Hi there....are these concepts and theorems covered/proved in your class ???
@PhDVlog77716 сағат бұрын
All the theorems and tools used in these problems were developed in the analysis course.
@samandersen12284 күн бұрын
Is the term "complex analysis" interchangeable with "complex variables" in a similar way to the interchangeability of "advanced calculus" and "real analysis"?
@PhDVlog77716 сағат бұрын
From my understanding, they are. But each institution has their own name for the course. They may call complex variables the undergrad version and the grad version complex analysis.
@samandersen12287 сағат бұрын
@@PhDVlog777 Thank you!
@douglasstrother65846 күн бұрын
That's impressive!
@douglasstrother65846 күн бұрын
"MY NAME IS GUNNERY SARGEANT HARTMANN, YOUR SENIOR DRILL INSTRUCTOR!" (Whispered voice) "Dude, are we in the right place?" (Whispered voice) "I guess. The sign on the door said 'Qualifying Exam'." "DO YOU CHATTERBOXES HAVE SOMETHING TO SHARE WITH THE GROUP?"
@douglasstrother65846 күн бұрын
Your proof was "all that and a bag of chips"!
@douglasstrother65846 күн бұрын
Success = Talent * Effort^Focus + Random Events.
@douglasstrother65846 күн бұрын
I didn't "get" Math until my Sophomore Geometry class in high school.
@douglasstrother65846 күн бұрын
"To use mathematics effectively in applications, you need not just knowledge but *skill* . Skill can only be obtained through practice.", Mary Boas in "To The Student" of her "Mathematical Methods in the Physical Sciences". This is true for both applied (computational-oriented) and pure (theorem-proof oriented) courses.
@douglasstrother65846 күн бұрын
"Applied Complex Variables" by John W. Dettman (Dover Publishers) is a great read (The Math Sorcerer has a video on it.): the first part covers the geometry/topology of the complex plane from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective. I've used Smith Charts (RF/microwave engineering) for years, but learned from Dettman that the "Smith Chart" is an instance of a Möbius Transformation. The Schaum's Outline on "Complex Variables" is a great companion book for more problems/solutions and content.
@douglasstrother65846 күн бұрын
My exposure to Real Analysis was limited to what is covered in "Calculus" (Marsden & Weinstein) and "Vector Calculus" (Marsden & Tromba) as an Undergrad. Since Calculus has such a strong geometric, visual nature, what makes Real Analysis so difficult?
@sis_sos7 күн бұрын
God damn your voice is annoying
@TermC-ni9kn8 күн бұрын
I remember in another video, you said after your PhD you will start looking for work. My question is do you plan to enter academia or are you going into industry?
@FractalMannequin8 күн бұрын
They're pretty standard questions. I thought it was much more challenging.
@erickleuro61598 күн бұрын
I got confused with your timeline, I thought you were already a candidate, either way, good luck and thanks for sharing your mathematical journey
@galaxy52018 күн бұрын
Are these all based on PhD course work or not???
@PhDVlog77716 сағат бұрын
Yes, all the tools needed to solve these problems are developed in the algebra course.
@LemonAdeYesPlease9 күн бұрын
Same thing applies to med students. I was natural born talent. IQ around 150. Could be more if internet wasnt discovered. School was B R E E Z E. College was tough. And ending was TOUGHHESTT. all hard working students breezed through. But because i didnt have habit of working hard i was struggling. I fell into depression, negative self talk, maladaptive dreaming, distractions, tiktok youtube addiction(still am) and yeah downward spiral for 8years. I passed. Coz others they studied for 6months on and off and got like 60-65. And i studied BARELY 6hrs entire semester and got 55. In final test i failed. And in retest i tried to study well. And guess how kuch i scored. I scored 75. You see its complicated. This whole life as genius is complicated. Especially in donkey world.
@jaimanparekh46169 күн бұрын
Is there a connection between the Radon transform and the Peter-Weyl theorem here?
@reversicle2129 күн бұрын
I'm an average IQ high school student who has no specific interest in any subject for college other than mathematics/physics. Now I'm sort of edging towards the mathematics side (bcz I find it more fun than physics, and also mechanics + thermal physics is horror to me). But as I said, I'm average iq not that intelligent + not the best all star 4.0 gpa guy.... so would you suggest someone like me to pursue math at college?
@danielmaxhoffmann19178 күн бұрын
Hey, I am an assistant professor dude in math and I spent in the bussines several years. From my personal experience, "commitment" > "iq". Sure, if you want to crack some hardcore branches of math, you need to be smart (otherwise you will be too slow to be effective enough). But here I mean - to solve problems in say additive combinatorics. There are many branches in math where it is more important to accumlate knowledge instead of getting this one nasty trick to solve the entire thing. Anyway, I had friends with high iq, which were already publishing scientific papers during their undergraduates, but they burn out, lost interest, or went to industry. I was not like them - I was more like you. After some time you will understand what are your weak-spots and strong-sides, and you will be able to use that to select the best strategies for you. And remamber - it does not matter where you started your journey, it matters how long and exciting it was!
@oo_rf_oo882410 күн бұрын
good luck on the conference!
@doublew881510 күн бұрын
I'm a simple man. I saw a book I am studying rn , I opened the video
@p4rity11 күн бұрын
Awesome picture on the board as always and have fun in spain! How did the exams(s) go last week?
@jamesromano328811 күн бұрын
I love you papi !!!! Why cant we see your face ? I would love to see it and more !!!💓💓💓💓💓💓🙀
@samsanchez74811 күн бұрын
I guess the Radahn Transform was applied to Mohg but that is a fringe application
@PhDVlog77711 күн бұрын
Reminds of the Malenia decomposition... oh the horror...
@abhijitbhattacharjee315711 күн бұрын
I want to ask a question : How many research paper does one need to publish for pure math PhD in your university / any university in USA in general ?
@PhDVlog77711 күн бұрын
It depends upon the advisor, the typical advisor will say two or three but if the result is big, then one paper may be enough.
@Blake_4712 күн бұрын
As a first year Physics student this is pretty easy 😜
@SergioAbarca912 күн бұрын
As a Dutchman who did 1 year of grad school in the US I highly recommend you come to Europe! After living in both the US and several countries in Europe I personally find Europe infinitely better! To each their own of course, but at least give it a try 😅
@Annihillation11 күн бұрын
Is the European system really different from the US? Like, do you spend all time doing research?
@avy111 күн бұрын
@@AnnihillationI think so, at least that’s how it goes in the Netherlands. You do your masters and then you can apply for PhD positions and you can immediately start working on your research. I think the university can still kick you out though in the first year of the PhD program.
@Annihillation10 күн бұрын
@@avy1 kicked out by some sort of qualifying exam? Or other requirements, like progress in research? I am sorry for guessing, I really don't know, but I am intrigued
@avy19 күн бұрын
@@Annihillation so in the Netherlands doing your PhD is a job, the university pays you to do research on the thing you were hired to do. If the university doesn’t like how you are performing at your job, they can fire you. But this is only for some grace period I think, after a year you are safe. That being said funding for your research does run out so it is in your best interest to actually finish what you started.
@noahgilbertson753012 күн бұрын
i love listening to you yap about maths
@1jamesreed12 күн бұрын
anyone remember what his brother does, he's said but I've forgotten. Thanks.
@galaxy520112 күн бұрын
Hi there ....I want to pursue research in mathematics....but what scares me is the qualifying exams that PhD students have to give to get into research fully......please share some tips on what are the basic topics that we need to cover before applying for PhD..and also tell me whether the courses on real and algebra is taught during first or second sem of PhD course???? PS I love your videos
@PhDVlog77711 күн бұрын
The biggest tip I can give to those studying for qualifying exams is to communicate directly with those writing the exam and understand completely what they expect form you. Tailor your studying to the demands of the department. Each department is different and will require its own unique approach. If you study pure math, then you must understand real/complex analysis (measure theory included) and abstract algebra (group theory, ring theory and field theory.) These topics are usually covered in the first year. It is good to pick up a few textbooks on these subjects and read through them independently alongside the class to get a greater understanding as well since each other approaches the topics in his own way. I hope this helps!
@galaxy520111 күн бұрын
@@PhDVlog777 thank you. Is there a way I can reach u directly via Messages….since you are also a PhD candidate I want to ask you few things….can you share any of your social media so that I can have a talk with you. Please.
@EdmondChoi51312 күн бұрын
I’m taking my first real variables course this summer and if I do well I think I will pursuit pure math. Thank you for your videos man they been super helpful to see what’s next but also ur just very entertaining. Keep it up mane
@profraihan12 күн бұрын
Where in Spain will the conf take place?
@felipevaldes767912 күн бұрын
excellent
@trixxy917712 күн бұрын
Did you visit Moraine Lake when you were in Banff by any chance? I know it’s very famous; I’ve been there a couple times.
@PhDVlog77711 күн бұрын
No, just Lake Louise, I did not get away from the conference hall much. Just the day we visited the amazing lake.
@ApxPenguin12 күн бұрын
That’s super cool that you’re going to Spain it’s a beautiful place I love it
@Preet_122312 күн бұрын
Woohoo, another grad student video! Question: do you plan on continuing the Interview series. Really enjoyed the collaboration with other people and seeing the inside of a PhD program
@jackbrolin770911 күн бұрын
I agree. Would love to see more detailed proofs and theorems about algebraic concepts, as you cover a lot of analysis
@PhDVlog77711 күн бұрын
I will do more interviews in the future but for right now, I want to focus on the measure theory review. The interviews were really fun, so I definitely want to return to them soon.
@natepolidoro456512 күн бұрын
3:52 "Convolving"
@galaxy520112 күн бұрын
Hi there, how do I prepare real analysis and abstract algebra for qualifying exam...please tell me the reference book and strategy.
@climitod852413 күн бұрын
do you read solutions to proofs if you get stuck? Please I need to know. Also do you try and find counter examples after you think you've proven it?
@PhDVlog77713 күн бұрын
If there are solutions then yes, I will read them. I think it is good to tweak the assumptions a little and try to come up with counterexamples. It gives a you a good intuition for this kind of math.
@saidneder4116 күн бұрын
Loving the Banff cap!! Greetings from Vancouver!
@KurdaHussein17 күн бұрын
pliz do NOT ever tell ur student "dont leave it blank". man wtf a bullshit on a paper should mean🤦♂️ that policy is nonsense, students pass just by written bullshit 🤦♂️. now students in my college are having 70 to 80 marks in Linear Algebra and yet cant prove a single assignment without AI (which means they didn't bring any learning outcomes )
@jonetyson17 күн бұрын
The speaker doesn't appear to realize there are many more PhDs issued than there are jobs as a professor.
@erikysilvagomes549617 күн бұрын
I simply love bartle's book!
@simon709319 күн бұрын
Right now im studying maths in my first year in Germany and we have the courses linear algebra 1 and 2 as well as analysis 1 and 2, and cover the themes of the books you mentioned for "Real Analysis" and "adv. lin. alg.". Im courious as to why you cover these themes only in your 3rd/4th year. On the other hand, things like ODE, PDE or number theory are strictly for the 2nd and 3rd years in germany, not for the first years.
@CarlosWilliamsMaximoGarciaGonz20 күн бұрын
math sorcerer?
@douglasstrother65846 күн бұрын
The Math Sorcerer's Apprentice!
@the_eternal_student21 күн бұрын
There should be "for dummies" books for graduate math.
@BlaiseLabs21 күн бұрын
K is a ball because a ball is the only convex body that has a constant volume of slices (through its center). Also the slice of any n dimension Ball is a ball in n-1 dimensions. That's my answer to the final question.
@Aarush_267322 күн бұрын
Can you please make a video on how one can study high level math and prepare for mathematical olympiads in high school?
Пікірлер
your explanation is very inspirational
Hi there....are these concepts and theorems covered/proved in your class ???
All the theorems and tools used in these problems were developed in the analysis course.
Is the term "complex analysis" interchangeable with "complex variables" in a similar way to the interchangeability of "advanced calculus" and "real analysis"?
From my understanding, they are. But each institution has their own name for the course. They may call complex variables the undergrad version and the grad version complex analysis.
@@PhDVlog777 Thank you!
That's impressive!
"MY NAME IS GUNNERY SARGEANT HARTMANN, YOUR SENIOR DRILL INSTRUCTOR!" (Whispered voice) "Dude, are we in the right place?" (Whispered voice) "I guess. The sign on the door said 'Qualifying Exam'." "DO YOU CHATTERBOXES HAVE SOMETHING TO SHARE WITH THE GROUP?"
Your proof was "all that and a bag of chips"!
Success = Talent * Effort^Focus + Random Events.
I didn't "get" Math until my Sophomore Geometry class in high school.
"To use mathematics effectively in applications, you need not just knowledge but *skill* . Skill can only be obtained through practice.", Mary Boas in "To The Student" of her "Mathematical Methods in the Physical Sciences". This is true for both applied (computational-oriented) and pure (theorem-proof oriented) courses.
"Applied Complex Variables" by John W. Dettman (Dover Publishers) is a great read (The Math Sorcerer has a video on it.): the first part covers the geometry/topology of the complex plane from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective. I've used Smith Charts (RF/microwave engineering) for years, but learned from Dettman that the "Smith Chart" is an instance of a Möbius Transformation. The Schaum's Outline on "Complex Variables" is a great companion book for more problems/solutions and content.
My exposure to Real Analysis was limited to what is covered in "Calculus" (Marsden & Weinstein) and "Vector Calculus" (Marsden & Tromba) as an Undergrad. Since Calculus has such a strong geometric, visual nature, what makes Real Analysis so difficult?
God damn your voice is annoying
I remember in another video, you said after your PhD you will start looking for work. My question is do you plan to enter academia or are you going into industry?
They're pretty standard questions. I thought it was much more challenging.
I got confused with your timeline, I thought you were already a candidate, either way, good luck and thanks for sharing your mathematical journey
Are these all based on PhD course work or not???
Yes, all the tools needed to solve these problems are developed in the algebra course.
Same thing applies to med students. I was natural born talent. IQ around 150. Could be more if internet wasnt discovered. School was B R E E Z E. College was tough. And ending was TOUGHHESTT. all hard working students breezed through. But because i didnt have habit of working hard i was struggling. I fell into depression, negative self talk, maladaptive dreaming, distractions, tiktok youtube addiction(still am) and yeah downward spiral for 8years. I passed. Coz others they studied for 6months on and off and got like 60-65. And i studied BARELY 6hrs entire semester and got 55. In final test i failed. And in retest i tried to study well. And guess how kuch i scored. I scored 75. You see its complicated. This whole life as genius is complicated. Especially in donkey world.
Is there a connection between the Radon transform and the Peter-Weyl theorem here?
I'm an average IQ high school student who has no specific interest in any subject for college other than mathematics/physics. Now I'm sort of edging towards the mathematics side (bcz I find it more fun than physics, and also mechanics + thermal physics is horror to me). But as I said, I'm average iq not that intelligent + not the best all star 4.0 gpa guy.... so would you suggest someone like me to pursue math at college?
Hey, I am an assistant professor dude in math and I spent in the bussines several years. From my personal experience, "commitment" > "iq". Sure, if you want to crack some hardcore branches of math, you need to be smart (otherwise you will be too slow to be effective enough). But here I mean - to solve problems in say additive combinatorics. There are many branches in math where it is more important to accumlate knowledge instead of getting this one nasty trick to solve the entire thing. Anyway, I had friends with high iq, which were already publishing scientific papers during their undergraduates, but they burn out, lost interest, or went to industry. I was not like them - I was more like you. After some time you will understand what are your weak-spots and strong-sides, and you will be able to use that to select the best strategies for you. And remamber - it does not matter where you started your journey, it matters how long and exciting it was!
good luck on the conference!
I'm a simple man. I saw a book I am studying rn , I opened the video
Awesome picture on the board as always and have fun in spain! How did the exams(s) go last week?
I love you papi !!!! Why cant we see your face ? I would love to see it and more !!!💓💓💓💓💓💓🙀
I guess the Radahn Transform was applied to Mohg but that is a fringe application
Reminds of the Malenia decomposition... oh the horror...
I want to ask a question : How many research paper does one need to publish for pure math PhD in your university / any university in USA in general ?
It depends upon the advisor, the typical advisor will say two or three but if the result is big, then one paper may be enough.
As a first year Physics student this is pretty easy 😜
As a Dutchman who did 1 year of grad school in the US I highly recommend you come to Europe! After living in both the US and several countries in Europe I personally find Europe infinitely better! To each their own of course, but at least give it a try 😅
Is the European system really different from the US? Like, do you spend all time doing research?
@@AnnihillationI think so, at least that’s how it goes in the Netherlands. You do your masters and then you can apply for PhD positions and you can immediately start working on your research. I think the university can still kick you out though in the first year of the PhD program.
@@avy1 kicked out by some sort of qualifying exam? Or other requirements, like progress in research? I am sorry for guessing, I really don't know, but I am intrigued
@@Annihillation so in the Netherlands doing your PhD is a job, the university pays you to do research on the thing you were hired to do. If the university doesn’t like how you are performing at your job, they can fire you. But this is only for some grace period I think, after a year you are safe. That being said funding for your research does run out so it is in your best interest to actually finish what you started.
i love listening to you yap about maths
anyone remember what his brother does, he's said but I've forgotten. Thanks.
Hi there ....I want to pursue research in mathematics....but what scares me is the qualifying exams that PhD students have to give to get into research fully......please share some tips on what are the basic topics that we need to cover before applying for PhD..and also tell me whether the courses on real and algebra is taught during first or second sem of PhD course???? PS I love your videos
The biggest tip I can give to those studying for qualifying exams is to communicate directly with those writing the exam and understand completely what they expect form you. Tailor your studying to the demands of the department. Each department is different and will require its own unique approach. If you study pure math, then you must understand real/complex analysis (measure theory included) and abstract algebra (group theory, ring theory and field theory.) These topics are usually covered in the first year. It is good to pick up a few textbooks on these subjects and read through them independently alongside the class to get a greater understanding as well since each other approaches the topics in his own way. I hope this helps!
@@PhDVlog777 thank you. Is there a way I can reach u directly via Messages….since you are also a PhD candidate I want to ask you few things….can you share any of your social media so that I can have a talk with you. Please.
I’m taking my first real variables course this summer and if I do well I think I will pursuit pure math. Thank you for your videos man they been super helpful to see what’s next but also ur just very entertaining. Keep it up mane
Where in Spain will the conf take place?
excellent
Did you visit Moraine Lake when you were in Banff by any chance? I know it’s very famous; I’ve been there a couple times.
No, just Lake Louise, I did not get away from the conference hall much. Just the day we visited the amazing lake.
That’s super cool that you’re going to Spain it’s a beautiful place I love it
Woohoo, another grad student video! Question: do you plan on continuing the Interview series. Really enjoyed the collaboration with other people and seeing the inside of a PhD program
I agree. Would love to see more detailed proofs and theorems about algebraic concepts, as you cover a lot of analysis
I will do more interviews in the future but for right now, I want to focus on the measure theory review. The interviews were really fun, so I definitely want to return to them soon.
3:52 "Convolving"
Hi there, how do I prepare real analysis and abstract algebra for qualifying exam...please tell me the reference book and strategy.
do you read solutions to proofs if you get stuck? Please I need to know. Also do you try and find counter examples after you think you've proven it?
If there are solutions then yes, I will read them. I think it is good to tweak the assumptions a little and try to come up with counterexamples. It gives a you a good intuition for this kind of math.
Loving the Banff cap!! Greetings from Vancouver!
pliz do NOT ever tell ur student "dont leave it blank". man wtf a bullshit on a paper should mean🤦♂️ that policy is nonsense, students pass just by written bullshit 🤦♂️. now students in my college are having 70 to 80 marks in Linear Algebra and yet cant prove a single assignment without AI (which means they didn't bring any learning outcomes )
The speaker doesn't appear to realize there are many more PhDs issued than there are jobs as a professor.
I simply love bartle's book!
Right now im studying maths in my first year in Germany and we have the courses linear algebra 1 and 2 as well as analysis 1 and 2, and cover the themes of the books you mentioned for "Real Analysis" and "adv. lin. alg.". Im courious as to why you cover these themes only in your 3rd/4th year. On the other hand, things like ODE, PDE or number theory are strictly for the 2nd and 3rd years in germany, not for the first years.
math sorcerer?
The Math Sorcerer's Apprentice!
There should be "for dummies" books for graduate math.
K is a ball because a ball is the only convex body that has a constant volume of slices (through its center). Also the slice of any n dimension Ball is a ball in n-1 dimensions. That's my answer to the final question.
Can you please make a video on how one can study high level math and prepare for mathematical olympiads in high school?
This is not olympiad mathematics
The Hawk Tuah meme AND math. Well done, sir.
Good luck in the exam on Monday