• Mathematician Chat V2
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[url]http://math.ucr.edu/home/baez/books.html[/url] [url]http://www.math.boun.edu.tr/instructors/ozturk/guz12m331/rud.pdf[/url] [url]http://math.ucr.edu/home/baez/Alex_Alaniz_Lie.pdf[/url] We sit together, the mountain and I, until only the mountain remains.
To the guy at the end of the last thread asking about how to get better at maths, I guess the best way is just to really pay attention in class, and then when you go home, do more questions. The only real way to learn maths, for me at least, is just to do some questions. It'd be even better if you actually did the questions after you got taught the stuff rather than a month down the track. Some people like to watch videos online if they don't understand the concept, I'm never really bothered, would just rather look it up in a book, but if you need something explained step by step that you can follow along with, then the online video stuff sounds like a perfect way for you to learn. Khan Academy Stuff and Patrickjmt are both pretty good from what I've seen. I'd give more advice if I could - I used to be heaps shit at maths in school, somehow got randomly better when I went to uni, dunno why, I didn't really try at all at school which explains the shitness then, but still don't try that much harder at uni, so really it just comes down to how you learn best, and in what environment. If you love going to a lecture/class and getting shit explained by a teacher or watching an online video, do that, if you want to self teach from a textbook, do that, or expose yourself to a bit of everything and see how it goes. I think the most important thing is to do with any method of learning though is to do a lot of example problems, and of course try not to cram shitloads of knowledge in before an exam unless you know you're actually good at it.
A great way to get good at math is find a topic you enjoy and get really good at it. So much of math is interconnected when I go back and investigate something I'm bad at it often makes sense in the context of a different subject. [editline]1st February 2012[/editline] Think I'm going to jump ahead in my real analysis textbook to the theory of differential forms. I think if I can understand that it will be a big leg up in understanding general relativity.
The below has a 100% emphasis on free resources. It is a work in progress. [B]What is Mathematics?[/B] [QUOTE=Wikipedia]Mathematics (from Greek μάθημα máthēma "knowledge, study, learning") is the study of quantity, structure, space, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof.[/QUOTE] However, the exact definition of mathematics is not concrete. [URL="http://en.wikipedia.org/wiki/Definitions_of_mathematics"]There is no generally accepted definition.[/URL] [B]1. E-Books[/B] * [URL="http://hbpms.blogspot.com/"]Pure Mathematics from Elementary to Graduate Level (How to Become a Pure Mathematician)[/URL] * [URL="http://ocw.mit.edu/courses/mathematics/"]Various Lecture Notes and Materials from MIT[/URL] * [URL="http://freebookcentre.net/SpecialCat/Free-Mathematics-Books-Download.html"]Library of mathematics books from FreeBook[/URL] *[URL="http://theassayer.org/cgi-bin/asbrowsesubject.cgi?class=Q"] Library of science, math, and computing books from The Assayer[/URL] * [URL="https://files.nyu.edu/jmg336/public/html/mathematics.html"]Online materials by New York University[/URL] * [URL="http://www.17centurymaths.com/"]Mathematical works of the 17th and 18th century in English[/URL] [sp]Linux distributions are everywhere if you know where to find them.[/sp] [B]2. Videos[/B] * [URL="http://khanacademy.org/"]Khan Academy[/URL] - Arithmetic to advanced with emphasis on understanding * [URL="http://patrickjmt.com/"]PatrickJMT[/URL] - Arithmetic to advanced, less emphasis on understanding * [URL="http://ocw.mit.edu/courses/audio-video-courses/#mathematics"]MIT OpenCourseWare[/URL] - Advanced * [URL="http://brightstorm.com/math/"]Brightstorm[/URL] - Algebra to Calculus * [URL="http://www.youtube.com/user/mathematicalmonk/videos?view=pl"]MathematicalMonk[/URL] - Probability, Information Theory, and Machine Learning * [URL="http://www.hippocampus.org/"]Hippocampus[/URL] - Arithmetic to Calculus * [URL="http://v.youku.com/v_show/id_XMTY0MjEwNTIw.html"]Japanese Video Site[/URL] - Introduction to Number Theory [B]3. Recommended self-learning through videos and E-books[/B] (WORK IN PROGRESS!! Need to find high quality free e-books for each subject, then expand to more) 1. [URL="http://www.khanacademy.org/#arithmetic-1"]Arithmetic Videos by Khan Academy[/URL] 2. [URL="http://www.khanacademy.org/#core-pre-algebra"]Pre-Algebra Videos by Khan Academy[/URL] 3. [URL="http://www.khanacademy.org/#core-algebra"]Algebra Videos by Khan Academy[/URL] 4. [URL="http://www.khanacademy.org/#core-geometry"]Geometry Videos by Khan Academy[/URL] 5. [URL="http://www.khanacademy.org/#trigonometry-1"]Trigonometry Videos by Khan Academy[/URL] 6. [URL="http://www.khanacademy.org/#probability-1"]Basic Probability Videos by Khan Academy[/URL] 7. [URL="http://www.khanacademy.org/#precalculus-1"]Pre-Calculus Videos by Khan Academy[/URL] 8. OPTIONAL: [URL="http://www.khanacademy.org/#statistics-1"]Statistics Videos by Khan Academy[/URL] Note for below: MIT OCW is recommended as main learning source with Khan Academy as review. 9. [URL="http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/"]Single-Variable Calculus Course+Videos by MIT OCW[/URL] OR [URL="http://www.khanacademy.org/#calculus"]Videos by Khan Academy[/URL] 10. [URL="http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/"]Multi-Variable Calculus Course+Videos by MIT OCW[/URL] Or [URL="http://www.khanacademy.org/#calculus"]Videos by Khan Academy[/URL] 11. [URL="http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/"]Differential Equations Videos by MIT OCW[/URL] OR [URL="http://www.khanacademy.org/#differential-equations"]Videos by Khan Academy[/URL] 12. [URL="http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/"]Linear Algebra Course+Videos by MIT OCW[/URL] OR [URL="http://www.khanacademy.org/#linear-algebra"]Videos by Khan Academy[/URL] 13. [URL="http://www.youtube.com/playlist?list=PL82AEB74C1E0435CA&feature=mh_lolz"]Real Analysis Videos by Harvey Mudd College[/URL] [B]4. Tools[/B] * [URL="http://www.wolframalpha.com/"]Wolfram Alpha[/URL] - Internet-based general knowledge engine and computer algebra system * [URL="http://www.sagemath.org/"]Sage[/URL] - Computer Algebra System * [URL="http://maxima.sourceforge.net/"]Maxima[/URL] - Computer Algebra System [B]5. LaTeX[/B] * [URL="http://www.andy-roberts.net/writing/latex"]Getting to grips with LaTeX[/URL] * [URL="http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:About"]Getting started in LaTeX[/URL] * [URL="http://www.lyx.org/"]LyX Document Processor[/URL] * [URL="http://www.tug.org/"]TeX Users Group website[/URL] * [URL="http://detexify.kirelabs.org/classify.html?"]Latex Symbol Finder[/URL] * [URL="http://www.codecogs.com/latex/eqneditor.php"]Online LaTeX image creator[/URL] * [URL="http://www.texample.net/"]LaTeX Examples[/URL] [B]6. Articles[/B] * [URL="http://www.maa.org/devlin/LockhartsLament.pdf"]Lockhart's Lament[/URL] - Essay on the state of mathematics education * [URL="http://www.artofproblemsolving.com/Resources/articles.php?"]Art of Problem Solving[/URL] - Articles with advice, tips, and other suggestions. * [URL="http://oakroadsystems.com/math/"]Mathematical articles by Stan Brown[/URL] [B]7. References[/B] * [URL="http://mathworld.wolfram.com/"]Wolfram MathWorld[/URL] * [URL="https://oeis.org/"]The On-Line Encylopedia of Integer Sequences[/URL] [B]8. Miscellaneous[/B] * [URL="http://ocw.mit.edu/donate/support-ocw-by-shopping-at-amazon/"]Donate to MIT OCW through simply shopping with amazon![/URL] * [URL="http://www.khanacademy.org/contribute"]Donate (time or money) to Khanacademy![/URL] * [URL="https://giving.mit.edu/givenow/ocw/MakeGift.dyn"]Donate (money) to MIT OCW![/URL] Contributions will be [URL="http://ocw.mit.edu/donate/individual-supporters/"]listed[/URL] in [URL="http://ocw.mit.edu/donate/individual-supporters/donor-recognition/"]tiers[/URL].
I'm in a sophomore level Intro to Proofs class as a requirement for my recently added math major. Some of the questions asked in there boil my blood. The professor wrote a definition for the least upper bound of a set of real numbers the other day. It was something like "u is an upper bound for set A of reals if u is an upper bound for A and if for every epsilon greater than zero there exists b in A such that b > u - epsilon." Then someone says, "So epsilon has to be zero." The professor says, "No, epsilon is always positive." "So epsilon is a limit?" Grguhagugughh.
Let f be the real-valued function on the unit interval [0,1] given by f(x) = 1/n if x = m/n is a rational expressed in lowest terms, 0 if x is irrational. Show directly (without using Lebesgue's theorem) that f is Riemann-integrable over [0,1] and the integral equals zero. Shit, this is a weird function.
This thread is ALREADY making me feel dumb. That has to be some sort of record. I'm trying to figure out a rational inequality. It's easy enough to get the answer, but I feel like I need a better explanation than "I drew the graph and looked at it". Anyone care to give some kind of step-by-step? (2x+1) / (x-2) < 3 The solution is 2>x>7, but how do you get to it?
I think the solution is x < 7, x =/= 2. Multiply both sides by (x - 2): 2x + 1 > 3(x - 2) distribute: 2x + 1 > 3x - 6 isolate variable: 7 > x x < 7, but since the denominator is x - 2, we can't have x = 2.
[img]http://dl.dropbox.com/u/6047805/Bilder/NerdShit.png[/img] It should be pretty clear from looking at this picture that any x value above 7 and below 2 means the whole thing is less than 3. I may have written that wrong in my last post, I'm no good with all of those fancy, mathy words when writing them like this.
You can also easily re-write it as (x-7)/(x-2)<0 and just take the solution from there. Octave's method seems to work fine though.
For anyone interested in LaTeX: [url]http://www.lyx.org/[/url] Free, powerful, and really easy to use LaTeX document processor. I type all my homeworks up with it now. :D
It pisses me off when you did a bit worse on a test than you thought, it's multiple choice and they don't give you back the paper. It's not even an important test: worth 10% of my maths module this year, which is itself only 20 credits out of 120 over my course this year. I'm in my first year, so nothing yet even counts towards my degree. Yet it's still annoying me. I'm being thick.
If 48y2 + y &#8722; 6778 = x, then what does y smell like?
panini
[QUOTE=dvc;34532005]If 48y2 + y &#8722; 6778 = x, then what does y smell like?[/QUOTE] [IMG]http://upload.wikimedia.org/wikipedia/fi/math/3/d/4/3d43df0a013f60c96d5a0bacdd53787b.png[/IMG] Just replace x with y.
"The nth term of a number sequence is given by n^2 + 2" The first 4 terms of another number sequence are 8, 35, 120 and 323. Write down an expression in terms of n for the nth term of this sequence. Any ideas? I usually find the difference between the terms until it becomes constant but in this case it doesn't seem to work. The first part is supposed to help in some way.
I... actually don't know. Neither does wolfram. Are all those numbers correct?
Hey, guys, you know how we can use Taylor series to find out out e? Just do it for e^x, a = 0 and x= 1 so e^1 = e^0 + e^0. 1 + e^0/2! ... Can we do a similar thing for pi? What's the derivative of pi^x? And, hell what about i^x?
Taylor series defines a function, you just need to put suitable values of x to get e or pi or whatever you want. For example, get the Taylor series of 1/1+x^2, and integrating both of them between 1 and 0 gives tan^-1(1) = Pi/4, so 4 times the taylor series of 1/1+x^2 integrated between 0 and 1 will give you pi. The derivative of pi^x is not particularly special i think. If we have y = a^x lny = xln(a) 1/y*dy/dx = ln(a) dy/dx = y*lna = a^x*ln(a) In general, d/dx(a^x) = ln(a)*a^x (when a = e, ln(e) = 1 so you can so how it works) so d/dx(pi^x) = ln(pi)*pi^x now I never thought about i^x, so it might not be right, but subbing in a = i gives d/dx(i^x) = ln(i)*i^x since i = e^(i*pi/2) ln(i) = i*pi/2 So d/dx(i^x) = (i^x)*i*(Pi/2) = i^(x+1)*pi/2 So it goes up powers if you differentiate it?? Or did I make a mistake?
[QUOTE=Collin665;34557699]I... actually don't know. Neither does wolfram. Are all those numbers correct?[/QUOTE] Well, those are the exact numbers from the worksheet. Unless there's a mistake.
Well it isn't an arithmetic or a geometric series, so it must be some weird thing.
[QUOTE=MountainWatcher;34557886]Hey, guys, you know how we can use Taylor series to find out out e? Just do it for e^x, a = 0 and x= 1 so e^1 = e^0 + e^0. 1 + e^0/2! ... Can we do a similar thing for pi? What's the derivative of pi^x? And, hell what about i^x?[/QUOTE] heh, we're learning that right now
Math is some goddamn fucking mind-blowing trippy bullshit. The fact that there is a function which is discontinuous everywhere and whose whose value is always > 0 on the interval of integration which is Riemann integrable and whose integral is 0 is like WAT.
I thought for a function to be Riemann integratable it could only be discontinuous at a finite amount of points? Very strange.
Whoops, didn't mean discontinuous everywhere. It's only discontinuous at countably many points. Still more than finite.
[QUOTE=Pedophila;34555422]"The nth term of a number sequence is given by n^2 + 2" The first 4 terms of another number sequence are 8, 35, 120 and 323. Write down an expression in terms of n for the nth term of this sequence. Any ideas? I usually find the difference between the terms until it becomes constant but in this case it doesn't seem to work. The first part is supposed to help in some way.[/QUOTE] Well n=1 => n^2+2 = 3 and 8= (3+1)*(3-1) = 4*2 n=2 => n^2+2 = 6 and 35= (6+1)*(6-1) = 7*5 n=3 => n^2+2 = 11 and 120= (11+1)*(11-1) = 12*10 n=4 => n^2+2 = 18 and 323= (18+1)*(18-1) = 19*17 so for that sequence, the nth term is (n^2+1)(n^2+3)
[QUOTE=ThisIsTheOne;34600528]Well n=1 => n^2+2 = 3 and 8= (3+1)*(3-1) = 4*2 n=2 => n^2+2 = 6 and 35= (6+1)*(6-1) = 7*5 n=3 => n^2+2 = 11 and 120= (11+1)*(11-1) = 12*10 n=4 => n^2+2 = 18 and 323= (18+1)*(18-1) = 19*17 so for that sequence, the nth term is (n^2+1)(n^2+3)[/QUOTE] Wow. How did you figure out the link?
I noticed that the sequence they wanted you to figure out increased a lot faster than the given one, but the numbers in the first sequence when squared stayed close to the respective term in the sequence you were trying to figure out, so it most likely had something to do with the sequence squared or something similar. I then noticed 4*2 and 7*5 had factors 2 numbers apart, and tried to figure out a pattern to get the next number in the sequence to be 10*12. Then i noticed the number in between the 2 factors for each one was in the given sequence. I only used 323 to see if the sequence worked for the next value of n.
Nice. I hate number patterns. So I just began learning A Level mathematics and I came across this when I was learning binomial expansion. What does |x| < 1 mean? Modulus of x is lesser than 1?
[QUOTE=Pedophila;34617182]Nice. I hate number patterns. So I just began learning A Level mathematics and I came across this when I was learning binomial expansion. What does |x| < 1 mean? Modulus of x is lesser than 1?[/QUOTE] Absolute value, as in the distance from 0 on a number line. |3| is 3, as is |-3|.
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