• Mathematician Chat v. 3.999...
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Had my first taste of higher categories in lecture today. I'm sure a year from now I'll be sitting in my underwear in the dark editing nLab pages and rambling something about stable homotopy categories of spectra.
Might be a silly question, but I just got my B.S. in Applied Mathematics: Computation. Essentially math with computer programs. What can I do with it?
[QUOTE=nerdster409;51763760]Might be a silly question, but I just got my B.S. in Applied Mathematics: Computation. Essentially math with computer programs. What can I do with it?[/QUOTE] Congrats mate. If you know Ops Research you could try to join a consulting company that does optimisation. If you know financial maths you can try to get into an investment company. If you know stats you can get into data analytics, which covers a huge range of industries. If you only know pure maths, you can enjoy collecting welfare checks.
[QUOTE=Wunce;51764159]Congrats mate. If you know Ops Research you could try to join a consulting [B]company that does optimisation.[/B] If you know financial maths you can try to get into an investment company. If you know stats you can get into data analytics, which covers a huge range of industries. If you only know pure maths, you can enjoy collecting welfare checks.[/QUOTE] Good money.
If you like science you can join any research group that numerically computes stuff (quantum systems, image processing, comp. neuroscience, ... the list is endless ). Here in dMRI we have engineers, mathematicians, physicists, computer science, DSP, ... Maths + coding = any field where shit has to be calculated, (sort of) obviously...
If you want to do video games, you will have easy time doing 3D (and any other math) and hard time fixing random bugs.
[QUOTE=Wunce;51764159]Congrats mate. If you know Ops Research you could try to join a consulting company that does optimisation. If you know financial maths you can try to get into an investment company. If you know stats you can get into data analytics, which covers a huge range of industries. [b]If you only know pure maths, you can enjoy collecting welfare checks.[/b][/QUOTE] pure maths still gives you a leg up in most other vaguely math related fields over anyone who hasnt done a specialised course not to mention, at least over here, the only places that would do a mathematics+computing course and not teach something besides pure maths would be the most prestigious unis, and having a piece of paper from them gives you an advantage anyway
So many things to do, yet I can't find any of them nearby. Looks like I'll have to move in order to get them.
[QUOTE=papaya;51765568]pure maths still gives you a leg up in most other vaguely math related fields over anyone who hasnt done a specialised course not to mention, at least over here, the only places that would do a mathematics+computing course and not teach something besides pure maths would be the most prestigious unis, and having a piece of paper from them gives you an advantage anyway[/QUOTE] It's an old joke lmao. The pure mathematicians I know had no trouble getting jobs in OR and insurance because employers are thirsty for anyone with mathematical maturity.
I've been trying to develop an intuition as to why an argument with true premises and a false conclusion must be invalid. According to my book, a valid argument is an argument in which it is impossible for the conclusion to be false given that the premises are true. Based on that definition, anyone can look at an argument, see that it has actually true premises and an actually false conclusion, and say that it is invalid. However, I want to know why that is. I've been staring at this book, and googling things for days, but the only thing that has happened is that I've gotten very frustrated, and my brain has turned to mush, so apologies if I haven't mentioned all relevant information needed to fully understand my problem. I'll come back to this tomorrow because I know I won't be able to understand anything right now.
[QUOTE=elevate;51781503]I've been trying to develop an intuition as to why an argument with true premises and a false conclusion must be invalid. According to my book, a valid argument is an argument in which it is impossible for the conclusion to be false given that the premises are true. Based on that definition, anyone can look at an argument, see that it has actually true premises and an actually false conclusion, and say that it is invalid. However, I want to know why that is. I've been staring at this book, and googling things for days, but the only thing that has happened is that I've gotten very frustrated, and my brain has turned to mush, so apologies if I haven't mentioned all relevant information needed to fully understand my problem. I'll come back to this tomorrow because I know I won't be able to understand anything right now.[/QUOTE] I'm confused as to what you're looking for exactly. That's the definition of what it is to be valid. Essentially it's capturing the idea that an argument is "formally true." If you accept its premises as given, the conclusion is true because the form of the argument is valid. For an invalid argument, even if the premises are true, the conclusion does not necessarily follow from the premises. Some prototypical examples would be: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." or: "All cows are green. I am a cow. Therefore, I am green." These are both valid. They are both of the form: "All things in this class have property P. Thing 'x' is in this class. Therefore, thing 'x' has property P." Obviously the premise of the second one is untrue, but that's fine. It doesn't affect the validity of the argument. The first argument was valid and sound, the second is valid, but unsound. On the other hand: "All men are mortal. Socrates is mortal. Therefore, Socrates is a man." is not valid. We may know that men are all mortal, but we don't know that the only mortal things out there are men, so knowing that Socrates is mortal doesn't guarantee that he is a man. This argument is neither valid nor sound. So if you accept the truth of a valid argument's premises, the conclusion must be true. If your argument is invalid, even if you accept the truth of the premises, they don't guarantee the truth of the conclusion. Even if we accept that all men are mortal and that Socrates is mortal, that doesn't guarantee for us that Socrates is a man.
Time to retake calculus, stats, discrete math and logics :v: Quite embarrassing, I already have a bachelor's in computer science & enginnering and kinda working on my master's thesis, both rather math heavy. But I haven't actually passed the basic year 1 and 2 math courses. I thought I could let them rest and take more interesting courses. Turns out it's a requirement at our department to finish them before you're even allowed to start on the master thesis work. My idea was to finish them while working on my master's. I fucked up son.
[QUOTE=Swebonny;51827904]Time to retake calculus, stats, discrete math and logics :v: Quite embarrassing, I already have a bachelor's in computer science & enginnering and kinda working on my master's thesis, both rather math heavy. But I haven't actually passed the basic year 1 and 2 math courses. I thought I could let them rest and take more interesting courses. Turns out it's a requirement at our department to finish them before you're even allowed to start on the master thesis work. My idea was to finish them while working on my master's. I fucked up son.[/QUOTE] Lol, that sucks. I had to take a semester of advanced calculus to fulfill a requirement despite the fact that I had already taken the year-long real analysis course which is a straight up harder version. I just didn't go after a few lectures, and got A's anyway. Could you just skip out on it basically?
[QUOTE=JohnnyMo1;51828459]Lol, that sucks. I had to take a semester of advanced calculus to fulfill a requirement despite the fact that I had already taken the year-long real analysis course which is a straight up harder version. I just didn't go after a few lectures, and got A's anyway. Could you just skip out on it basically?[/QUOTE] I doubt it, our department are quite strict about the mandatory courses. I've passed bunch of courses that have the required math courses are prerequisites though :v: Guess I'll just officially start on my thesis in August instead.
[QUOTE=Swebonny;51828640]I doubt it, our department are quite strict about the mandatory courses. I've passed bunch of courses that have the required math courses are prerequisites though :v: Guess I'll just officially start on my thesis in August instead.[/QUOTE] Like, you are forced to go to them somehow even if you can pass the tests? That's silly.
[QUOTE=JohnnyMo1;51828754]Like, you are forced to go to them somehow even if you can pass the tests? That's silly.[/QUOTE] Forced to take the exam in order to pass yeah. Guess I'll do something fun with the time, write a guide about stats or something :S
What do you guys think of [I]Mathematics: From the Birth of Numbers[/I]? I got it and it's a pretty nice read so far. Seems to be a good reference book, too.
[QUOTE=Matthew0505;51920026]Are additive identities of different types considered equal to each other? e.g. does [0, 0] = 0? are matrices of different size filled with zeroes actually any different to each other? are 0 seconds equal to 0 metres?[/QUOTE] No. We often use the size of a matrix or vector to record important information. For example look at the adjacency matrix of a graph. It may be filled with zeroes (indicating no edges) but the number of rows tell us how many vertices are present. [editline] Hi Mum [/editline] I should add that 0 seconds is not the same as 0 metres. If I divide 0 metres by 1 second, I get 0 m/s. The value may be nothing but the units are still important.
[QUOTE=JohnnyMo1;51763731]Had my first taste of higher categories in lecture today. I'm sure a year from now I'll be sitting in my underwear in the dark editing nLab pages and rambling something about stable homotopy categories of spectra.[/QUOTE] I'm going to be self studying basic category theory next quarter. Seems interesting, but I don't really know very much about it yet. In my class on homotopies, whenever category theory is involed in part of a proof the professor makes a comment on how he doesn't like category theory lol
[QUOTE=doom1337;51928162]I'm going to be self studying basic category theory next quarter. Seems interesting, but I don't really know very much about it yet. In my class on homotopies, whenever category theory is involed in part of a proof the professor makes a comment on how he doesn't like category theory lol[/QUOTE] Your professor almost certainly is not a homotopy theorist, lol. People who don't like categories always seem a bit odd to me. Categories are the most elegant thing. They subsume so much of the math you know and make it easy to see the connections between them. It's hard going at first. I had to stare at the definition of a product for ages to figure out what it was trying to do. But universal properties are so cool. They're like "the deep explanation of what this thing is doing." Like the free group on n generators can be defined concretely with this whole spiel about reduced words on the generators and concatenation, but the universal property says "The free group generated by S, F(S), is a group where you take the generators to some other group via a set function S -> G, and there's a unique group homomorphism F(S) -> G that does the same thing with the generators." I think that's cool. Homomorphisms out of the free group are uniquely characterized by telling the generators where to go, so if you have a group that does that, you know it's the free group up to isomorphism. [editline]7th March 2017[/editline] And when you've seen that you can go "hey vector spaces have a property like that with bases and linear maps, are they free in some way?" Yep. Vector spaces are all free modules.
[QUOTE=JohnnyMo1;51928274]Your professor almost certainly is not a homotopy theorist, lol. People who don't like categories always seem a bit odd to me. Categories are the most elegant thing. They subsume so much of the math you know and make it easy to see the connections between them. It's hard going at first. I had to stare at the definition of a product for ages to figure out what it was trying to do. But universal properties are so cool. They're like "the deep explanation of what this thing is doing." Like the free group on n generators can be defined concretely with this whole spiel about reduced words on the generators and concatenation, but the universal property says "The free group generated by S, F(S), is a group where you take the generators to some other group via a set function S -> G, and there's a unique group homomorphism F(S) -> G that does the same thing with the generators." I think that's cool. Homomorphisms out of the free group are uniquely characterized by telling the generators where to go, so if you have a group that does that, you know it's the free group up to isomorphism. [editline]7th March 2017[/editline] And when you've seen that you can go "hey vector spaces have a property like that with bases and linear maps, are they free in some way?" Yep. Vector spaces are all free modules.[/QUOTE] Yeah, it definitely seems like a cool topic to look into. It's interesting to be able to deal with things like the category of all sets for example. And that's super neat about the vector spaces. I'm actually just learning about modules right now in my algebra class, but it makes sense. Also I'm realizing that homotopy theory is not for me. Pictures are not my favorite things, as I don't seem to have as much of a geometric intuition as most people sadly [editline]11th March 2017[/editline] Also I can't tell if I like Hatcher's Algebraic Topology book. On one hand it isn't too heavy of a reading, but on the other it can be super confusing and hard to follow sometimes
[QUOTE=doom1337;51942853]Yeah, it definitely seems like a cool topic to look into. It's interesting to be able to deal with things like the category of all sets for example. And that's super neat about the vector spaces. I'm actually just learning about modules right now in my algebra class, but it makes sense.[/quote] It's neat but the abstraction can be tough. I'm working on a homework problem at the moment that involves the category of elements, so we pick some category C, and we're looking functors from the category of functors from the category C to the category of sets TO the slice category of functors from the category of small categories to the category C. It's making my brain hurt. [QUOTE=doom1337;51942853]Also I'm realizing that homotopy theory is not for me. Pictures are not my favorite things, as I don't seem to have as much of a geometric intuition as most people sadly[/QUOTE] I like having geometric intuition because it feels like I'm proving tangible things when I can picture them, but when the thing is complicated enough that it's hard to picture, having facility with just the definitions probably leaves you better off. [QUOTE=doom1337;51942853]Also I can't tell if I like Hatcher's Algebraic Topology book. On one hand it isn't too heavy of a reading, but on the other it can be super confusing and hard to follow sometimes[/QUOTE] I think that's a very typical feeling about Hatcher. It's a good read sometimes but it can be too wordy, so the important stuff can really get lost in there. We're using May in my algebraic topology course, and it's basically the polar opposite. It takes a really neat view through the subject that's super different from Hatcher's, but it's so concise it would barely qualify as lecture notes on the subject.
[QUOTE=Matthew0505;52143402]Is there any literature on studying functions and relations purely in terms of their graph of ordered pairs (or tuples for three or more variables)? I can't seem to find anything about them. Example of what I'm talking about: given the graph S ⊆ ℝ^n of a implicit function ϕ(X_1, ..., X_n) between n real variables, define the derivative at any point where applicable in S. :snip: I can't be the only person who's tried to define derivatives and tangent vectors in set theory right?[/QUOTE] Is [URL=https://en.wikipedia.org/wiki/Differential_geometry]Differential Geometry[/URL] any help?
It's 23:15 and I'm watching Khan Academy vids.. Spoke to the Uni today, and I am considering going back and finishing the degree. Also, when I was in hospital, over the easter long weekend I made some headway on that e^-x circle problem; will share when back on PC.
Why is it that no matter how many times I learn the lesson "It's easier to learn things as you go than to try to learn everything from a whole semester in a week before the final," I still seem to do the harder thing? Though I was keeping up alright on homework, so maybe the pace of these last few weeks just make me feel like I haven't been keeping up. :v: On the plus side, my skills at making commutative diagrams in LaTeX are getting good. [editline]5th May 2017[/editline] Commutative diagrams are one of the greatest notational conveniences. They really make relations between things so much more intelligible.
Has anyone used textbooks by Strang? I'm wondering if I should start with his Introduction to "Linear Algebra" or "Differential Equations and Linear Algebra"
I'm having trouble understanding my professor's notes. I understand Linear Recurrences a bit, but he does the following: [img]http://i.imgur.com/WuBC6T6.png[/img] (Note the difference between "a" and "alpha") I simply don't understand how he made the final step, concluding that: [img]http://i.imgur.com/KDMllBQ.gif[/img] Is this just intuition? [editline]9th May 2017[/editline] Plugged in 1 for the alphas in the a[n] equation and I'm a fucking idiot
[QUOTE=thefreemann;52204091]Has anyone used textbooks by Strang? I'm wondering if I should start with his Introduction to "Linear Algebra" or "Differential Equations and Linear Algebra"[/QUOTE] I think his linear algebra textbook sucks, but it probably depends on what your major is and what you intend to be doing.
Has anyone taken differential geometry? I'm about to finish my course in it and I still don't have a good idea of what this class is about despite getting good grades on nearly everything. So far it's good for making maps and I think its best application would be for plotting missions on foreign bodies. Such as if you have the radar scannings of a planet's surface, you can use them to calculate the shortest routes(shortest route becomes a lot more complicated when you're travelling on a surface) for a lander on the surface of a planet or an asteroid. This would explain why the NASA rep in my class brought up that he was taking the class to learn how to map Venus' surface from the radar scans. Is anyone else specializing in mathematical biology? My neurogenetics professor was very excited for me when I told that's what I'm studying since we're rare and there are a lot of jobs for us. My group was excited too because it means that they don't have to worry about the calculations that go into calculating the area under the curves of the calcium spikes in C. elegans when it detects a pheromone.
[QUOTE=proboardslol;52208188]I'm having trouble understanding my professor's notes. I understand Linear Recurrences a bit, but he does the following: [img]http://i.imgur.com/WuBC6T6.png[/img] (Note the difference between "a" and "alpha") I simply don't understand how he made the final step, concluding that: [img]http://i.imgur.com/KDMllBQ.gif[/img] Is this just intuition? [editline]9th May 2017[/editline] Plugged in 1 for the alphas in the a[n] equation and I'm a fucking idiot[/QUOTE] [t]https://i.imgur.com/PNw1Cd8h.jpg[/t]
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