Your first year in a PhD Program

[@kausthubhmanda9389]

As an Undergraduate wanting to persue a PhD in MaThematics and Computer Science your videos mean a lot to me.

[@douglasstrother6584]

My experience in first-year Physics Grad School: (1) Concentrate on performing well in the Core Courses: Classical Mechanics, Electromagnetism, Quantum Mechanics and Statistical Mechanics (get at least a B); (2) Practice on Qualifying Exam Problems (content & time management); (3) Attend the weekly Colloquia and get to know the Faculty (don't be a hermit).

[@asn65001]

Very cool. I really enjoyed this video. Something I've learned about you is how hard you studied and how committed you were as a student. That's good to know because as a student I've always felt like I just "had to know" the material and that the knowledge should have been obvious and intuitive. That misconception made me feel insecure in my math knowledge for a while, but thanks to your videos I've been breaking through that now. Thank you!

[@JoelRosenfeld]

You’re welcome! Everyone hits a wall at some point, and it’s hard work to get through it. And honest, that work is what makes math fun

[@Flowreac]

I’m starting my very first semester of math this fall, and I am sort of pondering what path to take. Of course options such as a PhD at this point are wayy into the future, but I enjoyed the insight into what it might be like. This video was very interesting and entertaining and made me a little bit scared, but in the sort “ I have a lot of respect and I need to take this seriously”-kind of way, and at the same time very excited. Let’s see what the future holds. Thank you for taking the time and effort to make this video, I appreciate it!

[@JoelRosenfeld]

I’m glad you liked the video! If you have any questions about undergrad programs, I’d be happy to answer them

[@tinyleopard6741]

Congratulations, and thanks.

[@ghevisartor6005]

Im amazed by your effort. I was good in school but i always felt getting no where with studying so i skipped university. I self taught programming and got a job. Now im 27 i spend a lot of time also watching science related topic and tried even learning math again seriously. But it's so hard, you really gotta love it. I wonder if i could ever have archieved a phd. Well at least my taxes will help fund people like you, which is probably better. I'm sorry i've made this comment about me, congratulations on your journey.

[@JoelRosenfeld]

Hey I’m happy to hear from you! I make these videos to connect with people, and help those on the same journey. That’s amazing you were able to teach yourself coding and to get a job doing it. Many people would give up on that journey too. We each have our own paths, and it sounds like you are doing well on yours.

[@scorch25able]

First year in my PhD research in Engineering (based in Australia) ---- five years after I have completed a non-technical Master's Degree, and more than 15 years after I have completed my Bachelor's Degree in Engineering. Thanks for this encouragement as at the moment, I feel lost. I regularly communicate with my main PhD supervisor but I don't get much feedback from him. It's like every one of us are waiting for something before we can kick-off with my actual research, but I am doing a lot of reading and constructing framework for design and technical analysis about my topic. I have been doubting myself for a few weeks now if I actually deserve to be in this program, but thanks to you, I feel that I can keep at it, and will continue communicating with my main PhD supervisor. Fortunately I do not have to do PhD exams but I have to present and defend my progress during milestone presentations, which are open to the staff at my school (division) at my university.

[@JoelRosenfeld]

Bust of luck, man! A PhD is a tough journey for anyone. One advantage that you have is that you have the maturity of coming back to academics after leaving to try other things. Many other students go straight in without really thinking about their life much, a PhD is “just the next step” for them. This change in perspective can help keep you focused.

[@David-pq6wt]

I enjoy your videos. I have a bachelor's in mechanical engineering and have been out of school working for 10 years. I always loved math and wanted to take real analysis in school but it dudt work out. For the past few month I have been going thru calc again with George Simmons book with the hopes of going thru understanding analysis by Abbott after that.its so satisfying when your work hard on a problem and finally get it. Looking forward to more videos

[@mmariokart231]

I just got in to my program and am about to start in the fall! Thank you for this video!

[@JoelRosenfeld]

Congratulations! I really enjoyed the challenge of my grad school years. Lots to look forward to.

[@ssgamer5693]

1:56 The real identity of a PhD student is wearing 2 watches at the same time on both arms LHS=RHS

[@lupinthe4th400]

I am applying for a PhD in Philosophy at the University of Kentucky, which offers about the same in stipends and grants. Thanks very much for the information. I am Greek, and a PhD in Europe is totally different from that offered in the States.

[@JoelRosenfeld]

I’m glad I can help! Good luck! Let me know if I can answer anything else for you

[@reversicle212]

awesome vid man

[@mincedmeatchops3208]

Very informative and well presented. Thanks for sharing! I’m only a 2nd year undergrad, but this is a mountain I intend to summit. Subbed for sure

[@JoelRosenfeld]

Happy to have you here! Let me know if you have any questions!

[@dylanellis7656]

Very similar experience and I only managed to get what is similar to a master pass on Real analysis for the 3rd try. And went on to pursue PHD in a branch of algebra much later. I still don't know much about analysis even now.

[@JoelRosenfeld]

lol yeah don’t ask me anything complicated about groups.

[@bugzbunny109]

Excellent video dude! I love the personal touches you add.

[@JoelRosenfeld]

Thank you! I'm glad you like it

[@numericalcode]

Great overview! Thanks!

[@JoelRosenfeld]

I’m glad you liked it!

[@acerbic-piglet]

At 2:56 in the video, I think question 6's premise is wrong. One could have f' be a linear function f'(x) = x on x< 1 and f'(x) = x+1 on x>=0. Do let me know if I am missing something but I believe this question is incorrect or I am misreading it.

[@JoelRosenfeld]

You are a very diligent viewer! I like it! Part of the hypothesis is that the function must be differentiable at every point in the interval. I don’t think your example would be. But you are hitting on just the right part of it. A monotonic function can only have jump discontinuities (like the example you gave), and so that’s what you are left with ruling out.

[@acerbic-piglet]

@@JoelRosenfeld Ah yes. You are completely right. Maybe I'll try proving this then.

[@Luarhackererreape]

Que gran video, gracias por contar tu experiencia!

[@JoelRosenfeld]

You are welcome! I’m glad you enjoyed it.

[@axe-vw6ek]

dude I am literally reading Analysis Now by Pedersen, love the book

[@JoelRosenfeld]

It’s fantastic!

[@safeyyaalyahia7198]

I am grateful for this video

[@JoelRosenfeld]

I am glad you like it!

[@InfinityMW2]

Great video, hopefully going into Master's program for engineering after graduating

[@JoelRosenfeld]

Thanks! Best of luck to you!

[@Podzhagitel]

i feel better about getting annihilated by calculus I to III now that i know that getting annihilated never stops

[@JoelRosenfeld]

Lol you just start to get used to getting beaten down

[@ethanbottomley-mason8447]

I am currently in my second last year of undergrad. I found it funny when you said that graduate classes are generally easier. I guess that it very much depends on the university, because I have taken quite a few graduate classes and the core graduate classes, real analysis I and II, and complex analysis, are probably some of the hardest classes I have taken so far, especially complex analysis.

[@JoelRosenfeld]

I’m not saying the content is easier. Certainly, conceptually, the sophistication goes way up. But at the same time, most of the courses are graded easier (or not at all) especially when you move from the more introductory courses like real and complex analysis and move on to courses directed at current trends. This also isn’t necessarily university depended as much as professor depended

[@Aj-oz3ek]

Thanks for the video professor :)

[@JoelRosenfeld]

You’re welcome! Thanks for watching!

[@american-professor]

In my PhD CS program my comps were waived because I had 2 papers published in the first 2 years. It was typical to have them waived like this in my program

[@DarthArtoo4]

Thanks for the great video! I’m currently in my first year of a Math Masters program after teaching at the HS level for 9 years now - I got my BS in MathEd in 2014. My dream is to get a Pure Math PhD but I’m afraid that I’m not qualified highly enough to be a competitive candidate. I’m excelling in the Masters program and have had multiple professors tell me that I’m capable of a PhD, but with no research experience or other accolades to bulk up my applications, on top of a respectable but not amazing GPA from undergrad, I’m really hesitant to get my hopes up. Any advice for what I can do over the next year or two to set myself up for success in the applications process? I do plan on obtaining a research apprenticeship at my school and I’m intentionally taking PhD-related courses as they’re available, but with how competitive Math PhDs are, I don’t think that’s enough. Thanks in advance for any guidance you may have!

[@aloksahu1783]

Hi hope you can make a video on maths topics and resources to brush up for master program in computer science and control engineering

[@JoelRosenfeld]

I'll give it some thought. It's a tricky thing to answer, since CS and Control Engineering are pretty diverse, so there isn't a good "one size fits all" prep that I can recommend, off the top of my head. From my own experience, having a good foundation in Analysis is helpful if you are studying Nonlinear Systems Theory (ala Khalil), but most controls engineers really just need a solid background in undergraduate ODEs and Laplace Transforms for Linear Systems. For CS, it's all over the place. If you work in machine learning, then a strong linear algebra background is essential. Algorithms require a good amount of Discrete Math (or Combinatorics), and a good knowledge of Power Series is helpful for algorithmic complexity and generating functions.

[@jackdirac2145]

How can i get a Phd in pure math in U.S.A? I don't have a bachelor degree, only self studying.

[@JoelRosenfeld]

You need a bachelors degree to even be considered. Then good recommendation letters from your professors, and a good GPA.

[@LucasDimoveo]

Can you go into what relevance Algebra played in your research? I've recently discovered Algebraic Geometry, and it seems like this field would naturally be vital for Analysis. Please excuse if the question is foolish - I am a lowly undergrad

[@JoelRosenfeld]

Not a foolish question. The truth is, in my research it doesn’t come up very often. Most of my work, as you have seen, is related to Hilbert Space theory and Analysis. There are aspects of algebra that can come up, and there are a good number of people that study operator algebras. Personally, I only use a light touch of algebra in my work.

[@ethanbottomley-mason8447]

Algebraic geometry is quite distant from analysis until you get to some of the more hard-core material like gaga or langlands. Algebraic objects come up in analysis, but not things like schemes, moduli spaces, stacks, etc. like you see them in algebraic geometry. It is more so fundamental Algebraic objects like vector spaces, algebras, groups, Banach and Hilbert spaces, etc. Where analysis and Algebraic geometry meet is in complex Algebraic geometry, where the rigidity of complex analytic functions is much more reminiscent of Algebraic functions. This is where magical facts like the equivalence of categories between projective schemes over C and compact complex manifolds arise. You also have results like Kodaira vanishing which rely on the fact that you work over C. There is also stuff like derived C^infty geometry which might be related to analysis at least by the name, but I do not know much about it.

[@RyanG3105]

Curious, is that an actual picture of your analysis qualifying exam? (I’ve never seen another institution’s to compare to my own experience.)

[@JoelRosenfeld]

That particular exam wasn't my exam. Right as I was leaving, they restructured the exams at my particular university, where they split the first year exams into four exams. Analysis and Algebra, but Fall/Spring exams. So this is the Fall exam for Analysis at my Alma Mater now. So instead of representing an entire year of material, this one represents one semester. If you want to see a large bank of old exams from my university, you can find them here: gma.math.ufl.edu/past-exams/

[@RyanG3105]

Thanks for the reply! I’m really liking your content and would have found it particularly helpful in grad school-many of the suggestions you made I learned through experience but it would have been nice to have a heads up from year one! Will certainly recommend your channel!!

[@JoelRosenfeld]

I’m glad you have found it helpful! Is there anything you’d like to know more about?

[@kevinpostillon8846]

Hello, I'm a senior math undergrad, I have the following questions: Does ba and bs make a difference when applying to graduate programs? My 2nd question is could you put the link of the website at 5:22 Thanks and great video!

[@JoelRosenfeld]

What is important is not so much the BA or BS, since the requirements can change from institution to institution, but more about the classes you’ve taken. You should have Linear Algebra, Abstract Algebra, and the Real Analysis or Advanced Calculus sequence under your belt. Then a smattering of mid level and high level electives. That signals the committee that you have the experience necessary to succeed. Bonuses would be undergraduate research and possibly a graduate course. I’ll have to get back to you with link.

[@kevinpostillon8846]

@@JoelRosenfeld Found the website, thanks for your reply. Thanks you gave me a lot of ideas in your video.

[@JoelRosenfeld]

@@kevinpostillon8846 I’m glad you found it helpful :)

[@sorenman1]

Out of curiosity, what is a person thought about working full time but doing your Ph.D, is it too demanding and not possible?

[@JoelRosenfeld]

That's a good question. Is it impossible? No. There are certainly people that do it. But I wouldn't generally recommend it. It is very challenging. Especially in the first couple of years, you'll have to manage your schedule between classes and work. Since classes are taught largely during work hours, it can be very difficult. Most PhD students come in on a teaching or research assistantship. This comes with a small stipend and a tuition waver. If you are working full time, then you'll have to pay the tuition out of pocket, which is very costly. Then there is the question of doing research, which is probably the hardest part of the job. For a good dissertation, you'll need to really throw yourself at the research, study manuscript, and think. Finding that space in your life on top of a full time job is going to be really challenging. Can it be done? Yes. But most people I have seen try it drop out after the first year or two.

[@justforfunforever1010]

I think your education system is so strange. You do a undergraduate degree, which I think is equivalent to a bachelors degree(?) and then you go straight into a phd program, where you do courses for a couple of years and then start research. In EU the common mathematics path, is a three years bachelors degree in mathematics where you learn all the basics. Calculus, Linear Algebra, real analysis, complex analysis and so on. Then you can apply for a 2 year masters degree, where you dive deeper into one area in the first year, like analysis or geometry, and then you write a thesis in the second year. And after this, you can try to apply for a fellowship, which is just like applying for a job at the university where they fund your research for a few years. And if you manage to write a thesis in these years that comply with some standards, you will finallt get your PHD. So what I’m saying is that you will have to study math for at least 5 years before you can even consider doing a phd. And even then it’s just like applying for a job with A LOT of competition. I wish we had a system like in the US where you could just get high enough scores on exam and they would just fasttrack you to a phd.

[@JoelRosenfeld]

We call it a PhD program, immediately following the bachelors degree, but really you don’t start the PhD in earnest until the third year of a “PhD program.” This follows after a couple years of coursework and exams. It amounts to about 6 years of preparation. And just getting through the exams is only a part of it. You aren’t automatically matched with a professor to do your PhD work with. This takes a good amount of negotiation, and if you did not perform well on your exams or coursework, then you might not be able to find a PhD adviser and you’d have to drop out anyway. It’s still very competitive. About half of my initial cohort either failed out or dropped out without getting a PhD.

[@mickeykozzi]

This PhD style isnt done in Europe and Australia. A PhD is 100% research driven. There are no classes or exams and the rest of the bull crap. Its 100% real, hardcore research. That's why PhD lengths in the US is about 50 000 words, and everywhere else double (100,000 words), please doing 3-5 research conferences and 3 published papers.

[@JoelRosenfeld]

Ultimately, it all lines up in the end. The first two years in the U.S. is roughly masters degree material, and then the subsequent three years is focused on the PhD work. That latter half is usually just research. I’m working on a collaboration to start comparing the PhD process in other countries. My audience is primarily US based, so this was directed at them

[@mickeykozzi]

@@JoelRosenfeld no it does not line up at all. US students do not publish 3-5 papers, conduct 3-5 conferences and produce a 100,000 word thesis. The US programs are half of this.

[@JoelRosenfeld]

@@mickeykozzi What world are you living in? This is pretty standard description for students in the US. It's not always a hard written requirement, but it's often a requirement by the individual advisers. When I was a postdoc in Mechanical Engineering, 3-5 papers was on the low end for students graduating with a PhD. I knew at least three students that had over 10 publications at the time of graduation from that lab. They also participated in national and international conferences, and they had substantial dissertations. Though, I admit, I did not count the number of words.

[@gassenweg]

You're mentioning it briefly at the end of the video but I think it should be stated more clearly that this is a very US focused video where everything is much more like school. This has basically nothing to do with a PhD in Europe-

[@JoelRosenfeld]

It is different in the first year. This would essentially be the first year of “graduate school” or a masters degree in Europe, since it’s common there to do a masters first rather than having it all lumped into one. Everything lines up more once you hit year three in the US, where that would be the start of the three years of a PhD program in Europe. At the end of the day, I’m a professor in the U.S. so this is my perspective. I don’t mean to misrepresent anything.

[@JoelRosenfeld]

I plan on Talking about the differences between academic cultures in the future. But that will require a collaboration to make sure I get the details right

[@gassenweg]

@@JoelRosenfeld that sounds like a very interesting topic and I think there is a lot to cover! I would like to see that as I am really not familiar with the US system :)

[@dustinkingsbury5554]

Work 16 hours a day?

[@drticktock4011]

Not the pinnacle. Read "so long and thanks for the PhD," especially the end.

[@JoelRosenfeld]

Thanks! I’ll check it out

[@drticktock4011]

@@JoelRosenfeld was helpful going through my PhD program at Stanford.

[@VenSensei]

Sophomore in college and I feel like I don't know anything.

[@JoelRosenfeld]

Don't worry. I'm an assistant professor, and I don't feel like I know anything either. Just keep working at it, and knowledge will come. The imposter syndrome never goes away.

[@kshitijshekhar1144]

Hi Professor, i forgot the video you mentioned this story in cuz ive turned off watch history on KZbin. But it was along the lines of a promising PhD student you knew who got his academic career destroyed by a nasty LoR from his PhD advisor? I wanted to ask if you had more details? Was he bad at research, what were his grades like? And how would a budding PhD student like myself(I'm an undergrad in CS, wanting to do a PhD in math), avoid such mishaps? I've watched your PhD guide, so don't bother listing out best practices you mentioned there. Thanks again.

[@Grassmpl]

I'm jealous. Your TAship seems a lot like an instructor. Where I study us TAs have very limited permission in terms of what we are allowed to do. We have to follow the instructors wishes. For example, we NEVER conduct exams on our own apart from the instructor. Lucky you.

[@JoelRosenfeld]

Some semesters we were pretty independent, and others, especially in the beginning, was like you describe.

[@Grassmpl]

Why are you in a hotel? Are you at a conference? I hope this isn't your long term place to live.

[@JoelRosenfeld]

Lol The past year I have been traveling a lot. This was recorded when I was traveling for a program review for AFOSR last August, and today, I just happened to get back from this year’s review.

[@jamesromano3288]

You will get a job making 45K a year.....if you became a Sanitation man.....u make 100K like my pal Gus......now who is the smarter of you two papi ?

[@JoelRosenfeld]

Getting a PhD doesn’t make someone smarter. It’s what you need to get if you want to go into academia and be a professor. Nothing wrong with getting a job in sanitation. Though as a professor, I do make substantially more than 45k. Most assistant professors in STEM start at 90k at my university.

[@jamesromano3288]

@@JoelRosenfeld ...If you say so papi......💩💩💩

[@hjl8492]

The cruel thing is Your professor is younger than you(way younger than u) and this phenomenon only occur in math major There are so many fields, you end up only know a small chunks of it, and every small chunks of mathematician are facing much open question Last but not least, your goal,? field prize?! , When you prepare graduation, you will face a problem that is nobody even your instructor don't know the solution, and eventually you would find out are you suitable for doing research, being a mathematician. PhD in math is rare, can get into the industry is really rare, have field prize nomination is extremely rare, and even so, tons of open math problems are waiting u to deal with, (and u are just in one particular field) you must love maths, and dedicated your whole life in solving most harsh problem in the world. Once you graduation, tech or finance, all of your knowledge in mathematics study couldn't apply, but you must tell your boss you keen on solving complicated problem and have really patience mindset. Sad really sad

[@JoelRosenfeld]

This is a strange comment. First of all, forget the fields medal. This is only for a very select group of mathematicians. There is plenty of good work to be done that will never see anything close to a fields medal. You can also do mathematics and be successful with just a 9-5 schedule. You don't have to throw your whole life away for it. Most professors are much older than their students. The average age of an incoming graduate student is about 23 to 25, but the average professor's age is probably in the 40s or 50s. As far as the utility of mathematics in industry, that's on the student to be prepared. You can spend all of your time doing pure mathematics, but you can also work to equip yourself with tools that the industry needs. There are loads of internship opportunities where you can see what the industry needs from you. There are also many classes in engineering and computer science you can take to help prepare you for an industry position. Many of my students prepare themselves by doing exactly these things.