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/sci/ - Science & Math

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[ERROR] No.3622990 [Reply] [Original]

I've got about an hour to kill. Ask a math prof something, /sci/.

>> No.3622993

you seems to be getting addicted to /sci/, Professor. You were here yesterday.

>> No.3622992

Do you come here every day or something? I'd think guys like you had research or something they should be doing.

>> No.3622996

>>3622990
Do you think it is easier to get a PhD in math today, or 30 years ago? On one hand, more people have already researched the low hanging fruit. On the other, math studies seem to have spread out farther for more kinds of fruit.

>> No.3622998

Welcome back, Professor Mathfag. Will this be on the test?

>> No.3622995

Are there infinitely many real quadratic number fields with unique factorization?

>> No.3623012

How's that $300k and starting doing for you?

>> No.3623016

Welcome back.

How many females have you fucked who wanted an A in Calc 1?

>> No.3623017
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Are you making 300k while having sex with many women?

>> No.3623047

>>3623016
When I was TAing Calc, I had one whore come up and say she really needed extra help,

I asked her which sections or offered some study time, and he just kind of got sad and walked off.

Bitch didn't know anything about calculus. And I'm not going to risk losing my job for some dumb bitch.

>> No.3623078

>>3622992
>>3622993

Woah, this was fast. School starts on Monday and my office had a gas leak, so I can't get to any of my work. I just got done writing letters of rec, so I am mentally exhausted.

>>3622996
It is definitely harder to get a phd today than, say, 30 years ago. On the other hand, way more students go to college today than back then, and the material is more "user-friendly", let's say. I'm not quite that old, but back when I was doing research we needed to limit a lot of the problems because computers were not really an option and it was unreasonable to expect students to be able to look for help online since --- well, it didn't exist yet.

>>3622995
The last QNF I used was the Gaussian field, and that was at least 10 years ago. So I know there exists at least one. Maybe if I had my Dummit and Foote, I could tell you more.

>>3623016
You would be surprised at how some professors "brag" about hitting on undergrads years ago. Now-a-days, it is nearly impossible to do such a thing. And, honestly (and maybe this is a sign of age more than anything) the teeny-bopper constantly-texting early 20 year old pre-med "want to be a doctor so i can help kids!" girls don't quite do it for me.

>>3623017
I got married, so, not so many women. Because you all are so nice, I'll tell you something a bit embarrassing: she makes more money than I do.

>>3623047
I kind of agree with this. I don't want to lose my job over some one time deal. At least not until I get tenure.

>> No.3623090

Could you list your favorite texts for a few topics?

>> No.3623102

>>3623078
>the teeny-bopper constantly-texting early 20 year old pre-med "want to be a doctor so i can help kids!" girls don't quite do it for me.

Lol. Premeds are cancerous.

>> No.3623115

What do you find the most interesting area, field or development in mathematics?

>> No.3623118
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>>3623078

Do you admire Andrew Wiles, or do you think he is a nerd fiend? Just look at the fucker....

>> No.3623141

>>3623090

If you get specific, I'll recommend more specific. But I'll just list the books I usually go to as a reference if I need something from somewhere.

Analysis: Rudin's Complex.
Functional Analysis: Lax's Linear Algebra.
Algebra: Dummit and Foote or Lang.
Point-set: Munkres.
Algebraic Topology: Spanier (yes, I was pre-Hatcher), or Bredon.

For Calculus, I use Stewart whenever I can help it.
For prob and stat, I write my own notes.

These are all relatively standard books, and they're standard for a reason: they're good. Two notes: Lang is almost never good to learn from, but almost always good as a reference; also, I hear people swear by Hatcher's Algebraic Topology (which is free) but, to be honest, I wasn't thrilled with it. It may be a good learning book, but it is certainly not a good reference.

>> No.3623158

Fuck yes Dummit and Foote 2nd edition is the best book ever.

>> No.3623167

As a Physics major (interested in plasma and nuclear physics and nuclear chemistry), what is the highest math I should expect to encounter?

>> No.3623172

>>3622990

Two trolls are arguing about decimals over at
>>3615163
one says that 0.999...N isn't a decimal number, the other says it is. My friend agrees with the one saying it isn't, I agree with the one saying it is, though neither of us are qualified to really tell who is right (I'm an engineering stupid and he's physics, we're both second years)... Are you able to settle this?

>> No.3623178

>>3623118

I have never talked to him, but, of course, he is a good mathematician. Some mathematicians I know are not really fond of him because he got fame for Fermat, which, arguably, is no more difficult than many other unsolved problems today and is certainly much less useful. For example, Milnor virtually created fields which had huge impact on modern science and mathematics, but no one even knows who he is unless they study math. But I've heard he's a very nice man.

>>3623115

When I was a student, I thought algebraic topology was just about the coolest thing ever. In the last few years, comp neuroscience has really gotten off the ground, and it's quite interesting.

Recently, I've begun swimming through a number of things Robert Ghrist has been doing in applied topology. You can read more about it here:

http://www.math.upenn.edu/~ghrist/preprints.html

but a lot of this is good to give to students who think that topology can't do anything in the real world. I also mentioned yesterday that genetics is a new-found interest of mine, and I've been trying to look around for ways to apply my research to some of that.

Of course, my interests don't encompass even the tip of the iceberg of interesting developments happening now in mathematics.

>> No.3623179
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>>3623141

>no love for Hartshorne

>> No.3623180

Why are most of you so fucking lazy?

>> No.3623189

Euler's identity blows my mind. How do you raise a number to an imaginary power?

>> No.3623192

>>3623189
Taylor series

>> No.3623199

What's the highest level discrete mathematics can get to?

>> No.3623205

>>3623158

If you are into algebra, Hungerford is a great way to supplement Dummit and Foote. Herstein is also a good book, but it only covers undergad topics in much less detail than D&F and with a less pretty format.

>>3623167
I don't know how to rank the "highest", but you should probably be proficient in multi-variable calculus, elementary group theory, and (especially) complex analysis. I'm not exactly sure, though, and it depends on what you will need for your specific study. Complex is probably one thing that physics students learn at the last minute that they probably should be learning right at the beginning, though.

>>3623172
I refuse to turn this threat into a 0.999... = 1 thread, but, of course, both the former and the latter have decimal expansions. They are, in fact, equal. There are a number of excellent ways to show this. Some are elementary, and some are kind of neat. For those of you who have studied the construction of the reals, it is a nice exercise to show that a cauchy sequence converges to 0.9999... if and only if it converges to 1. Thus, we say, that these numbers are "topologically indistinguishable", in that there is no set of disjoint open sets containing one but not the other. You may also think of the reals as all rational cauchy sequence limits modulo the topologically indistinguishable elements.

>> No.3623206

>>3623141
Have you ever looked at Kreyszig's Advanced Engineering Mathematics? Its one of my recommended texts and I've been thinking about getting it...

>> No.3623210

>>3623206

Not OP, but that was the standard reference for applied math courses as far as third year. It's a good book to have around as reference for, well, engineering mathematics. It's not pure math by any means though.

>> No.3623223

I'm sorry, but I was a math major with a philosophy minor so I have to ask you this: what is the ontological status of mathematical entities?

If you think this is a stupid question I don't mind, but I've always been curious what people in math think about this (if they are so bold as to actually think about it), as they deal with more concepts than just "numbers and variables" which it seems is often all a philosopher who asks this question is capable of working with.

>> No.3623230

>>3623205
How would you say the job prospects are for someone with a PhD in math? I am considering it, but it seems like it would be much easier to go with a bachelors/masters in Computer Sciences/Engineering (for myself), and then perhaps doing a math degree while working.

>> No.3623229

>>3623205
The discussion isn't about whether they equal 1, its a bit more sophisticated of a debate that's arisen, I don't really understand what either of the guys are saying to be honest, but I'd still like to know who is right. One guy says its not decimal because the N has no finite place value, the other guy says it does have a finite place value in another ordinal, but then the first guy says that you can't have several ordinals of place value, or something. I don't really follow it so this probably doesn't explain it very well, I just want to settle the debate with my friend.

>> No.3623236
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>> No.3623239

>>3623199

This can get intense. Discrete overlaps, eventually, with algebraic number theory as well as other interesting topics like this. Of course, these are still active areas of research. I don't know much else about it; it's more of a computer science thing, I feel.

>>3623189
This is at the beginning of any complex course. It's kind of neat. Lots of different ways to approach it, but my favorite is: define e^{z} int he complex plane, and then define the complex Log(z) = ln(r) + iArg(z), where ln(r) is the real log. If you have something like a^b where a is a complex number and b is a complex number, then you prove that

a^b = e^Log(a^b) = e^{b*Log(a)} = e^{b(\ln(r) + iArg(a)}

And letting b = x + yi, you can further reduce this. For example,

i^i = e^(i*Log(i))

And note Log(i) = ln(1) + i* pi\2,

==> i^i = e^{-pi / 2}.

Of course, my Arg is the principle argument, but we have a countable number of solutions by adding 2pi ik to the definition of Log(z).

>> No.3623243

>>3623205
How did you become proficient at writing proofs? Please be completely honest!

Another question: How important are recommendation letters for Grad School? Secondly, does GPA always make a huge contribution or does research trump GPA? Do rec. letters trump GPA? I don't have a low GPA, btw; I'm an A- avg. Just asking because I'm curious.

>> No.3623255

I skipped trig and went straight to pre-cal and failed a quarter but begged to let them keep me in. Pre-cal was pretty hard for me. how do I not fail AP calculus? And do you think i can just take The state wide trig test without actually taking the class?

>> No.3623269

>>3623206

I have not read it, but he wrote a book about Differential Geometry which I didn't like all that much. Though, if it is the standard, he must be doing something right in it.

>>3623223

If you can justify the study of ontology without using ontology, I will answer this question.

But, for me, I don't think about it too much. Do I think numbers really "exist"? Well, what do I mean by "really exist"? This kind of thing was fun when I was in undergrad, but I've decided to just not think about it too much.

>>3623230

None of the grad students I've had has had any trouble finding a job in the last year or two. I'm just glad I have a job now, because I don't really want to be serving coffee at Starbucks and wiping down tables with my PhD.

>> No.3623286

>>3623269

PhD student here. Advanced Engineering Mathematics is a very dry book, but it's full of useful integration formulae. That's about it really. Engineers use it a lot for some reason.

>> No.3623304

>>3623229

This is actually tipping onto something which is mathematically interesting:

http://en.wikipedia.org/wiki/First_uncountable_ordinal

But, of course, there is no way to make a number which has, "a countably infinite number of 9's, and then a 1." The decimal expansion just does not work that way. But, we can have a system where we make a topological space out of the first uncountable ordinal in the order topology.

But, no. You can't have something like 0.99999... and then a 1 at the end or whatever. Not in the standard system. Not even in the non-standard system. You could probably make a system where this is true, but my gut feeling is that the only model for it would be the trivial model.

>>3623243
Practice. Make people criticize your proofs. Read other people's proofs, and then try to prove it that way yourself. It sounds really bland, but that's how you learn. Like, "How do you become a better writer?" Well, write. My proof quality increased exponentially in Abstract Algebra during my undergrad work, and then again in Algebraic Topology in my grad work (because my teacher was extremely strict about what was and wasn't to be in a proof).

>>3623255
It has been a long, long time since I've taken calculus. I feel, though, that trig is the hardest part of calculus or students, and pre-calc, as I recall, has a large Trig section in it. I'm not sure, though, take it up with your teacher and see what they think you should do based on your previous work. it's kind of silly to stick to a class if you're going to be struggling to breathe and aren't getting anything out of it.

>> No.3623312

>>3623269
>If you can justify the study of ontology without using ontology, I will answer this question.
Touche

Nevertheless I still think it's an important question when it comes to understanding the relationship between mathematics and science (especially physics). But if that's not your bag then how about this: why is math so fucking powerful when it comes to understanding physical phenomena? Or, if you'd prefer, is that question meaningless and why?

>> No.3623315

>>3623223
you dropped a terse bomb "what is the ontological status of mathematical entities"

then spent two sentences insulting anyone who thinks that's a dumb question.

So chill. What did you think ontological status means? I'm not familiar with a general usage.

I'd guess ontologies are heirarchies of meaning, and then I'd say that the notions of zero and one are quite fundamental in the grand scheme of idea ranking.

Which, as mathguy said, is a waste of life time. We've got other work to do, with variables. That make apparent immediate sense.

Concrete objects take place in the real world, and if you ever want a job when you grow up, study the real world, not Topology. (no offense to the topologists, but you know you're different in the head)

although I believe in gross anatomy, humans are all topologically equivalent to a triple layered coffe cup torus thing.

>> No.3623334

>>3623315

Don't you be badmouthing topology you motherfucker.

>> No.3623339

>>3623312

Mathematics, as a language, provides a way to speak about things in the models we create in physics which are to represent the real world. Mathematics, as a study, provides "ideal situations" and properties of these situations with respect to ideal morphings of these situations.

In short, then, physics models the real world and we get an approximation by using mathematics to mess around with the model. Of course, a "perfect circle" as we imagine in mathematics may not actually exist, but it is more than enough to consider how to design stove burners that heat and cool with maximum efficiency.

>>3623315

This reminds me of a joke I saw a while ago: why are topologists the dumbest mathematicians? They can't tell their ass from a hole in the ground.

>> No.3623348

>>3623315

...wat? I insulted no one. I merely stated that it's OK for him to think it's a silly question, but that if he didn't I'd be interested in hearing his point of view as a mathematician and not a philosopher...

>> No.3623351
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>> No.3623361

>>3623339
Good good. That's more or less the answer I get from most mathematicians, and I tend to agree with it.

>> No.3623367

>>3623361

Without claiming some kind of objective truth in the universe, it's the best I can do.

>>3623351

If and only if c = b, or 2a = -b. Cross multiply, solve.

>> No.3623392

>>3623367
As a mathematician, you'd think objective truth would be right up your alleyway though... methinks you've got a little bit of an opinion on that ontological status question after all...

>> No.3623412

>>3623392

I don't think that every mathematician thinks of their work as objectively true. It is, of course, relatively "true" based on the axioms and the methods of proof (which are DEFINED to be true and to take "truth to truth"). Based on this system, we have an artificial layer of truth and we are building up all sorts of things which are true relative to these things. Of course, are our definitions "true" to begin with?

And I think this is where ontology, as a study, would begin. I'm not a huge fan of philosophy, but it is important to note that I cannot say something like, "oh, the triangle equality holds true in metric spaces" and have it be OBJECTIVELY TRUE in the universe (whatever that means) but it should at least be relatively true based on our axioms and systems of proof which are taken upon faith and defined to be true and, again, to map truths to truths. Whatever "truths" are, anyway.

>> No.3623413

>>3622990
>>I've got about an hour to kill.

I initially interpreted this as saying you had an hour to commit murder

call me back when that's the actual thread...

>> No.3623442

Alright, I'm going to get off of here and do some sort of sleeping. Feel free to use this post to have 0.999... arguments, or talk about why topology is the best kind of math.

>> No.3623509

God damn dude, every time I try to ask you a question this thread ends up 404ing cause I have school.

>> No.3623529

>>3623315

Excuse me, but doesn't topology now have a direct application in physics? I'm thinking about topological insulators which I thought were an area of active research and some excitement.

>> No.3623546

Did you ever take the putnam exam as an undergrad? If so, how did you do?

>> No.3623729

>>3623412
I disagree. The triangle inequality holding in metric spaces is objectively true, because a metric space is a place defined as having the triangle inequality hold, so soon as it doesn't hold we're no longer talking about a metric space.

In general I believe mathematics is objectively true, because we start with assumptions (note, we do not assume our assumptions are true, we talk merely about the case of their being so), the most basic assumption being that our basic principles hold, should they not hold we make no claims, so what is to be untrue about an unmade claim?

>> No.3623790

Should I bother with real and complex analysis?
>Physics major

>> No.3624926

>>3623790
Not OP or anywhere near his... learned-ness. I minored in physics and majored in maths, real and complex as far as I could tell had no real relation to physics.

>> No.3625050

Could you recommend me a Number Theory textbook?
I'm enjoying H. E. 'Rose's A Course in Number Theory', but it's a bit dense.
Is there a more user friendly alternative?

>> No.3625059

if you were sent back in time to when you were 10 years old, and retained all the knowledge you currently have, would you enter academia again and go through the process of regaining your current position, or would you feel satisfied with knowing what you know, and do something else instead?

>> No.3625151

What's your wife work?

What does she think about math in general?