What always intrigued me is how deep math gets. What also intrigues me is how professors see these deep concepts as elementary.
@brennenhorton2493
Жыл бұрын
When you teach the concepts, you have to understand them at a more fundamental level in order to provide metaphors that everyone can understand. This comes naturally through time and practice. Then, once you've learned the concept, you don't ever "unlearn" it so it seems elementary to you. Good professors are those who understand that the things they take for granted were not always easy.
@olem4841
Жыл бұрын
@@brennenhorton2493 Sometimes...
@piggynatorcool668
Жыл бұрын
@@brennenhorton2493 with the exception of my teacher
@timonbubnic322
Жыл бұрын
burden of knowledge
@sherlyn.a
11 ай бұрын
Many students learn this stuff just to pass a test. Professors keep re-using and re-using what they learned, so eventually it has to become elementary
@jackbrolin7709
Жыл бұрын
I’m glad myself and many others are finding your channel. This “in the trenches” style of mathematics grad school videos are super informative to many undergrads like myself
@stacia6678
Жыл бұрын
And to high school students like me! I think getting exposure to more complex mathematics at an earlier age is more beneficial.
@legacyrxt7570
8 ай бұрын
its also just entertaining and interesting
@stevenmccallan9202
Жыл бұрын
After putting my name on the paper, I'd be lost. That's why I'm not now, nor ever will be a PhD candidate with math.
@poere1234
Жыл бұрын
Haha same 😅🤣
@geometrividad7716
6 ай бұрын
it's not too bad, but you do need to take some courses on linear algebra, abstract algebra and possibly field theory, relatively elementary courses should get the job done, the problems shown weren't that difficult. All the problems were pretty standard. it's a skill obviously, nobody is born knowing this stuff
@86_beans
Жыл бұрын
In an engineering vector calculus exam, there was a question to solve for the tangent plane. The examiner forgot to specify powers such that the question in fact asked for the tangent plane of a plane rather than a more complex surface like a sphere or cone. I sat there for 10 mins second guessing myself and bit the bullet and just wrote the equation that was on the exam on a blank page and got 15/15 for the question. I love trivial questions!!
@zakaryjaynicholls9867
Жыл бұрын
As a grad student in applied math/astrophysics, it's neat to see what others in doing in other grad programs. Your exams are like bizarro world versions of my exams with different content. The classic grad exam setup seems to be: the questions are quite complicated, quite a few of them were homework set examples from homework sets that took bloody ages to do, and you sort of have to have done the questions beforehand to get them right in the exams. We all get to suffer together.
@ordenax
Жыл бұрын
Hey man! I am applying for an Astrophysics master's course. I do have basic understanding of the varied fields in it. Stellar physics, Observational, Computational, Theory of relativity. And my Maths is decent, that I am quite fine with Differential Equations. What else should I be aware of, before I join the course. Could you help me please?
@zakaryjaynicholls9867
Жыл бұрын
@@ordenax That's about it, It's also very helpful to be good at latex as well as python/julia/matlab. A good understanding of physical mechanics and electromagnetics is also super valuable. This was the case for my programs.
@ordenax
Жыл бұрын
@@zakaryjaynicholls9867 Yeah Physical Mechanics and Electromagnetism and even a basics of Quantum Mechanics I understand. To help with QFT. Sure, The maths would be advanced, but it is something I hope I can manage
@zakaryjaynicholls9867
Жыл бұрын
@@ordenax In astrophysics, the math is really not that hard compared to doing graduate courses in actual math. So as long as you're good at single var calc/multi variable calc/basic ODEs/basic PDEs/numerical modelling/statistical modelling as well as numerical computing, you can probably learn what you need as you go along.
@ordenax
Жыл бұрын
@@zakaryjaynicholls9867 Thank you for replying. Helped me. 👍
@youtubepooppismo5284
Жыл бұрын
Please keep up these videos I love them so much
@mathmetal1979
Жыл бұрын
Thank you for sharing this! Going to be going for a Ph.D. in Mathematics where I will be studying Algebraic Geometry. This is just getting me excited, yet nervous. Thanks again!
@kevinpostillon8846
Жыл бұрын
Algebra is by far my favorite subject, and this exam looks approachable, except for the field theory part. I really like that this connects to Analysis and Topology I believe we should not separate it, it's really exciting when it all makes sense finally why in school they make us do functions and equations in a certain manner because R is a field, and why we extend it to C to make it algebraically closed having them as integral domains because every field is sol, while this all happening in a topological space of collection of basis as domain and range. it's reassuring that every math discovery came out natural. I wish you a happy career wherever it leads you.
@limefish865
Жыл бұрын
Bro just started speaking a different language
@worldblazin4209
Жыл бұрын
Thank you so much! Finishing calculus 2 this semester and starting Group Theory either 3rd or 4th semester (parents want me to leave off math for just Major courses in the Fall 2023). Truly shocked at how you wrap your brain around this, its like how I worked during High School Honors Geometry ("Pre-AP") but with confident whereas I was the study crammer before tests. Pursuing a Computer Science major but want to continue Math courses for a while since this was just my Freshman University year. Thanks again!
@realtechhacks
6 ай бұрын
@@limefish865 Watches video about a graduate level math exam. Is surprised when people use mathematical language in the comments.
@algorithminc.8850
Жыл бұрын
Enjoying your channel ... a great find. Cheers
@Grandplat_Freestyling
Жыл бұрын
Im not even near this level but its still super interesting, ive been watching for about a month now, maybe more, keep it up:)
@Minexorek
Жыл бұрын
Damn, these videos are doing pretty well. Keep at it :)
@mytube650
Жыл бұрын
I have two actuarial exams this week. This video is oddly reassuring. Thanks for posting. The KZitem algorithm has done something right.
@owenjackson4751
Жыл бұрын
Im using the Sheldon Alxler book for advanced linear right now. Its the first pure math course I've taken other than formal logic and Its super interesting to see how abstracted all the things I learned in my first linear algebra course were and I didnt even realize.
@ClumpypooCP
Жыл бұрын
Yeah thats always a cool thing of learning higher math
@mastershooter64
10 ай бұрын
I mean....it's not necessarily "advanced linear algebra" it's undergraduate linear algbera. Advanced lin alg would be something like Advanced Linear Algebra by Steven Roman
@user-hy6cp6xp9f
Жыл бұрын
Love your content from Colorado ❤️ never got to pursue a math education formally, living vicariously through you. Would love to see what you’re curious about research wise
@otinane4051
Жыл бұрын
Really interesting vids! Math undergraduate here(4th year),it is interesting compared to your Real analysis exam (i could not do much) your algebra exam is something i would be able to solve a few. Linear section problem number 2,Group Theory problem number 2....not looking good so far but in Ring theory can do problems 2,3,4, and Field theory can actually do 1,2,3,4,5 except 4 c. 4 was actually an exam problem in Galois theory (Without C).
@narwhaletuber
Жыл бұрын
I love your video because it can be applied to life in general. That's how scary math is... If you have the capacity to imagine more abstractions, you are scratching the itch of existence.
@ayushgupta4725
Жыл бұрын
i found your channel just yesterday and dude i am obsessed with you ...i soo relate to u (i am an undergrad student studying electronics) ...love your videos ..hope to see more of your content in future ..keep it up ..ps would really like a entire day in a life type video
@extreme4180
Жыл бұрын
U studying in India or overseas?
@ayushgupta4725
Жыл бұрын
@@extreme4180 india
@larryyonce
Жыл бұрын
Now I know what a qualifying exam in Algebra looks like! Congratulations on passing it. 👍 Job well done I say.
@PhDVlog777
Жыл бұрын
Thank you very much!
@prithvidhyani2002
Жыл бұрын
as an undergrad, wtf is going on?
@rylanbuck1332
2 ай бұрын
Lmaooooo. Felt. This used to be me, and now my qual is in like 4 days 🙈😭
@glattt4283
Жыл бұрын
what is the website that you mentioned that has the pool of algebra problems?
@glattt4283
Жыл бұрын
great content btw
@00tact
Жыл бұрын
This is much easier than the algebra qualification we had in the mid 1980’s. Any old timers like myself think’s so? That group theory looks almost first year undergraduate…. No offense btw.
@algebraist3212
Жыл бұрын
This exam is pretty easy compared to the ones in other universities even today.
@TomokoAbe_
Жыл бұрын
I admire your discipline.
@trs80model14
Жыл бұрын
Oh my I remember that linear algebra problem! I think it was a homework problem - and I took grad Linear over 35 years ago
@savagelove1939
Жыл бұрын
My brain can't handle such questions as these
@wwebadgerse
Жыл бұрын
I'm surprised tbh, i'd expect it to be harder. Especially the field theory bit given that phd level field theory is so technical. Though i imagine the marking is very strict.
@silversky216
Жыл бұрын
I think the test consists of Problems which look "easy" but you start the problem and get stuck halfway in...That happens to me always.
@AquilusObscurum
Жыл бұрын
I wish my qualifying exam was this easy, my school does 6 really hard problems where a 50% is a pass for theirs and they were absolutely brutal
@pandabearguy1
Жыл бұрын
Haven't done much abstract algebra tbh (having a masters in probability theory (and mathematical finance)), and have only scratched group theory surface a bit out of curiosity.
@kd1389
Жыл бұрын
My interests are applied math but I’m taking the required analysis courses right now… respect to anyone studying this at higher level because it is hard work
@honkhonk8009
Жыл бұрын
shouild i go for that shit? i wanna do computers but back in highschool i tried figuring out how neural networks worked. Then i got hooked into math. Now I feel like doing some math shit too in some combined degree. Hopefully itl help me differentiate between other junior devs and hopefully i wont get stuck churning out fucking webdev soycode. Is it interesting shit? What are some applications of the shit u learn?
@taxtr4535
Жыл бұрын
@@honkhonk8009 im doing cs and math at uni. i wouldnt say pure math has an obvious application to cs. but its defo very fun and makes you stand out i reckon. itll also be much more difficult than your cs units so be prepared for that haha
@Castellante
Жыл бұрын
I know two folks that graduated in degrees of applied math from respectable colleges, and both have been looking for work for over a year.
@waterguyroks
Жыл бұрын
@@Castellante Same. It's quite discouraging. They ended up just becoming software engineers at startups (one of them quit shortly thereafter). The pure math career path seems brutal. It's one thing to do it for the love of it but I would hedge my bets in that regard with some more directly applicable studies
@quinnherden
Жыл бұрын
@@honkhonk8009 I recently graduated with a CS degree. Take as much math as you can, so long as you enjoy it. It will only serve to make you better at your craft.
@ThaWaffle
Жыл бұрын
Thanks for the cool video! I also wondered what website you were talking about, containing all the problems. Any way you could link the website?
@DominicNJ73
Жыл бұрын
After seeing the questions on that test I will never again bitch about how hard my qualifying exam was for my Ph.D in Anthropology. LOL
@topsgaming4266
Жыл бұрын
Teacher: "Don't worry, the test won't be that hard." The test:
@adw1z
Жыл бұрын
Surprised how in my second year of undergrad math and those exact 3 questions of the linear algebra section were on my example sheets, and in fact the same with some of the group and ring theory problems; not the easiest, but still very much doable! Gosh graduate level maths must be so stressful still
@malteborgmanm2626
Жыл бұрын
Yeah I was surprised how much of this I have seen. All of those questions must have been in the scope of my first three semesters in my bachelors in mathematics. (I probably would have failed the Ring and Field theory parts)
@_iakvb771
Жыл бұрын
Yeah that's the point of a qualifier lol
@geraldnavida183
Жыл бұрын
I am also taking PhD Math qualifying exam this Midyear term. Thank you for these sample problems. I would try to solve them.
@richardsimon395
Жыл бұрын
Great channel! I'm also an analysis PhD student, working with operator means in C*-algebras. My abstract algebra skills are quite rusty. :D However one problem from the test seems trivial: P2 from the ring theory part. One can use the binomial theorem in commutative rings, and if x^m=0 and y^n=0 then it follows trivially from the binomial theorem that (x+y)^{m+n}=0. For the ideal property, we already proved that sum of nilpotents is nilpotent, and the product property is even easier. If x is nilpotent with x^n=0 and r \in R arbitrary then from commutativity we get that (xr)^n=x^nr^n=0r^n=0. Seems super easy compared to your analysis exam problems :O
@aidanhennessey5586
Жыл бұрын
Undergrad here! Maybe it’s just easy bc I’m taking galois this semester, but problem 3 from field theory is also super straightforward: A we know a polynomial f has repeated roots iff deg(f)>1 and gcd(f, f’) != 1. Consider an irreducible polynomial with degree >1. Its gcd with its formal derivative must be 1 or itself. f’ is non-zero (characteristic 0) and lesser degree than f, so the gcd can’t be f and must be 1. Therefore f does not have repeated roots. This is true for all irreducible in our char 0 field, so the field is perfect
@PhDVlog777
Жыл бұрын
That is pretty much how it is done :)
@fadeidham2932
Жыл бұрын
Yeah. The identity seems to be unnecessary as well.
@worldblazin4209
Жыл бұрын
Thank you so much! Finishing calculus 2 this semester and starting Group Theory (i think if its allowed). Going to perform Group Theory for Undergrad either 3rd or 4th semester (parents want me to leave off math for just Major courses in the Fall 2023). Truly shocked at how you wrap your brain around this, its like how I worked during High School Honors Geometry ("Pre-AP") but with confident whereas I was the study crammer before tests. Pursuing a Computer Science major but want to continue Math courses for a while since this was just my Freshman University year. Thanks again!
@fuxmajor
Жыл бұрын
Hey, I'm also into C*-algebras. Are you going to YMC*A?
@gegebenein.gaussprozess7539
4 ай бұрын
I like your channel very much. As a side note: I also learn English with you! You said that you didn't pass the exam with "flying colours." In German we say "mit fliegenden Fahnen" (with flying flags). All the best!
@dcpugh
Жыл бұрын
I'm disappointed not to see Pugh's Real Mathematical Analysis in the stack. I may be a bit biased, but I hear that's a solid work. :) Keep up the good work!
@thekraken4265
2 ай бұрын
As an undergraduate student going into his fourth year, doing a math minor I’m happy that I can do all the group theory questions in this video after taking a course on group theory lol
@Hilltop_Hero
Жыл бұрын
Hey! I am a PhD student in pure math who is preparing for qualifying exams also. Is there any way you could link the website you mention at 2:49 ? Please don't if you would get in trouble with your program for some reason, but this would be immensely helpful. Thanks! Sam
@souraldandothi5681
Жыл бұрын
hey could you share the link with me too?
@brianthiongo489
Жыл бұрын
hey could you share the link with me too?
@ii_ragee752
9 ай бұрын
hey
@TranquilSeaOfMath
Жыл бұрын
I struggle with understanding field theory. ☹ Your time to completion sounds reasonable. Congratulations on passing.
@nono-mu9rw
Жыл бұрын
i just started my masters degree and have done lots of algebra and algebraic number theory, this looks pretty doable
@heartpiecegaming8932
Жыл бұрын
Hi, I'm a fellow grad student at a different institution (who likes algebra). I can tell you how to do 5 on Ring Theory - take any unit u, and the conjugation map r --> uru^-1 is a ring automorphism. By assumption, this is the identity, so r commutes with all units. Since every nilpotent+1 is a unit, nilpotent elements must commute! The rest is easy. You know, I envy you for the fact that at your uni, your quals are not crazy hard (like they've been getting at my uni)! I wish you luck with your future research!
@kikewickens6324
Жыл бұрын
These are great! We need a complex analysis exam now! :)
@Grassmpl
Жыл бұрын
Here's a tough one: use Morera's theorem to show that the Gamma function is analytic on its domain of definition.
@DavidVonR
Жыл бұрын
Abstract algebra is badass!
@NitBeanTheMachine
Жыл бұрын
Do you know what website they pull problems from? I've never heard of this.
@ayman1515
Жыл бұрын
Can i get solution of exercise 3 and 5 in group theory section please today, since tomorrow i have an exam in it
@spinyslasher6586
Жыл бұрын
Are a lot of these problems from Dummit and Foote? Cause I vividly remember doing them last year in my Abstract Algebra course.
@Yougottacryforthis
6 ай бұрын
Pleasantly surprised I could do the linear algebra q3 in like 5 minutes. Couldn't get the first 2 but hey i didn't learn jordan form so :p
@thereccher8746
Жыл бұрын
I'm used to 2 to 5 problems in an exam. One or two in a midterm. 10 sounds like overkill.
@johncillis3431
Жыл бұрын
Wow, such a test, though I excelled in Trig in college 40+ years ago, would give me nightmares. My trig tests were easy compared to this, I even challenged my college's algebra program by taking their final so I would not have to enroll in those classes, which were prerequisites (always dreaded that word in those days) for Trig. I was a liberal arts student, with the goal of learning business and teaching in that field, which I eventually did on the customer and guest service, and systems side. Trig completed my math requirements in addition to the courses I challenged and I loved Trig especially the way our teacher taught it. It was funny, six years after I left college I was taking the airport bus from Napa to San Francisco, on my way to a trip to Washington DC. My former college Trig teacher boarded our bus bound for London, what serendipity. I aced all of his trig semi-finals and finals and he'd return the tests to me with red ribbons around them, embarrassing me in front of some students who were math majors unlike me, and I knew them as the sharpest minds from my grammar and high school. Like "Good Will Hunting", when it came to trig, or tutoring my friends in calculus, I could "just play" though over the years, all that stuff fell out of my brain so I could leave space in my brain for enjoying retirement, and my career allowed me to retire early just doing odd projects since if asked as a consultant. I am drawn to videos like yours because of the intelligence you have in sharing mathematics, a skill my father also had, and sharing how those going for their PHD in this field of study are tested. My daughter chose to major in liberal arts like I did, so she can teach and travel like I did, and she embraced mathematics in the way I did, embracing the practical courses. My fav math course when I was "yiddle" was learning how to count US money. I thought "Wow, this is what math is for, I love it already!". I loved math even more when I learned algebra, I loved balancing equations and inequalities due to the simple way my dad, who was a physicist, taught me, that all balancing equations was about was keeping a scale of weights balanced--it helped me in Chemistry too, I loved balancing Chem equations seeing its similarity to Algebra, especially in advanced chem. Thanks for sharing this, I will have to watch your other videos. Math is such a wonderful language that is part of all of us.
@andreshernandez7785
Жыл бұрын
The exercice 3 in linear algebra has something to do with projections right ? The minimal polinomial for a projection is X^2 - X and a consequence for the projection is V = kerp + Imp . That's the first thing I thought
@Grassmpl
Жыл бұрын
You can prove it directly. Any x in V is in kerT + ImT and their intersection is 0.
@matthewgillespie4408
Жыл бұрын
Just wanted to say your videos are super awesome. I’m pure math PhD student as well in analysis. Im currently working on some ongoing research with my advisor on groupoid cross products over Fell bundles (advisor is an operator algebraist, and im hoping to become one myself lol). Which subfield of analysis are you interested in?
@PhDVlog777
Жыл бұрын
I am still figuring this out, I did research in the past on Cantor sets in the complex plane and measured Hausdorff dimension. So I will hope to do more with this but ultimately it will be whatever my advisor thinks I should do
@xicad1533
5 ай бұрын
What is the website at 2:50 you mentioned that has a lot of extra problems?
@stanleydodds9
Жыл бұрын
Am I missing something with the 4th group theory question, because it seems too trivial to me: Suppose g is in G_b, so g*b = b. By transitive action, we have b = h*a for some h in G. So g*(h*a) = h*a, then (gh)*a = h*a, then left multiply by h^(-1) and use group action property to get (h^(-1)gh)*a = a. So h^(-1)gh is in G_a = {1}, so h^(-1)gh = 1. Rearrange, or notice that 1 is trivially central, to get g = 1. Any element of G_b is 1, and 1 is trivially in G_b, so G_b = {1}. This feels like the sort of thing you would see as just an example when you first learn about group actions, so like first year (or earlier) group theory - the entire proof is just basic use of the properties of a group action and rearranging group elements, so most of the steps are so trivial that ordinarily I would just leave them out and write the trivial fact: if b = h*a then G_b = G_a^h (where ^h means conjugation by h).
@heartpiecegaming8932
Жыл бұрын
Yes, it really is trivial. Idk, the entire exam seems to be fairly trivial to me, but then again, I've taken much more advanced classes in algebra. The only one that I thought was somewhat nontrivial was #5 on Ring Theory, but I've figured it out!
@Grassmpl
Жыл бұрын
@@heartpiecegaming8932 what about group theory q1? I don't know how to approach that one.
@mostordinaryexistence
Жыл бұрын
Your choice looks really reasonable for me that I would pick exactly same problems if I was taking it lol
@mostordinaryexistence
Жыл бұрын
I'm not sure if I could get correct but at least some problems look more comfortable
@newwaveinfantry8362
2 ай бұрын
2:53 - What is the website called?
@josephcao7180
8 ай бұрын
If you do more than 10 problems how do they choose which ones are counted towards the score?
@bedashrutiray8141
Жыл бұрын
Do you suggest wanna book where i can findthis type of problems and theorems
@starguy2718
Жыл бұрын
2:27 A trivial solution, to a problem, is usually something like 0 = 0
@enigma7791
9 ай бұрын
I can read the first page instructions...how many marks for that?
@nkanyezitshabalala5256
Жыл бұрын
What's the time allocation?
@bensaidfire8760
Жыл бұрын
Can you pute the file in a Format pdf in description,thank you
@sherryfireconley6876
3 ай бұрын
Excuse me What kind of Linear Algebra and Abstract Algebra textbooks for qualifying exam ? Bachelor or Master degree ? Mathematics are interesting
@adebayoemmanuel911
Жыл бұрын
Please, can you share the website they pull the problems?
@gianmarcomarin8391
Жыл бұрын
When you refer to homework what do you mean?
@LLL124Original
Жыл бұрын
How do you get copies of these tests?
@simonreiff3889
Жыл бұрын
I have a stupid question. So P4 in the Rings section looks easy enough if we can use the fact that if R is an integral domain, then so is R[x]. (The result follows immediately if we can use that fact without proof: For any p(x) € R[x], if deg(p)>0, then it cannot be a unit--e.g., f(x)=x does not have an inverse in R[x] because 1/x is not in R[x], and similarly with higher order polynomials--and accordingly, f(x) is a constant polynomial and thus is in R.) But do you have to write out the proof on such an exam that R being an integral domain implies that R[x] is too, or can you just assume that without proof? Also--thanks for sharing this! Best of luck.
@danielmaxhoffmann1917
Жыл бұрын
I am pretty sure that you do not need to reprove Noehter's theorem and just assume it. But you dont need it. Look, if f(X)=aX^n+... has degree n>0 and you multiply it by some polynomial h(x)=bX^m+... of degree m - it is enough to look at the coefficient at X^{n+m} which is ab, and which is non-zero unless h(X)=0. Thus fh can not be 1.
@simonreiff3889
Жыл бұрын
@@danielmaxhoffmann1917good point
@Kirilov3
Жыл бұрын
goddamnit. I've been graduated for several years... almost forget everything
@suthiraphanassarat8669
Жыл бұрын
What university is this abstract algebra PhD qualifying exam taken from?
@garrettshum7392
Жыл бұрын
Best of luck with everything! Remember, the more intelligent you are, the more you doubt yourself and your capabilities. Keep going!
@taha-rn5sl
Жыл бұрын
3rd question in linear algebra we had it in homework in algebra 2 . 1st year of college 🗿
@henoceros
Жыл бұрын
Interestring, I didn't had too much trouble with the analysis test you showcased, but I don't even understand most of the Algebra problems
@PhDVlog777
Жыл бұрын
I would much rather be in your position lol
@henoceros
Жыл бұрын
@@PhDVlog777 I guess I need to find a good Algebra book to fill my gaps
@Tj-ho2fs
Жыл бұрын
I’d just cry.
@DVAcme
Жыл бұрын
Watching this, I feel like what the rest of the Fantastic Four must feel like when Reed Richards goes on a rant.
@aniksamiurrahman6365
Жыл бұрын
What's that magical website?
@SpidermansSymbiote
Жыл бұрын
This literally looks like I'm reading another language. I have NO idea what any o fit means but it's still neat
@NikoNikomedes
Жыл бұрын
I finished my masters in pure maths a short while ago and I am already working. I haven't done any algebra at the end of my studies. Can you link the website with all those problems you mentioned at the start because I don't want to become super rusty at algebra as I actually enjoyed much of it.
@NikoNikomedes
Жыл бұрын
I think the last "algebraic" course I have taken was algebraic topology, but that was basically just group theory :/
@asadcake6375
Жыл бұрын
I wonder why the questions are all pretty much first-second year undergraduate abstract algebra ? Since you do a PhD after doing graduate type of math why isn't there any graduate-level math ?
@Bringiton513
Жыл бұрын
Thank you for discussing this material with us. I wish you the best for having chosen mathematics as your profession: this subject is my life, love and joy. I only wish that God gave me more brain power to invest.
@marvelstarwars__
Жыл бұрын
I barely passed stats last semester as an undergrad…what in the world is this 😵💫
@daddybutterunboxings2180
Жыл бұрын
Cool!
@a_random_person5651
Жыл бұрын
What college do you attend?
@littlenaro1700
Жыл бұрын
Im a comp sci student, these videos motivate me to keep pushing in my math classes even though i slightly hate math. 1 question, what is the end goal for you? You obtain a phd, then look for a job aligned with your qualifications? The amount of effort put would rival med school. Or is it just the nature of curiosity that keeps you wanting to learn more? I myself find it difficult to find purpose, im primarily doing it for money. Again thanks for making these videos, it keeps me pushing seeing someone else also grinding out their education especially in math. Hope you the best.
@nicolaasdaer
Жыл бұрын
You don't hate math, you just don't perceive it from physics reference, which makes it absurd. It is like trying to prove immagination is true. You can't you need phyiscs point of reference to make it dance with the math. Hope it helps you, have a nice one
@nuggetmaster05
Жыл бұрын
imagine this is your homework and you try to find the answers on chegg
@iElephant24
Жыл бұрын
at 2:50 what is that website called?
@masonmarshall9727
Жыл бұрын
Ive taking Abstract Algebra 2, about 5 years ago, and I'd say 80% of this looks quite familiar. How much more past Abstract Algebra 2 would you say this content is?
@PhDVlog777
Жыл бұрын
It’s about the same. I haven’t taken anything last graduate level algebra
@him21016
Жыл бұрын
May I ask which university this is?
@alje311
Жыл бұрын
This might as well be written in a foreign language because I don't understand any problem at all
@duckymomo7935
Жыл бұрын
can you link this test
@HotPepperLala
Жыл бұрын
What is G' in question 1? What do the primes mean here? I've never seen this notation.
@PhDVlog777
Жыл бұрын
It denotes the commutator subgroup (or derived subgroup) of G. Extra primes mean derived subgroup of the derived subgroup and so on.
@juandiegoparales9379
8 ай бұрын
how much time were you given?
@ErwinSchrodinger64
Жыл бұрын
I've extensively applied linear algebra (quantum mechanics), group theory (X-ray structure analysis), field theory (applications on differential geometry), and you're beginning to see ring theory being applied in a lot chemistry/molecular physics especially dealing with aromatic structures. We skim over the algebras but dear all that is unholy, seeing this type of mathematics in the forms of proofs... that's a completely different animal. Thank you for studying such subjects. Physics and chemistry are heavily indebted to the mathematicians.
@humbledb4jesus
Жыл бұрын
it's bitter sweet...they are vile creatures for introducing reminder theory and modulus...
@Grassmpl
Жыл бұрын
How to solve group theory q1?
@ashishkujur8169
Жыл бұрын
What area of Analysis do you work in? :)
@PhDVlog777
Жыл бұрын
At the masters level, I did research involving Cantor sets in the complex plane and measured Hausdorff dimension. I might switch to geometry. Honestly, whatever gets me my PhD I will be happy with lol
@baronvonbeandip
Жыл бұрын
I woulda probably chose the same problems too.
@MATT-ll2zf
Жыл бұрын
Iam 16 and aspring mathematican Is there a Phd Qualifying exams at MIT, Cornell, Princeton, Caltech etc..
@aidle
Жыл бұрын
Obviously, most US universities require quals for phd
@abhisheksoni9774
Жыл бұрын
Can you provide its PDF
@daveb970
Жыл бұрын
Glad I changed my major from math after the first year. Life is too short.
@foobar5809
Жыл бұрын
the first question seems off to me. Am I stupid? Any diagonal matrix commutes with any other. But I cant write diagonal matrices with different entries on the diagonal as polynomial in an nxn Jordan-block, right?! easiest example. Let A be a 2x2 Jordan block for Eigenvalue 0(a 1 top right, rest 0s). And let B be diag(1,0), so a 1 in the top left. Clearly A is a Jordan block and they commute, but B is not a polynomial in A…
@hakerfamily
Жыл бұрын
A and B don’t commute in your example.
@foobar5809
Жыл бұрын
@@hakerfamily shouldnt diagonal matrices commute with all other matrices?!
@foobar5809
Жыл бұрын
oh, they dont, you are right, I am stupid
@CleanStringsO
Жыл бұрын
can't believe I passed all this shit
@baileyarzate1
Жыл бұрын
Yeah.. that’s why I’m going into applied stats for grad school
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