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/sci/ - Science & Math

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[ERROR] No.3725021 [Reply] [Original]

Hey again, /sci/.

I'll be up for the next hour or so, so feel free to ask a math professor things.

>> No.3725032

Is it possuble to make a matrix where its entries are other matrices?

>> No.3725033

I know about functions and derivatives. Now I want to get into the real thing before college. What calculus book do you suggest for an starter?

>> No.3725037

What's going to be on the quiz tomorrow? Be as specific as possible.

>> No.3725042

Will you tutor me?..


I'm a completely lost student.. that is trying to get back into his studies again.

>> No.3725043

>>3725032

Of course; this is called a "block matrix." Sometimes this makes calculations significantly easier. Recall, also, that a matrix is just a convenient way to represent data (in finite dimensions this is n^2 dimensions) which has that weird matrix multiplication inherent in it. You'd be surprised at how many things naturally require matrix-like multiplication.

>> No.3725048

Solve this please!!

>>3724908

>> No.3725050

What process converts an expression to its inverse? It's been so long that I have just forgotten what you're actually doing when you convert something to its inverse.

>> No.3725054

>>3725043
What sort of jobs are there for a math major and are they good?

>> No.3725060

How do u tackle stats problems:

if it rains on 1 day, there is a .7 cahnce ti will rain the next day.

How are these events not dependent? They seem pretty dependent to me, but the answer is simply that there is a .7 chance it will rain the next day.

shouldn't you have to use like some sort of dependence thing?

>> No.3725074

>>3725048

This is solved in the thread. It doesn't look too bad; just label all the angles you know.

>>3725033
What do you mean by the "real thing"? Calculus? Or Calculus with proofs? For the former, the standard book is Stewart [any edition, really] and the latter is Spivak's Calculus. Just get a cheap copy of Stewart and work out lots of problems, that's the best way to learn Calculus, imo.

>>3725037
Once I had a student who would make up a "checklist" for me and ask me to check off topics that would be on the test.

>>3725042
If you want to know things, you first must know yourself, etc, etc.

>> No.3725075

>>3725021
What field do you do research in? Where did you get your PhD from?
What was graduate school like while you were transitioning from undergrad? What do you think are the most important things for an undergrad to do to get into a good grad school?

>> No.3725083

Can you recommend a good set theory textbook?
Perhaps just a brief introduction as opposed to an exhaustive, course covering ordeal.

>> No.3725091

ok, so before i ever actually learned how to add, multiply etc. i had my own theory of what they were and they worked...just the "reality" of what they taught was different, so i re-learned the shit basically back in elementary...why was i so bored in school?

>> No.3725097

How old are you and where do you teach

>> No.3725101

<span class="math">x^{x}=7[/spoiler]
Find X, how do I make that?

>> No.3725109

Do you make $300,000 starting?

>> No.3725110

>>3725050
An expression? Do you mean a logical expression? Or something like a function or a matrix or something like this?

>>3725054
I listed off a bunch last time I was here, but, in general (and maybe not in the hard economic times of the right-now, but in the near future, perhaps) things with money like banking or business as well as things with science like, you know, design or consulting. You can also do teaching and research. The government also frequently requests mathematicians to help with projects at the DoD or other related branches.

>>3725060
I am not a statistician, but I went to a lecture that talked about dependence. This is not so trivial a topic as they make it seem in school. Your example, for example, points to this: the weather, daily, is not independent of...itself?...each day. Thus, it is more likely to rain on consecutive days than it is on non-consecutive days, and so forth. But, in general, when you are just learning probability we tend to simplify this in the following way: it would not change TOO much if we assumed these things were independent.

>> No.3725112

faggot freshman engineer here..

My math curriculum only goes up to diff eq, would studying analysis/topology/set theory/number theory after my curriculum in my spare time yield any tangible results?

This purely out of interest.

>> No.3725113
File: 57 KB, 320x240, 5949.gif [View same] [iqdb] [saucenao] [google]
[ERROR]

How do I make the matrix?

>> No.3725115

>>3725110

Logical expression.

>> No.3725124

>>3725075
Currently, my field is too specific [and unpopular] so my name would turn up right away. Suffice it to say that I work in a tiny subsection of algebraic topology currently, but I have done other things in the past. I have stuck close to topology, though. I also don't want to give away where I went to college.

But, since I have worked on boards which accept new grad students, I have some hints to getting in:

- First, don't think the GRE is stupid and worthless. It is, but just do it. I have heard more times than I can count, "Well, (s)he's good, but her GRE scores are terrible." Of course, some professors don't take this into account at all (like myself) but others weigh on it quite a bit.

- Second, research is nice. If you can't research, at least do something like an REU or summarize some work that you've read through in a paper. Show us that you care about mathematics and are not just doing this because you have nothing else to do.

- Third, grades are important. Yes, this is irritating, I know. But now-a-days, if you've got straight A's but have only taken up to Analysis, you've got a better shot at getting in than if you've got a C+ average and have taken Differential Topology, Algebraic Geometry, and Complex Algebraic Curves. This is one of those things that "just is"; it's upsetting, but it is how the schools work now-a-days.

Last - Request an interview if you don't get one. Feel free to email professors you are interested in working with to see what their research is on. Don't be SUPER casual, but don't be pretentious either. We once had a student applying who actually wrote things like, "I may not be a good student in my classes, but when I shoot the breeze with mathematicians at my school like (big name here), they say I'm much smarter than my grades tell." This will not win my heart.

>> No.3725130

Is it true that I can become God by studying mathematics?

>> No.3725143

>>3725083

I think the Topology Police would arrest me if I didn't recommend Munkres' first few chapters, which go through all the set theory you need to know to get to topology. For easier introductions, I've heard there is a Schaum's outline which is not too bad and full of solved problems.

>>3725091
Maybe you should have doodled more. I don't know. Mathematics is standardized but, of course, not unique. There are many ways to do the same thing, but having one way to write it makes it significantly easier to share ideas.

>>3725112
For engineering? Probably not. For your own enjoyment? Definitely. I would, honestly, ask a professor at your school who does pure math to help you along with these things. Most of the time (okay, well, sometimes) the professor will be so excited that someone shares their interest that they will be more than happy to help you through it. Because Algebra/Topology require a HUGE shift in thinking (as opposed to calculus, etc.) this is almost necessary. I know very few people who have self-studied Algebra/Topology and have gotten much out of it.

>>3725115
It's been a bit, but I think to convert a first-order logical expression it suffices to negate free (I think?) variables and exchange the existential qualifiers. This should be enough to get your negation. I don't know if this is what you meant by "inverse."

>> No.3725166

>>3725124
TOPOLOGY FUCK YEAR
Maybe you'll meet me at a conference somewhere or be my advisor and never know it was me who you were talking to on 4chan. I am suspicious about a professor being on 4chan but it's not impossible so I'll just indulge my imagination.

I'm definitely in the school of "just do good because you have to" when it comes to the GRE. I have done a little research.
I guess my problem is with this interview and e-mailing professors stuff. It sounds hella awkward.

>> No.3725180

Given A=24m, E and B=50m,S (east , south)
A+By (b) B-A
You are a god if you can solve this for me.

>> No.3725202

>>3725143

Why won't you answer my question faggot?!?

>> No.3725207

>>3725166

It is entirely possible! The only hint that I can give you, really, is that I have a picture of my Dachshunds on my desk. So if you see that, you'll know.

As for the emailing and interviews, a number of graduate applicants email me while applying here and, generally speaking, there are a few that are obviously interested in topology and a few which just want to go to school here ("I've never taken topology, but that tea cup thing is neat..."). It's not required to shoot an email to people you are interested in working with, but it does add a nice touch sometimes.

The interview is almost necessary. If you have two students who are essentially the same grade, research, etc.-wise and one spot left, who is going to stick out to you: the one you had a nice conversation with or the one that you have never talked to?

More generally [the previous example is a bit uncommon, but does happen] if I talk to someone about what they want to study, then I feel it's more "real" than if they just email me topics they are interested in. In particular, sometimes I feel like students just copy-paste off of wikipedia for some things.

>> No.3725223

>>3725101

Right off the top of my head, I would say to use complex analysis to get some estimates. x^x is not a kind function, but it is at least approachable if we consider in as the complex z^z = e^{zLog(z)} where the Log is the complex log here.

>>3725180
I'm not going to do your intro to physics homework.

>> No.3725232

>>3725091 again
>>3725143
definitely..i mean i got straight a's until i got heavy into drugs in high school but are there classes where it's more about the philosophy of math instead cause i shit you not, ive got some crazy shit i came up with for that whole "r=0 singularity" jive that has "derp'd" people before..i just don't know what the hell i should do with it.

>> No.3725243

>>3725232
and by derp i mean my dad has a masters in physics

>> No.3725247

>>3725207
>>3725207
Hah! What kind of undergrad applies to grad school without even taking an intro to topology class?
Ah well anyways. I personally know just enough about math to know that I don't know much math. Even graduate courses are just introductions to subjects. Like measure theory and set theoretic topology. They don't go too deep into the subject. At least not the grad classes I take at my university.

>> No.3725253

>>3725232

Yes, there are "philosophy of math" courses, but it seems like you just want to do the Philosophy of Science. Generally speaking, this is not a popular stand-alone subject (since there are only a few people who do it without being, themselves, scientists) but I would highly (and I'm emphasizing highly here) recommend first taking courses in Formal Logic and courses for which you have ideas relating to. For example, I know physics can be boring, but no one is going to listen to someone ranting about physics who has never taken a course on it [or who is otherwise distinguished]. Think of it like this: would you read a book about how it feels to have no legs from a guy who has both of his legs? That's a weird analogy, but the idea is more or less the same.

I also just want to note that, even if your ideas are wonderful, finding an audience is not easy. And getting an audience to respect you is far harder.

>> No.3725294

>>3725247

Standard classes in grad school are meant as introductions to these subjects --- usually, the big three: algebra, analysis, topology. Usually, these are paired with "topics" courses which go more in depth into the topic. After or while doing these, you should be reading about things by yourself and doing reading courses with professors whose subject you are interested in. After taking your qualifying exams and your oral(s), you should be at the point where you can really "teach yourself" much of the stuff you want to do, and your advisor should only be used to help guide you along (theoretically). So, that's kind of standard for grad school stuff.

>> No.3725318

>>3725253
word bruh.

>> No.3725353

I want to relearn Euclidean geometry. Is Euclid himself the best source to learn from?

>> No.3725373

>>3725353

No. No. No.

Any high school textbook should be okay for Euclidean Geometry. There are also modern ones [besides high school ones] but they are significantly more complex than high school books. Dan Pedoe, for example, has a number of texts on the subject but they are all quite dense.

Also, for the rest of you, I'm going to bed now. I'll be back eventually.

>> No.3725374

>>3725353
Definitely.
Nothing else compares.

They should just abolish introductory geometry classes and hand out copies of Euclid's "Elements" instead.

>> No.3725379

Has a student ever tried to bribe you for a grade?

>> No.3725390

Is discrete mathematics just a glorified English class taken for math credit?

>> No.3725399

>>3725390
Why would you think that?? At least at my school, that couldn't be farther from what it is. Here, it's a transition from the computational math found in lower div calculus and linear algebra, to the proof-based upper division courses. It just so happens that the vehicle chosen for this transition was an array of introductory topics in "discrete mathematics".