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1. Question about counting degrees of freedom

This makes sense. Then it makes me wonder, since you can't assume WLOG that the first component is 1, how do we argue that there are n-1 DOF rather than n? What about this simpler case: we want to solve for x\in\mathbb{R}^9 and to do so we collect constraints a_i^Tx=b_i. If we can find 9 of...
2. MATLAB Calculating similarity between users using matlab

Hi, if I were you I'd encode all attributes as integers, so that all records can be stored as rows in a matrix of type int. I'll assume that you've done this, and your database is a matrix "db" of size [numusers 4]. I'll let you work out the details of that. First, let me give names to the...
3. Question about counting degrees of freedom

Suppose that for some application it is mathematically convenient to represent certain objects of interest (e.g., lines or conics) as n-dimensional vectors. That such a representation exists let's us conclude that in order to specify such an object, no more than n values are necessary. That is...
4. How were these line fitting equations derived?

What an amazing reply! Thanks so much. It's so simple now that I see it, haha.
5. How were these line fitting equations derived?

I've run into these formulas many times but I've never seen how they were derived. Say you want to fit a line to some data. Your data is a bunch of (xi,yi) pairs. Through some kind of magic, the slope m and the y-intercept b are given by these formulas...
6. Is this MathWorld page wrong? (it's about hyperplanes)

Here's the page: http://mathworld.wolfram.com/Hyperplane.html They say that the set S is a subspace of R^n. Is that true? Doesn't c have to be zero in order for S (the hyperplane) to be a subspace?
7. Rows that get zeroed out during elimination

This is something that's bothered me for a very long time... Say you're doing Gaussian elimination on some matrix. Now suppose during the process, some row gets zeroed out, say row j. Now it makes perfect sense for me to say that row j was a linear combination of the previous rows. But...
8. Intuitively, shouldn't variance always be 0?

Ok I see. I forgot that E[...] is kind of like the average of many repetitions. I see what you guys are saying, it makes sense that the average of a bunch of positive numbers is positive. Thanks :)
9. Intuitively, shouldn't variance always be 0?

Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should always be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect: 1) The variance is the expected difference from the mean...
10. I don't understand the exponential distribution at all

This is driving me completely crazy! QUESTION 1: There are two interpretations I find for the exponential distribution: 1) It models the lifetime of something that does not age in the sense that the probability of functioning yet another time unit does not depend on its current age. So...
11. How is this probability reasoning wrong?

Thanks for the replies everyone, but I'm still kind of confused as usual... Forget my first post and tell me what you think of this: Which sentence in that reasoning is wrong?
12. How is this probability reasoning wrong?

If there was only one pair of each (2 light, 2 dark) and the first two were the two lights then the is no third light sock so the probability would be 0..? Hmm I don't really see what you're getting at, sorry...
13. How is this probability reasoning wrong?

How is this probability reasoning wrong?? Homework Statement Homework Equations The professor didn't say it explicitly, but I'm pretty sure that sock choices are taken to be independent, so P(A,B,C) = P(A)P(B)P(C). The Attempt at a Solution The last part is easy...the correct...
14. What good is linear algebra?

I'm not a math or physics guru like these guys so I can't really speak from experience, but I've run into some articles on the Web talking about all the linear algebra that Google uses that I think you might like. Here they are: How Google Finds Your Needle in the Web's Haystack The...
15. A big book of problems for highschool level math?

This is a great book. It isn't filled with tons and tons of problems (it's not a textbook) but it's still very good. It really cuts through the wordy BS and gets to the heart of things. Remember that if you really can't afford too many books you could very likely find this one at a library...
16. Calculating percentages

Here's how I think of it: 40% of Assignment1 + 60% of Assignment2 = 100% of your grade 0.40(56) + 0.6(62) = 22.4 + 37.2 = 59.6 100% of 59.6 is 59.6.
17. Nonselfish Reasons to Pursue Pure Mathematics

I remember reading an interview in a newspaper with a mathematician who I think won the Fields Medal and finding one of his comments really interesting. He said that studying math is actually very ethical, as studying math doesn't pollute the environment, doesn't use natural resources, and...
18. Programs Note-taking in undergrad degrees

I like to take notes because I like looking back on them to reminisce about all I've been through. I still have my notes from so long ago when I first got to college, when I took my first calculus course, when I took my first philosophy course, etc. It's a lot of fun looking through them and it...
19. Courses How rigorous do these courses look?

I just transferred from a CC in California to a UC school, so I'll say a few things. Don't go for an associates. It won't help you transfer. Also, DON'T talk to your CC's counselors for advice on transferring to a UC school for a math-oriented major (math, CS, physics, etc.). They will give you...
20. I'm illiterate in math

I would suggest getting yourself a Nintendo DS and buying Brain Age. Here's a picture Brain Age's calculation game: http://image.com.com/gamespot/images/2006/128/931667_20060509_screen001.jpg [Broken]. The game is a lot of fun and it'll help you at the same time.
21. I love math but I'm not that smart. I don't know what to do

Thanks for the inciteful comments everyone. I'm going to try and stick it out with CS for a little while longer and see how things go, and continue thinking this over. The double major sounds like a great idea, but I don't think it's going to happen. I think it would be cool if I could maybe...
22. Do formulas prevent students from understanding concepts?

I'm taking an introductory physics course at my university right now. Let me say something about myself: I *hate* memorizing things. I do anything I can to avoid it. I've held on strong to this viewpoint for years but this physics class is starting to change my mind. I've spent the...
23. I love math but I'm not that smart. I don't know what to do

I'm sort of in a bad dilemma right now and need some advice. I'm a CS major and I've slowly grown to like math more and more and coding and the usual CS stuff less and less. In short, math has become my new passion and I'm thinking of changing my major even though I'm 2.5 years into my CS degree...
24. Changing periods. Very confusing

This is driving me nuts: How do you show that that's true?!? How do you prove it? For the life of me I can't see how this holds despite the fact that I've wasted the past two hours working at it. I can't think of a technical explanation for it (a proof) OR an intuitive one... Please help.
25. Complicated definitions of linear independence

I'm pretty dumb...I've got a few more questions. My brain doesn't handle matrices very well.. I see your point gonzo how the determinant must be 0 when the columns are dependent. So in other words I can see that dependent columns imply a zero determinant. But...how can I show that a zero...
26. Complicated definitions of linear independence

Well, again I've run into another issue... I'm running into a lot of problems where I'm required to find if some vectors are independent and often the criteria I see used for solving the problem is taking a determinant. It's said that if you make a matrix out some vectors and find that the...
27. Complicated definitions of linear independence

Thanks guys it makes more sense now.
28. Complicated definitions of linear independence

My teacher gave us an intuitive idea of what it means for two vectors in \mathbb{R}^2 to be linearly independent (they aren't multiples of each other) and for three vectors in \mathbb{R}^3 (they aren't on the same plane). Now the book has generalized the idea of linear independence to n...
29. Telling if three vectors in the same plane? Help

Telling if three vectors in the same plane?? Help! Hey guys I've got a question about vectors that's confusing me. Here's what my book says: I don't understand the example... How do you tell if three vectors in R3 are in the same plane? Why does adding the first two and getting (1,1,1) show...
30. Why save endangered animals?

Animals such as tigers and owls are intelligent, living things like you and I and thus some would argue that to kill them unnecessarily is evil. It would follow that if your people had a part in almost annihilating that animal's entire species then it would only be right to at least make an...
31. Studying for Exams: Late Night in the UK

I too hate exams. The finals week of this last semester I pulled three all nighters. The only thing that kept me going was me constantly reminding myself that once all this cramming was done and the tests were taken I would then immediately be able to come home, jump on my bed, go to sleep, drop...
32. Programs Should CS majors take multivariable calculus?

Thanks guys. I've been wondering about this lately. I thought that if any field of CS would make use of calculus 3 then it would have to be 3D graphics, but the more I think about it the more that seems wrong. Where would multidimensional calculus come in handy for graphics programming...
33. Programs Should CS majors take multivariable calculus?

At my school multivariable calculus (aka calculus 3) isn't required under the computer science corriculum. I'll have to take other math courses but we're not forced to take calculus 3 and as far as I know it is not a prerequisite to any computer science course my school offers. The subject seems...
34. Plotting Graphs: Tips & Shortcuts

The program I like to use is called Graph. You can get it from www.padowan.dk. I like it because although it lacks some of the more advanced features (like 3D graphs) it is very easy to use. You don't have to spend days in front of your computer figuring out how to use it; you open it up, click...

I don't get it... The paper says nA but StatusX is saying An and AKG is saying An. Is there something I'm missing? Edit: I see now! AKG what you're saying is now making sense to me. Sq(w)(A) is an infinite set of functions. Therefore u and v being members of Sq(w)(A) means that they themselves...

PLEASE help me understand this paper! (Formal math stuff) Right now in my class we're being given a short introduction to theoretical CS. We're learning not from a book but from our teacher's Ph.D. thesis! The thesis is HEAVY on formal math and I can't follow it... I've been trying for DAYS and...
37. How old is spongebob?

Now these are the kind of math topics I like! I was just browsing through the board "tensor analysis and differential geometry," came back to the general math section and see "how old is Spongebob." :D
38. Show me some Leibniz theroems

Whenver I want to read a biography about anyone my first move is always to check Wikipedia. I searched it this time for "Leibniz" and found an excellent biography: http://en.wikipedia.org/wiki/Leibniz. See also the section "External Links" at the bottom of the page for even more stuff to read.
39. Me Solve this Integral

The derivative of cos2(x) is -2cos(x)sin(x) but I don't see what you're trying to tell me... But anyway thanks for your help guys. I just now finally succeeded in getting myself to really understand the error and why it is happening. I just sat down for a while and studied the graphs of...
40. Extremely discouraged by this one guy

I feel your pain JasonJo... I have similar issues but not particularly with anyone in my class. People always say learning math is not a race but it's extremely discouraging to know that there kids out there that take calculus 2 in high school (I only know of only one but I'm sure there are...
41. Me Solve this Integral

Hmm I don't really understand the point you're making... Argh I'm stupid. Okay I'm going to switch the topic to a new problem that focuses more directly on the problem I'm having. This will help me explain to you guys the trouble I'm having. Consider this integral...
42. Videogame Programmer

I'm not a game programmer but I've read numerous websites on how to get into the video game industry and have read a book on it (becoming a game programmer is my dream). The obvious choice of a degree when going for a game programming position is computer science, though it is definitely not...
43. Me Solve this Integral

But the integral from 0 to pi/2 is 2*sqrt(2). 4 times that equals 8*sqrt(2). edit: nevermind, I see what you were saying. Is there a way to do this problem without changing the bounds? I mean since the cosine function is negative from pi/2 to 3pi/2 isn't there a way to rewrite the integral as...
44. Me Solve this Integral

Hey guys, I'm having trouble solving this definite integral. I'm doing work with polar equations and I was led to this: http://img404.imageshack.us/img404/6021/first4hv.gif [Broken] which I simplified to http://img404.imageshack.us/img404/669/second8qs.gif [Broken] And, using the...

Thanks a lot homology. I saw your message early yesterday but couldn't get to reading it until around 8pm. Anyway I stayed up until about 3am reading every single website I could find trying to make sense of it. Well after seven hours and about four pieces of paper I got it. I forgot to mention...