuff regarding gear ratios, etc. etc. I'm an undergrad 1st year Mechanical Engineering student. The problem in question is this:
Produce a design for a lifting platform for a wheelchair user weighing 100Kg to allow them to negotiate a 600mm high step up to a raised patio area in their garden. (There is insufficient space for safe ramp). As there is no electricity available, the platform must be self-powered by use of the arms (the client has full upper body mobility and average strength – capable of exerting a force of 200N). There is no specific time constraint on the completion of the raise, although at all times the platform must remain level and the chair
secure on it (unable to roll off).
I was thinking of a hand chain hoist, or some sort of flat platform that is raised and lowered via rack and pinion. I just haven't got the faintest idea of how to calculate the gear ratios / output force that would be available to ensure I can lift the 100kg person as well as wheelchair + weight of platform which would roughly be another 30kg on top of that. I need help figuring out how my ideas can translate into a solution that can output 1,300N of force to raise the platform and everything on it.
I've tried researching hand hoists, but the only thing that comes up are either electric-powered ones or websites selling them!
How would I calculate how far away the hoist has to be from the platform to produce enough lift to slowly raise the platform?
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