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/sci/ - Science & Math

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talk maths, formerly >>10229303
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Did I find an error in this proof? if not what is wrong with this line of reasoning?

http://www.ams.org/journals/tran/1975-209-00/S0002-9947-1975-0409255-0/S0002-9947-1975-0409255-0.pdf
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I will give 10^6 USD to whoever solves the Twin Prime Conjecture
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>tfw taking Real Analysis using baby rudin this semester
>tfw dirty stats major
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>>10260573
>>tfw taking Real Analysis using baby rudin this semester
Rudin is a meme.
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>>10260582
Rudin is a meme. is a meme.
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>>10260582
Reading baby rudin for self study is a meme, baby rudin + real life classes is not a meme
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hey /mg/. I'm in the market for a new laptop and I'm thinking about getting something like a surface book (pic related) for doing math on. Anyone use anything like this to do math, or have any other thoughts on what to get?
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>>10260650
Get an iPad Pro. You can draw on it. Seriously, you won't ever go back to using a laptop.
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>>10260671
I feel like a keyboard is kinda necessary for things like $\LaTeX$, computer algebra, etc.
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>>10260689
You can get a keyboard, and there appear to be apps which let you do Latex. I'd love to hear from anyone who's tried to use it this way whether it's any good though.
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>>10260573
Please don't post such lewd Remimis.
>>10260592
Essentially this. The exercises are based.
>>10260650
>>>/g/sqt
Or was it >>>/g/qtddto?
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>>10260671
Don't listen to this retard you can't code on a tablet
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>>10260650
>daaaaaammmmmnnnnn unix looks like that?????
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I've come up with a result that gives a field that has a subfield isomorphic to every other field with characteristic 0.
Is that old or should I at least post it here?
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Why do the majority of pure math faculty at my uni use Apple computers? I've considered getting one just because Sagemath seems to run a lot better on their Macs than on my PC
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>>10261083
>a field that has a subfield isomorphic to every other field with characteristic 0.
seems like there is an obvious cardinality problem with that
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>>10261106
I thought the construction of the surreals took care of that, so I can only really call it "a process that takes a cardinal and gives a field that contains a subfield isomorphic to any subfield with at most that cardinality."
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Could someone explain to me exactly why the graph of a liner equation is, well, linear? What's the intuition behind it?
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>>10261083
lmao, you mean prime subfields? Yeah, Q is a subfield of every field of characteristic 0
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>>10261142
It's the set of scalar multiples of a vector.
>>10261146
Backwards, it's a method to generate fields that contain every other field.
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>>10261148
Then no, as the other anon said, there's a cardinality issue with that.

And if K is your field, then surely K(t) has characteristic 0 and is not contained in K?
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>2/3 of my references haven't submitted their letters of recommendation yet
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>>10261153
It's not contained but not necessarily not isomorphic to some subfield, which is the crux of the issue.
Hilbert switcheroo is possible if it is at least uncountable.
And yes, the other anon has already pointed out the cardinality issue, you didn't need to repeat it.
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>>10261094
University provided laptops.
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>>10261161
I didn't graduate on time, but took the extra time to write a very good thesis and now I'm taking a year break. I don't regret it to be honest, the break let me cool off and read stuff that I want to.
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>>10261083
Never mind, it's a trivial result to beat out of Frobenius's theorem, so it's probably old.
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>>10261172
I like the idea of a break between undergrad and grad school, though I'm also lazy and don't trust myself to consistently maintain any sort of discipline outside of a school setting.
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https://terrytao.wordpress.com/2018/12/29/jean-bourgain
>I have just learned that Jean Bourgain passed away last week in Belgium, aged 64, after a prolonged battle with cancer. He and Eli Stein were the two mathematicians who most influenced my early career; it is something of a shock to find out that they are now both gone, having died within a few days of each other.

>Like Eli, Jean remained highly active mathematically, even after his cancer diagnosis. Here is a video profile of him by National Geographic, on the occasion of his 2017 Breakthrough Prize in Mathematics, doing a surprisingly good job of describing in lay terms the sort of mathematical work he did:
https://youtu.be/gbRnLrlpLPo

>..I last met Jean in person in November of 2016, at the award ceremony for his Breakthrough Prize, though we had some email and phone conversations after that date. Here he is with me and Richard Taylor at that event (demonstrating, among other things, that he wears a tuxedo much better than I do).

>[UPDATE, Dec 31: Here is the initial IAS obituary notice for Jean.] https://www.ias.edu/news/2018/bourgain-obituary-notice
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Ok /mg/, I will learn about category theory, where do I start?
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>>10262482
With algebraic topology.
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>>10260650
How much do you actually need to do beyond LaTeX and PDFs?

I literally use a fucking raspberry pi and a bluetooth keyboard. Any seriously computationally heavy work gets done on the beefy campus computers.
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what's the geometry behind linearly independent/dependent vector subspaces? For reference, a collection of subspaces, $M_{1},\dots M_{n}$ is said to be linearly independent if for any $i=1,\dots n$, $M_{i}\cap ( M_{1}+\dots +M_{n}) = \{ 0 \}$
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>>10259038
hey sci fags, happy new year.
so I was wondering which book do you prefer for pre-calculus. It must be consice with enough practice problems. my pre-cal dick is a bit rusty now. Want to lube it good.
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>>10262635
They're like planes or lines that touch on one point.
>>10262965
Lang is recommended a lot.
But it's literally precalc, I can't imagine some PhD out there actually being retarded enough to somehow write a bad precalc book.
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>>10262977
Basic mathematics by lang.?

Seems legit, I tought it was a meme book. Many pre-cal books are unnecessary lengthy. Lang's seems quite concise.
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>>10263011
Automatically disregard any post that says "x book/author is a meme". Your life will be much better.
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>>10263055

Explain. what do you mean, and why do you say that.
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>>10262635
Direct generalisation of a set of vectors being linearly independent, but instead of considering single vectors, you consider sets of vectors.

Thinking strictly finite-dimensional, any subspace $M$ (of a vector space $V$) has a basis $\{a_i\}_{i=1}^n$, so you can think of the subspace as the space spanned by the basis in $V$. If you have two subspaces $M_1,M_2$, they define two distinct spanning sets, $\{a_i\}_{i=1}^n,\{b_j\}_{j=1}^m$, on V, and when merged together, $\{a_i,b_j\}$ defines a single bigger subspace $M:=M_1+M_2$ that contains both subspaces. But since $M$ is spanned by at most $\dim M_1+\dim M_2=n+m$ vectors, then $\dim M\leq n+m$. You may want to find a criterion on when $\dim M= n+m$, then from theory you know that this is only attained if and only if its spanning set is linearly independent, and this is only attained if and only if $b_j\not\in \text{span}\{a_i\}=M_1$ for every $j$. This latter condition is equivalent to $M_2\cap M=\{0\}$.

Now geometrically this is very simple. It just means that $M_1$ and $M_2$ don't intersect anywhere but at the origin. One of the only visualizable examples is in $\mathbb R^3$: take a subspace $M_1$ to be a line through the origin and $M_2$ to be a plane through the origin. There are only two possible configurations: either the line lies on the plane, or the line doesn't lie on the plane. If the former, then in particular, the two vectors that define a plane can form a linear combination to form the vector that defines the line, and we have that $M=M_1+M_2=M_1$, so that $M_i\cap M=M_i$ for $i=1,2$. In the other combination, the line only intersects the plane at the origin and nowhere else, and clearly, all three fill up the whole space.
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>>10259038
What exactly "is" (co)homology?

I know everyone laconically describes singular/simplicial homology as counting the number of "holes" in each dimension. But this doesn't make sense for spaces like $\mathbb{R}P^k$ where you can have $\mathbb{Z}/2 \mathbb{Z}$ worth of a "hole." And then you have other homology theories which only seem to have in common that they satisfy the Eilenberg-Steenrod axioms.

The whole thing seems incredibly unmotivated to me. Is it just a technical gadget that makes classifying spaces easier? Why bother with the general Eilenberg-Steenrod setup anyway? Are abelian categories just really nice to work in?

Also I know cohomology has a ring structure while homology does not. So what good is it to use homology and cohomology instead of just say cohomology? What does one tell you that the other doesn't?
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>>10263011
Use Basic Mathematics if you lack even basic algebra, if not then first chapter of Lang's Calculus will do fine but iirc it skips Trigonometry so you might want to use Basic Mathematics chapter for that
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Who can advice calculus book. I already know calculus, but terms in my native language
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>>10263278
Schaum's Outline of Calculus.
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hi i get lost at 2:30 what is gather the x's together? for case (b) = 6x? do i disregard the -3x on the right hand side? that leaves me with 3x on the left hand side and 3x on the right hand side and then do i do no maths and just 'gather' the x's which amount to 6?.
second part of case (b) is 7, how does 7 happen? i see a +11(how do you describe the magic that using cases of +ve = -ve created +11?) and a +4 if i add them together i get 15? i could use the negative infront of the -3x and put it infront of the +11 giving me minus 11 and then add +4 which is the incorrect answer , the only way is to transfer the negative on the left infront of the plus 4 so negative -4 +11....why?
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>>10263447
>posting high school homework on /mg/
Negro.
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>>10263447
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>>10262977
>Lang is recommended a lot.
Lang is a meme.
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Help I memed myself into a top 25 phd program by being 'smart but lazy' in undergrad but now I lack the work ethic to succeed in grad school and I'm falling apart
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>>10263820
if you don't like it enough to work for it, why bother?
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>>10263849
Thanks I needed that
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>>10263082
damn m8, thanks.
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How hard is it to get into grad school?

I have been told im the type of person who should go to grad school but I'm trying to figure out if getting in would require me to kiss too much ass or not
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>>10261612
https://www.trin.cam.ac.uk/news/sir-peter-swinnerton-dyer-1927-2018/
>Sir Peter Swinnerton-Dyer, 1927–2018

>The College is saddened by the death of Honorary Fellow, Professor Sir Peter Swinnerton-Dyer Bt KBE FRS, on 26 December 2018 at the age of 91.

>Sir Peter’s long association with Trinity began in 1945 when he came up from Eton to read mathematics. He would turn into a leading number theorist of his generation. His research was supervised by J. E. Littlewood, whom Sir Peter described as ‘one of the greatest mathematicians of the twentieth century in a distinctly old-fashioned way’ (interview with social anthropologist and Fellow of King’s College, Alan Macfarlane, May 2008, available to view online at https://sms.cam.ac.uk/media/1131073)

>After a Research Fellowship at Trinity, he spent a formative year in Chicago as a Commonwealth Fund Fellow where he was ‘kidnapped’ (his word) by another great mathematician, André Weil. He returned to Trinity in 1955 as a College Lecturer in Mathematics where he also served as Dean from 1963 to 1970. He was elected to an Honorary Fellowship in 1981.

>Initially unsuccessful in achieving a University post in Mathematics (on one occasion being pipped by future Master, Sir Michael Atiyah), he found a position in the Computer Laboratory. In the autumn of 1958 he began collaborating with Bryan Birch, another Trinity mathematician, in experiments on the early EDSAC computers that led to their famous joint ‘Conjecture’. Birch describes the next four years as ‘probably the best of my life […] We were under no pressure to publish: we both had Fellowships, and knew we could get another job whenever we needed one’.
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>>10263180
>singular/simplicial homology as counting the number of "holes" in each dimension
No, the ranks of the homology groups do that, not the groups themselves, and it's one-half of the rank that tells you the number of holes. If you think about CW complexes, using Hurewicz's homomorphism you can consider $H_1$ as an Abelianization of $\pi_1$.
For the projective plane we know $\mathbb{R}P^2 = S^2/\mathbb{Z}_2$ where $\mathbb{Z}_2$ is the group acting on the sphere by antipodal inversion $x\mapsto -x$. Even though all loops on $S^2$ are contractible, the path from one point to its antipode will descend to a loop on $\mathbb{R}P^2$. This is why you only have two loop classes in the projective plane, which lift to a trivial loop and an antipode path, respectively, on the sphere. Also since $S^2$ is simply connected and $\mathbb{Z}_2$ acts freely and properly discontinuously on it, we know $\pi_1(S^2/\mathbb{Z}_2) \cong \mathbb{Z}_2$.
>The whole thing seems incredibly unmotivated to me
Not at all. De Rham cohomology is extremely well motivated in physics, specifically classical EM. Not to mention topological quantum anomalies are classified by homology groups on spin $G$-bundles via the Atiyah-Singer index theorem.
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>>10263180
Having $\mathbb Z /n\mathbb Z$ homology still makes intuitive sense. In the case of say, $\mathbb RP^2$, we have that its first homology is $\mathbb Z/2\mathbb Z$ since going around the equator is like going around the circle twice. In general, a degree $n$ map of the circle creates a $\mathbb Z /n\mathbb Z$ homology term, corresponding to how many times yo go around the circle when moving across the equator.
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what a mess

bump
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>>10264385
>>10264395
As another anon trying to learn homology right now, these are extremely useful posts. Great intuition. Thanks!
It can be easy to get lost in the sauce of exact sequences and to forget how the geometric interpretation works.
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>"presentation (10%)"
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
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>>10266009
kek, how bad can it be
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>>10266015
I've only given one presentation in a math course before but it was on something so brain dead simple that you literally could not mess it up (https://en.wikipedia.org/wiki/Cramer%27s_paradox) . No topic list either (so far).
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>>10266019
Do it on topological tensor products.
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>>10266026
huh?
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>2020 = 4 * 5 * 101
>2019 + 4 - 5 + 1 - 0 + 1 = 2020
mindblown
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>>10266033
https://en.m.wikipedia.org/wiki/Topological_tensor_product
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>>10266009
Functional analysis can be fun, but I can feel your pain about presentations.
Had to do 2 smaller ones 30 mins and one larger one, 1.5h and they were all absolutely shit, although in principle I like the idea of explaining a concept to other students, but I am absolutely shit at it, I can't even write something readable on the blackboard...
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>>10266009
Do it on applications of functional analysis in physics
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>>10263864
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just got my teaching evaluations back today. most of them were good i averaged about 4.1/5, and i can tell my students do appreciate the effort.

but there are always a couple students who basically take no responsibility for their education. so when they get their C/D/F they take it personally and try ripping me a new one in the comments. idk why but it always bugs me for the rest of the day.
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>read seething rate my professor review that just amounts to "he made me work for my grade a bloo bloo"
Every time
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>>10266448
i'm at least glade rmp has that feature, but it's a terrible service. the only useful thing i've ever learned from it is whether or not a professor speaks english well.

at least at my university, the students are asked to complete the evaluation online to look at their final grade. i think if they were asked to report their grade before evaluating a teacher they might submit more fair reviews. otoh they might not be motivated to submit reviews at all if that were the case. i'm not sure what the administration does with that information. i know that some teachers get appointed different courses based on reviews.
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I understand the proof of linear independence, but I don't see how showing the constructed set is linear independent proves the theorem $m \leq \binom{n}{s}$.

The set of polynomials $f_i$ they refer to is 14.3 here. http://lovelace.thi.informatik.uni-frankfurt.de/~jukna/EC_Book/sample/175-176.pdf

Basically, $f_1,...,f_m$ is a representation of the sets $A_1,...,A_m$ as a set of trivially linear independent polynomials.
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>>10266561
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>>10266559
Yeah those reviews are important, both to admin people and the professors themselves, who can use the helpful/constructive feedback (if any) to improve their teaching. At my uni the reviews aren't mandatory and they are randomly determined to be conducted online or in person. The online evaluations have a low response rate because it's easy to forget to do them, but for the in-person evaluations, the prof leaves the room for 20 mins while all the students fill them out. A student volunteer passes out papers to everyone -- you would look really strange if you chose not to fill one out.
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>>10266575
>A student volunteer passes out papers to everyone -- you would look really strange if you chose not to fill one out.
that's how it was at my undergraduate university. honestly i never gave anything less than a 4/5 to a professor like wtf do i know about how to run a class as an undergraduate.
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>>10266561
I literally recognize no notation in that image, but I'll go on an absolutely wild guess and say that the constructed set has (n s) elements, spans the whole whatever, and logically any other linearly independent set has to have less elements.
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>>10266584
Yeah I'm an undergrad. I'm the same way, I've never had a bad prof in my department. I can usually provide a minor critique, but it's in the interest of improving the class and never something that ruined the whole class for me. Can't stand smartass classmates who always think they know better than the prof and who feel entitled to tell them what to do (it's always math education majors too, never the other math options).
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>>10266439
>letting that bug you
apparently it should because you're weak
>>10266448
>"class was SO HARD, exams were IMPOSSIBLE and i couldn't understand ANYTHING the professor was saying... HE WILL FAIL U!"
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>>10266670
being an internet tough guy must be exhausting
>in b4 you sperg out
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>>10266584
>>10266650
very based
i've never given a prof below a 5/5. i like them all as people, and i don't give a shit how they choose to run their class. it's more fun to adapt to someone's style and experience new ways of learning the material than just whining about how the syllabus has this slight imperfection and how the homeworks didn't hold my hand. it's impressive how many people do so.
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>>10266678
>it's more fun to adapt to someone's style and experience new ways of learning the material than just whining about how the syllabus has this slight imperfection and how the homeworks didn't hold my hand. it's impressive how many people do so.
it's exhausting. like the material is there and it's in abundance. try a library. try a wikipedia article. there are so many tools but they think that every course is a little puzzle that if they can solve it they can get an A.
i think the only 4s i gave were for professors that went too much off of the book lol. i always liked the ones that went completely off of memory.
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>>10266584
>like wtf do i know about how to run a class as an undergraduate.
Probably a lot, from my personal experience and from the constant begging of my professors to PLEASE fill in the text fields, where you are supposed to do more then give marks, standing in front of a backboard makes you really unaware of what you are doing right and wrong.

I don't mean like that you should whine about it and use it as an excuse, but if you have got the chance to tell them (eg. through an anonymous survey) do it,they might not have noticed.
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>>10266685
yeah if i can think of anything.
>from the constant begging of my professors to PLEASE fill in the text fields
i would guess this comes from admin suspicion as to why the text boxes aren't filled, not because they're going to respond to feedback, unless you went to a private/teaching oriented university.
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>>10266673
>insert long and exhaustive sperg-out here
nah i'm just not getting why the opinion of stupid undergrads has an impact
then again i tend to be pretty stubborn, and i can see it being rough on someone who takes a lot of the criticism to heart
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>>10266697
it's not so much their reflections of me i guess, but that my job might depend on it. the university does care that i pass the right amount of people and it relies on students being happy more than it does on them getting good grades.
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>>10266691
Well, there are some professors who are genuinely interested in feedback, but some might just want to get the administration from their backs, sure.
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>>10266702
ah, i immediately assumed TA but that sounds more like a full lecturer position if you're passing/failing people. that's probably stressful.
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i cant dl Grillets Abstract Algebra from libgen, anyone know of other good sites?
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>>10266737
The bold one is usually the best working one.
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>>10266670
>"class was SO HARD, exams were IMPOSSIBLE and i couldn't understand ANYTHING the professor was saying... HE WILL FAIL U!"
I have never seen this occur
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>>10266821
no seeders, but i found it eventually, ambry isnt letting me download anything at all now, shame
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>>10266870
Ah, whatever. Here. I have it by coincidence.
https://mega.nz/#!Ao1hDSyB!RBKwtds8Nixq9PJ9O8MKrd7yQs7c4_ENT_6LlQn3810
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https://arxiv.org/pdf/1901.00492.pdf
>The Non-existence of Complex Sphere Sn (n>2)
>Jun Ling
>(Submitted on 1 Jan 2019)

>We show the non-existence of complex structure on spheres of any dimension other than two, in particular, on S6. Therefore we solves the open problem on the non-existence of complex S6.
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>>10266009
How the fuck could you complain about this?Presentations are the most applicable method of evaluate that you'll actually need as a career mathematician. Good luck when you have to present at a conference.
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>>10259038
What are the basic rules in maths that apply to everything you solve
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>>10267748
This, also it's easy points. If you know enough about your subject and are confident enough to do some boardwork on the spot, you will have some success.
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>it's a yellow book
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>>10259782
that's pretty cool
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Is there a special name for a predicate $P(x)$ where $\forall x. P(x) \iff \exists x. P(x)$? I.e. there's at most one such x?
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Has anyone taken the GMAT? You never realize how much a math background makes you feel like king of the majors when you see their subjects.
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>>10269099
If and only if the one on the left is true or the one on the right is false.
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Is there any free software (I am poor and can't afford a license) that I can use to do boring algebraic computations like solving integrals, taking derivatives, solving equalities and inequalities and stuff like that? And if so, how much time would it take to learn how to use it to do that?
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>>10269234
wolframalpha.com
desmos.com
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Does anybody here know ramsey theory and want to hear my conjecture
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>>10267729
>put him to sleep then pump Atiyah's Alzheimer's for 5 hours
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>>10269234
Maxima
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>>10268299
yeah
but could you express it as a function?
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>>10269847
Is Mochizuki's early-onset senility your fault too?
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>>10270024
different anon
$\displaystyle (n+1)*10^{\displaystyle( 1+\left \lfloor{log_{10}(x)}\right \rfloor)} +n$

to concatenate any two numbers a, b in base 10 use
$\displaystyle a*10^{\displaystyle( 1+\left \lfloor{log_{10}(b)}\right \rfloor)} +b$
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I was about to post begging you folks for help because i thought i spotted two errors in my textbook, and while i was answering the >what did you try?, i resolved both issues. Why does this keep happening? I swear I can be stuck on a problem for hours, and the second im about to post here or on MSE i find the solution...
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>>10270067
Is this mystic code for "if the previous number has n digits, concatenate the (first n-1 digits plus one)(first n-1 digits)"?
I'm really not in the mood for making sense of long formulas.
>>10270080
Sometimes you think you're trying to solve a problem, but you're actually not, you're just staring at the textbook. Happens to the best of us.
The best tip I can give is "reread the definitions and theorems, and if it doesn't click actively try to track down equivalent statements until it clicks".
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>>10270090
Well, to be fair, most of the times I don't get pen and paper out and just solve the exercises in my head, because I feel that the second i start writing the details of the problem down, I'm just regurgitating facts without thinking
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>>10270090
the first one takes 9 then uses 10 and 9 and makes 109
or 10 turns into 11 and 10 and makes 1110

the second takes any a and b and makes a||b
ie a=84, b=877, a||b=84877
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>>10270115
Oh, nice.
By the way, I hadn't noticed earlier, but you were too focused on the second formula and put two variables on the first by mistake.
Should be something like
$a_{n+1}=(n+1)10^{log_{10}a_{n})+n$ where $a_0=10$
Except I don't remember how to make the biggest integer smaller than symbol.
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>>10269269
>Does anybody here know ramsey theory and want to hear my conjecture
Yes.
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>>10270103
not a mathfag so excuse me, but what do you do to deal with problems then?
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>>10270527

>MR0409255 (53 #13015) Reviewed
>Burr, S. A.; Erdős, P.; Spencer, J. H.
>Ramsey theorems for multiple copies of graphs.
>Trans. Amer. Math. Soc. 209 (1975), 87–99.

Theorem 2 in this is that every 2-coloring of $K_{5n}$ gives $n$ disjoint monochrome copies of $K_3.$

So they prove $r(nK_3) = 5n.$

Now, let $R(n)$ denote the normal (diagonal) Ramsey numbers.

Anon's conjecture:

$R(a)=m \implies r(nK_a)=m'n$ for some $m'\leq m.$

It would be good enough to prove that this holds when $m'=m.$
>>
>>10270533
Write a long post up for MSE and find the solution as I'm about to press "post"
>>
>>10270067
That x should be an n.
>>
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wow coq is rude
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>>10266311
>I like the idea of explaining a concept to other students
So do I, but what about the sharks? There are a number of students in my class who seem to live only to humiliate others for the smallest misstep while being oblivious to their own.
>>
>>10271164
I honestly have yet to meet such a person. I have had many presentations, by me or others, which really weren't all that good, but people were at least always polite.
>>
>>10270080
Similar things happen to me when I get mentally exhausted. I end up staring at the pages, retreading my attempts again and again, but only if I step away for some time I can actually get some progress.
>>
>>10270080
>the second im about to post here or on MSE i find the solution...
>>10270103
>most of the times I don't get pen and paper out and just solve the exercises in my head
>>10270533
>what do you do to deal with problems then?
>>10270573
>Write
>and find the solution

Gee, it sure is a mystery huh?
>>
>>10271185
to be fair, i've upped my time efficiency solving textbook problems overall by using this method
>>
>>10271090
yeah, whoops
>>
What the fuck does cyclotomic mean? Not mathematically, but like its dictionary definition. Where did it come from? It's an extremely cool word
>>
>>10272370

I actually happen to know the answer... It means "circle cutting."

So, the cyclotomic polynomial of order n is the minimal polynomial of a primitive nth root of unity, and roots of unity "cut" the unit circle on the complex plane.
>>
>>10272376
hmm, that makes sense. I thought it was somehow alluding to "cyclic" as in they form a cyclic group (which is directly connected to your reason anyways)
>>
>>10271169
I had a TA teaching calc and he was obviously nervous, and the teacher didn't really prepare him with any background of what we've gone over before the TA's day and people were literally blasting the guy for not knowing what he was doing. The back of his shirt was covered in sweat. He left the room for a second and everyone was talking shit, I felt bad for him.
>>
I'm curious what mathematical discussions among educated mathematicians are like.
Is this thread a good example?
>>
>>10272641
no
>>
>>10272698
What would be a good example?
>>
>>10272725
I saw a prominent old algebraic geometer fall asleep at a (phd) student seminar
>>
>>10272641
>I'm curious what mathematical discussions among educated mathematicians are like.
http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf
>>
>>10272641
IDK I'm just an undergrad math major, but I tend to spend a lot of time talking to my professor and this one grad student in particular. Math seems to me a subject that can only be explored in depth in writing. Sure, face-to-face conversations can be fun and interesting, but ultimately they seem to lack any significant depth (which is unfortunate). That being said, conversations with my profs often lead to interesting references, and/or insights into confusing topics that may not come for several hours, days, or even weeks.
>>
>>10272725

It seems that the most useful conversations I've had with professional mathematicians are the ones where they direct you to a better source
>>
Accidentally posted in /sqg/ so reposting here.

let $\ f:[a,b) \rightarrow \mathbb{R}$ be differentiable twice.
prove that if $\ f''(x) > 0$ then $\ g:(a,b) \rightarrow \mathbb{R}$ defined $\ g(x)=\frac{f(x) - f(a)}{x-a}$ is strictly rising

I've managed to solve this but I did it in a pretty brainlet-ish time consuming way. Can someone point me to an easy solution for this?
>>
>>10261114
Take an infinite cardinal k, choose a representative for each isomorphism class of field of characteristic 0 with cardinality <= k, take the tensor product and mod out by a maximal ideal
>>
>>10272641
Go to a conference
>>
>>10272998
Hint, by the mean value theorem you know that the there is always some $c(x)\in (a,x)$ such that $g(x)=f'(c(x))$ what can you tell about the funcion $c$?
>>
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>The more I have learned about physics, the more convinced I am that
physics provides, in a sense, the deepest applications of mathematics. The
mathematical problems that have been solved, or techniques that have
arisen out of physics in the past, have been the lifeblood of mathematics. ..
The really deep questions are still in the physical sciences. For the health of
mathematics at its research level, I think it is very important to maintain
that link as much as possible.
Math autists absolutely BTFO
>>
How do you learn math one you start getting outside of the calculus track with it's billions of materials to reference? I'd like to pretend I'm going for a PhD but still working on my bachelor's, and going on last year.
>>
>>10273021
I've proved it by taking $x_2 > x_1 \in (a,b)$ then saying $g(x_1) = f'(c_1)\ and\ g(x_2) = f'(c_2)$.
Then by contradiction proving that $c_1 \ngtr c_2\ and\ c_1 \neq c_2 \ \ thus\ c_2 > c_1$ which proves g is strictly rising. I don't follow exactly what you mean...
>>
>>10273053
Well as c is strictly increasing, and because the second derivative of f is greater than 0, the first derivative is also strictly increasing therefore the composition is increasing
>>
>>10273058
I know that f' is strictly increasing, but why is c being strictly increasing trivial?
>>
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>>10273034
>How do you learn math one you start getting outside of the calculus track with it's billions of materials to reference?
>>
>>10273062
Actually you don't need that function at all lmao. If you take the derivative of $g$ you get that it's only 0 if and only if $f'(x)=\frac{f(x)-f(a)}{x-a}$ Now if such and $x^*$ exists and we restric $g$ to the interval $(a,x^*)$ there is another $c\in (a,x^*)$ such that $f'(c)=\frac{f(x^*)-f(a)}{x^*-a}=f'(x^*)$ a contradiction as f' is strictly increasing. Therfore the derivative of g never vanishes and because f has a second derivative the first derivative is continuous and also the first derivative of g. And so it must be strictly positive or negative. Because the $lim_{x\to a}g(x)=f'(a)$ which is the minimum, it then follows that g must be increasing. Sorry for the brainfart, the properties of such function are derived from results like this, no the other way around.
>>
>>10272737
Who was it?
>>
>>10273071
No one can take on that program, r...right?
>>
>>10273447
What have you tried?
>>
>>10271358
>fly through easy questions but get stuck on harder questions
vs
>fly through easy questions and solve harder questions just fine

Get over yourself and put pencil to paper when you need to. No one is trying to tell you write down everything, but clearly writing down some things helps.
>>
>>10273447
It's not as hard as it looks, memorization is essentially the worst part, Tao literally did worse.
>>
>>10273774
Why would you lie?
>>
>>10259782
Whoa
>>
>>10273284
I've already doxxed myself once this week
>>
>>10268299
>>10273809
Brainlets
>>
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I don't see it. How does it follow from that?

The condition literally after 5.2.1 says that two p-adic integers are the same iff they have the same representation at every position?? Show the last condition be instead for all k large enough instead? Would make more sense with respect to the inverse limit definition
>>
>>10274052
should** not show
>>
>>10273810
wat
>>
>>10274052
A factorial.
>>
>>10274060
I'm pretty sure the exclamation mark is not meant to be a factorial sign there, but rather, a point of surprise
>>
>>10274052
Look at the condition given for two sequences to represent the same number. Now swap $y_k=x_{k+1}$.
Pay attention that the definition part is the whole italics.
>>
>>10274070
Right right right, you didn't make me understand it, but what was going wrong is that the $x_k$ represents the sum $\sum_{i=1}^{k-1}a_ip^i$, instead of the coefficients $a_i$ as I thought. I was confused since that meant every integer was 0 in the p-adics while theyre meant to embed nicely
>>
>>10274084
correction to that **every positive integer
>>
>>10263074
he means he’s misleading you into thinking you’ll be able to do difficult algebra and trig functions with just Lang
>>
>>10266575
I’ve chosen not to fill them out to spite the professor before in front of many other students who saw and realized what I was doing. Imagine caring about undergrad at all.
>>
>>10259038
Consider a unit vector in 2D space.
What are it's x and y component magnitude?
>>
>>10274294
D E P E N D S
E
P
E
N
D
S
>>
>>10262977
>Lang is recommended a lot.
Lang is a meme.
>>
>>10273785
>Why would you lie?
What do you mean?
>>
>>10274307
assume 30 degree with x axis
>>
>>10274388
Polar coordinates
>>>/sqt/
>>
>>
>>10275325
mine now
deal with it
>>
>>10275666
Epic win!! XD [checked]
>>
>>10275666
What's the most satanic piece of math out there?
>>
>>10275325
No, this thread usually only has bursts of activity whenever someone asks a question or makes a good shitpost.
If you absolutely need something to discuss:
Synthetic geometry>algebraic geometry>differential geometry.
>>
>>10260650
All you need is a pen/pencil, paper, laTeX and org-mode. C'mon!
>>
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Do any Cryptologists lurk ITT?
>>
Any recommendations for 3D-space and vectors and junk?

I'm working through Spivak's calculus, just got to chapter 4 appendix 2, which is on conic sections, and I have no idea what's going on with planes and intersections or anything here.

I'm guessing I skipped out paying attention when learning about planes and vectors back in high school?
>>
>>10276789
I think usually the best way to understand these sort of things is getting directly to the meat of the matter. As such, I think you should instead study locally 3D spaces, which is much more general than a global one. I would start with the proof of the Thurston geometrisation theorem and then work your way up
>>
>>10276827
>>
>>10276789
Any analytic geometry text. Can't recommend any in particular.
>>
>>10276832
In that case I would try studying vector bundles. You see, 3D space is a 3-vector bundle over a point. We can generalize 3D space in the following way: take a topological space X, and attach a 3D space at every point continuously, so that in any small open set U of X, the space looks like the cartesian product U x (3D space).
>>
>>10272641
Yes.
>>
ok who did this >>10276521
>>
>like wtf do i know about how to run a class as an undergraduate.
There was one time where I put more than I would on that section of the critique. IIRC it was what would you do to improve the class or something along those lines. Throughout the whole class a group of math education majors in an abstract linear algebra class kept asking why does (topic) matter or when are we going to use this? Shit was irritating. Just wrote to glance over questions like that and to encourage them to come to office hours to get answers to such types of questions
>>
>>10276973

Whenever anybody asks those questions, the teacher should be able to destroy them with the answer
>>
>>10276950
The representation theory part at the end, kek
>>
>>10276973
>>10276997
This.
>how about you suck on my killing vector
>>
>>10276973
Why do math education majors have to ruin every math class?
>>
>>10276997
Calm down, it's literally just a student asking for an application.
>>
>>10272381
Think "atomic" (a-tomic, cannot be cut). Tomic means cutting, the prefix 'a' means cannot. Then cyclo means circle, so cyclo-tomic means cutting the circle. A group that is cyclic is named like that because it can be identified to points on a circle.
>>
>>10259038
Although I have nothing to add to the thread, I wanted to let you know this thread is greatly appreciated. Please continue when this is archived. It's like a breath of fresh air.
>>
>>10277059
>yeah bro, $\mathbb Z^23$ is totally circular dude
>>
>>10277064
Sorry, I don't understand what you mean. Be less sarcastic next time.
>>
>>10277031
people who need applications to stay motivated should not bother with abstract mathematics
>>
>>10260582
How is Rudin a meme? It gives you everything you need.
>>
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>>10259038
oops i forgot about the math general. working through problems and got stuck and made a post, can someone help me figure out if this shit is possible

im a brainlet how
>>
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what kind of math is required to proof a solution exists?
>>
>>10277828
graph theory, it isnt possible on a flat piece of paper because of planar graphs
>>
>>10277828
this image isnt possible and everyone knows it
>what kind of math is required to proof a solution exists?
usually by contradiction if you dont have a constructive proof
>>
>>10277779
I am pretty sure you first try to do the FT of the derivative of that function. Recognize that the derivative is a constant 1.

Then use the table to get the FT of a derived f(t) i.e. work backwards in a sense.
>>
>>10277838
>>10277843
I am more interested in the branch of mathematics that would have this kind of problems. I was thinking topology but afaik topology deals with the continuous values.
Only graph theory? I though graphs don't care about the 'shape' i.e. intersecting lines are perfectly fine. i am obviously not a mathematicians (C.Eng) but if possible, the specific branch of graph theory?
>>
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>>10276973
Math ed majors are the scum of the earth. If I wanted to kill someone's interest in a math class and make them give up that topic for good, I would just tell them to ask a math ed major what they thought of the class.
>>
>>10277844
>Then use the table to get the FT of a derived f(t) i.e. work backwards in a sense
so after i take the FT of the derivative which is just the integral of e^(-jwt) from -1 to 1, how would i use the table with this? i tried a few things but nothing close

and tys 4 the help
>>
>>10277455
"Rudin is a meme" is a meme.
Lurk more.
>>
>>10277880
Dude you can fucking integrate te^(ct) can't you? Or just e^(ct) in this case.
This is fucking simple.
>>
>>10277779
>>10277925
Actually, just do the actual integration.
Note the Euler's formula: e^ax = sin(...) + cos(...)
>>
>>10277925
>>10277941

ya kept makin small errors so i t hought i was gettin sometin fundamental wrong

tyguys
>>
If I have a measurable space $\left(X,\Sigma\right)$ and a function $g:X\to \overline{\mathbb{R}}$ such that for all measurable functions $f,h$ (with the Borel sigma algebra in the reals), $mid{f,g,h}$ is measurable, where mid is a function that for every $x$ it selects the in-between value, then how could I show that $g$ is itself measurable?
>>
>>10259038
How do I into topology and algerbriac geometry?
>>
>>10277843
>>
>>10259038
What are some good algebraic topology books with a "textbook" feel (i.e. not Hatcher)? Thoughts on this book?
>>
>>10259942
he did. erdos is number 2
>>
>>10278187
Set f>g>h.
>>
>>10276161
GT
>>
>>10278338
>What are some good algebraic topology books with a "textbook" feel (i.e. not Hatcher)?
>>
>>10278296
>How do I into ... algerbriac geometry?
>>
>>10278296
>how do I into topology
Munkres is thrown around a lot.
>Algebraic Geometry
...............
Algeo is something of a meme here. It's not as cool as people pretend it is.
>>
>>10278296
before you can even begin, you need the basics of topology (first 5 or 6 sections of munkres), abstract algebra (aluffi is a good book and much shorter than lang, although less complete), linear algebra (Roman), galois theory (Morandi), commutative algebra (atiyah-macdonald), algebraic topology (hatcher is fast and good for beginners), homological algebra (rotman), sheaf theory (serre), superclassical geometry for motivation (coxeter), classical geometry for more motivation (Fulton), then you can start real algebraic geometry with either Hartshorne or Vakil (or EGA if you're feeling brave)
>>
>>10277850
In the simplest terms, graph theory studies networks of connected nodes. The way they are visualized is arbitrary.
>>
>>10277850
Technically, I think you can prove that image has no solution with the Jordan closed curve theorem instead of graphs, but I might be wrong.
>>10278557
He published more pages, but Erdos won in number of papers.
>>
>>10277031
Although I do agree to some extent, there's a time and a place for such questions. They usually asked it during times when probably the whole class was struggling with understanding the proof and they would ask meta questions concerning the class rather than the material covered which took time out of lecture that could've been better spent explaining the material
>>
The Einstein summation convention and the use of superscripts were mistakes and don't actually make literally anything easier to read.
>>
>>10279244
but abstract index notation can be interpreted in any compact closed category
>>
>>10278593
How do I know such functions exist?
>>
>>10279575
Hm?
Oh, my bad, I'd forgotten that a measurable function just had measurable pre-images.
Anyhow, assume there isn't. Set f=a and h=-a. Clearly, since mid takes only the value in the middle, it takes the value a whenever g>=f, and -a whenever g<=h. If you use two values of a you can basically box in the preimages.
I'll leave the formalization to you.
>>
early 1900s textbook writer:
>hmm, yes, this figure might help
>>
>>10279244
It's usefull in order to give general rules for efficient manipulation of the objects in Riemannian Geometry. It isn't supposed to give you any proper understanding of the subject, but physicists are so full of themselves they will tell you is much more physical and intuitive that way.
>>
>>10279593
>yes, yes... trivial
>>
>>10279593
>>10279598
>geometry is so beautiful
the worst fucking subject
>>
>>10279598
lol look at Mr. Circle crank man. ~laughs~ Tell me, how do you make money off it? ~wicked cackles~
>>
Can someone help me understand this statement? By the (1.1) sextic he literally means any sextic polynomial, and by 2-d sphere he means the Riemann sphere
>>
How do I write about my research interests in a master's program application? I've done some undergraduate research relating to my advisor's field of study and I think it's pretty interesting, but I have only the vaguest notions of what it's about. I want to learn more about it but I have no idea what specifically I want to research, I'm still just an undergrad and barely know anything yet.
>>
>>10280403
If it's a pure program, nobody expects you to know. Just list your general interests, what you liked about your research, what areas you used, etc
>>
>>10280403
Just write a bit about what fields you did research in and what areas you have a particular interest in.
I doubt anybody expects you to have done some major research or to know what exactly you will want to investigate further, before you even had the opportunity to dive into its full depth.

I had to write a letter of motivation for my masters program and that is basically what I did.
>>
wait what
>>
What is the dimension of a linearly independent basis that spans R^k as a function of k?
>>
>>10282672
k
>>
$log_{\partial}f(x)$
If you saw that on a text out of nowhere, you'd assume it's the logarithmic derivative, right?
>>
How do you prove:

- Real number multiplication is associative
- Real number multiplication is commutative
- That -1 * 1 = -1, and that -1 * -1 = 1

I'm just going over some things that I have never seen proof of, but I use all the time
>>
>>10282907
Depends. Are you using the Dedekind cuts approach, the Cauchy sequences definition, or the axiomatic approach?
>>
>>10282911
Does it matter? They're all wrong and on shaky foundations
>>
>>10282457
I had that nice little surprise when I tried to reference the Iris dataset. Bit of an elephant in the bibliography.
>>
>>10282911
I'm too new to pure math to even really know what you mean, sorry.

But I have had real analysis, so I know about cauchy sequences, but I don't see how that relates to what I want to do.
>>
>>10282927
Constructing the rationals is extremely easy. You define a field, and then you write down "the smallest field with char 0".
Constructing the reals is, on the other hand, a bit of a hassle. So there are a couple approaches:
You take the set of Cauchy-sequences of the rational numbers, and take the equivalence class of functions with the same limit. Sum and multiplication are defined pointwise. So the number one looks like the sequence {1, 1, 1, 1, .....}, pi looks like {3, 3.1, 3.14, ....}, and so on.
A Dedekind cut is a set that, if it includes some rational x, also includes every rational smaller than x. We set every Dedekind cut to be a real number, and sum and multiplication are set trickery.
The axiomatic approach is basically taking a field, and saying that it satisfies the Dedekind axiom.
Ultimately, those you asked are true because they're true in the rationals.
>>
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>>10282916
>They're all wrong and on shaky foundations
>>
>>10282916
Epic
>>
>>10282907
(1 - 1) = 0
(1 - 1) *1 = 1*1 - 1*1 = 0
1 - 1*1 = 0
-1*1 = -1

(1 - 1) (1 - 1) = 0
1*1 + -1*1 + -1*1 +-1*-1 = 0
1 -1 -1 + -1*-1=0
-1+ -1*-1=0
-1*-1 =1
>>
>>10282941
Thanks! That definitely helps, I think I can work out a decent enough proof using those definitions
>>
>>10280412
>>10281271
Thanks, that helps a lot. I'm stuck on the personal history statement they want me to write. It says it should be "a concise 1-2 pages" but if I'm being concise, I can only come up with two paragraphs. One is about how I became interested in math and another is about my financial situation. Not sure what else I'm supposed to write about.
>>
>>10277850
>Only graph theory? I though graphs don't care about the 'shape' i.e. intersecting lines are perfectly fine. i am obviously not a mathematicians (C.Eng) but if possible, the specific branch of graph theory?
There's a whole area of graph theory called planarity that studies non-intersecting "drawings" (embeddings) of graphs in abstract surfaces. It can be proven that a graph is planar (that is, can be drawn in the plane without edges intersecting in their relative interiors) if and only if it doesn't have the complete graph with 5 vertices and the complete bipartite graph with 3 vertices on each side as minors (equivalently topological minors). The graph that corresponds to the problem you posted happens to be the latter, and is therefore not planar (no solution exists).

In fact, it can be proven that any hereditary property about graphs can be characterized by a list of "forbidden" minors, though that's more advanced. Check out Diestel's Graph Theory book, specifically the Planarity section.
>>
>>10282916
Go to bed, Wildburger.
>>
>>10283473
> another is about my financial situation
Let me guess, you're american?
>>
>>10284108
Yep
>>
>>10283588
thank you
>>
>>10284138
God, the US is such a shitshow... So much for meritocracy
>>
>>10259038
Another question! How much time does it takes(on an avg) to complete basic mathematics by lang. Is 1month enough? To do every exercise. I don't know the difficulty level of that book.

I am an undergrad but still am nervous and feel like I don't quite have mastered all the basic concepts. I am familiar with 90% of the topics that are listed in the contents. The fear comes from my lack of practice in HS days.

So how many days will it take to finish the book cover to cover? I want to do this once and for all.
>>
>>10278338
Rotman.
>>
Is functor homology fun?
>>
>>10285155
is there any other homology?
>>
Pretty sad my undergrad is coming to end. Once I leave in May I'll never just have a chill time taking classes and learning cool stuff again, I'll either have to become a grad student which is an actual job or go at it alone.
>>
>>10282941
>You take the set of Cauchy-sequences of the rational numbers
why do I always see "cauchy-sequences" being used for this definition, and never just "convergent sequences"? Since they're equivalent, you'd expect to be able to define it using convergent sequences too
>>
>>10283473
Write about yourself. Presumably you've had a life beyond studying math for four years at a university.
>>
>>10285480
They're only equivalent in complete sets.
In the rationals, for example, you can make a Cauchy sequence which converges to an irrational, and therefore isn't a convergent sequence in the rationals.
>>
>>10285480
>Since they're equivalent
only in a complete space
>>
>>10285480
they're not equivalent in the rationals. if you took all the sequences which converge in Q, and took equivalence classes, guess what you'd get, the fucking rational numbers.
you need to allow for "things which should converge but might not" i.e. cauchy sequences and then the whole point of constructing the reals / constructing the completion of a metric space is "filling in the limits of those sequences."
>>
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>>10285481
imagine having a life outside of studying math. lol. what a loser.
>>
>>10285500
Post of the week.
>>
Find a bijective function $\pi:\mathbb N\to \mathbb N$ such that $\sum_{n=1}^\infty \frac{\pi(n)}{n^2}<\infty$
>>
my college has a 1 credit homotopy type theory class. I've taken mv calc and lin alg, and I know nothing about types or homotopy. Should I take it? What's it about in basic terms?
>>
>>10285544
you don't know any group theory or topology, do you? i don't really see why you'd take it
i don't know much about homotopy type theory, but those 2 things are essential for any study of homotopy.
>>
>>10285544
It's foundational shit, possibly interesting but useless to the working mathematician
>>
>>10285539
this sounds like something which really, really should not exist, but then again it is real analysis
>>
>>10285559
Yeah, I'm pretty sure it doesn't exist. Haven't played around with it or anything, but I think some sort of Riemann-rearrangement-theorem-type argument might work.
>>
>>10285539
There isn't one. Set up the sum as from 1 to N, and show that picking the N smallest numbers in the usual order always minimizes the sum.
For example, if N=1, picking 1 noticeably minimizes the sum.
>>
>>10285564
I'm not convinced that that proves anything. Seems like you're swapping an inf with a limit. Is that okay here?
>>
>>10285569
That's not quite the point.
You have $\sum_{n=1}^N \pi (n)/n^2$. You can show that, to any N, $\pi (n)=n$ gives a smaller sum than any other injective function.
>>
>>10285539
If one existed, since all the terms are positive the sum would converge absolutely. Therefore any rearrangement would also converge, in particular the one corresponding to $\pi(n)=n$.
>>
>>10285575
Yes, I understand. You're squeezing the sequence of partial sums to infinity. Not bad.
>>
>>10285597
That rearrangement would have different denominators.
>>
>>10285621
Yeah.
The rest of it is just the usual. If we could swap for smaller numbers, we would, so the image of minimizing functions fron 1 to N is always 1 to N.
If we could swap a smaller number to the left, the sum would diminish. Proving these two and joining them up for the lower bound is routine.
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>>10285626
Yeah nevermind I'm retarded.
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>>10285640
>routine
that's code for "I don't know how to do it, but it's a fairly obviously true statement"
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>>10285650
It's code for I'm not typing that shit.
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What are your favorite real analysis books? My course used Elementary Analysis by Ross, but I want to try using a different book for self-study
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>>10285799
My second course in analysis used Abbott and it was pretty good. I still prefer Ross though.
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>>10285799
>>10285811
imagine liking ross, god damn
rudin is a classic but I prefer pugh. it's far more readable and has great images, but it's not a book for literal children like ross. it's also got amazing exercises (better than rudin imo)
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>>10259038
What's the best tutorial to learn R?
I of course googled and it came up with an incredible number of links. Which is the best one?
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>>10285888
The best tutorial is always googling your way through an actual project
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>>10285401
Functor homology is a theory of its own.
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>>10259038
Hey /mg/, it has been a few months since I stopped coming here (or maybe a few weeks, I've lost track of time). Just came to ask, is this general still getting worse by the minute or has it finally hit rock bottom?
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What books have you used to learn graph theory and combinatorics?
I have been recommended 2 books one written by S. Pemmaraju, S. Skiena and one by J.M. Harris, J.L. Hirst, M.J. Mossinghoff.
Are these a good start?
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>open up a PDE book
>instantly become an algebraist
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>>10286913
Nobody posts here anymore. Feels like a total wasteland
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RIP Atiyah
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>>10287708
unfortunately, he did end up finding a complex structure in his heart
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>>10287708
F
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>>10287586
Holy shit, barely any posts in 8 hours. /mg/ really is dead. Also, Stein, Bourgain, Swinnerton-Dyer all died and scarcely a mention in these threads holy fuck.
>>10287708
This has not been a good two months for mathematicians.
>>10286920
Have you tried "A course in combinatorics" yet? Requires some basic abstract algebra but barring that it's fairly complete and has a low overhead.
>>10287539
There are many nice algebraic solutions to certain classes of differential equations.
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Show that for all real $x$, $\cos\cos x\geq|\sin x|$
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What are some of your favorite abstract algebra books? Looking for a 2nd text for my intro class this upcoming semester.

Here are some I've looked at:
Basic Algebra I, Jacobson
A First Course in Abstract Algebra, Fraleigh
Artin's Abstract Algebra
Dummit & Foote's Abstract Algebra
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>>10288283
>A First Course in Abstract Algebra, Fraleigh
This is a remedial textbook for future high school math teachers, actuaries, and cs majors

>Basic Algebra I, Jacobson
>Artin's Abstract Algebra
>Dummit & Foote's Abstract Algebra
These are good
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>>10288283
>>10288316
Also what's the "1st text" that the class uses? Herstein's Topics in Algebra?
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>>10287586
Because generals are cancer.

>>10288113
>Also, Stein ... died and scarcely a mention in these threads holy fuck
>Elias Menachem Stein (January 13, 1931 – December 23, 2018)

;_;
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>>10287708
https://www.maths.ox.ac.uk/node/31190
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>>10288328
Looking at some of his lectures and talks it's clear he was a cool guy, plus his analysis texts were actually ones I liked a lot.
For those who haven't seen some of them
[spoiler]Serre is probably next[/spoiler]
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>>10288378
>gromov
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>>10288378
I demand a sticky if Serre or Witten die.
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>>10288317
https://www.amazon.com/Abstract-Algebra-Course-Dan-Saracino/dp/1577665368

This one.
I'll buy Jacobson's and the Dummit & Foote one on amazon since they're pretty cheap.
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>>10288283
Fraleigh, Dummit and Foote, Herstein
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>>10287708
Fuck this shit
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>>10288428
Witten is still in his 60s so he's probably safe
>>10288427
>gromov
Delete this right now.

Actually, now that I think about it, Conway and Langlands are getting pretty old as well.
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>>10288704
Fuck, Milnor is almost 90

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