I feel like I have done nothing for 2 years | math phd update

[@CHALKND]

I actually found out at 4am that the preprint from this video: kzbin.info/www/bejne/n4DOqYJtg5iqi80 was accepted by the journal that we submitted to. So maybe if I filmed this 19 hours later I would have felt differently about how things were going... life be like that sometimes :D

[@kikokawamura3449]

Congratulations! Do you know that it is rare to be accepted in the decent math journal so smoothly, even after getting a PhD? Your future is bright! Keep going, Nathan!

[@kikokawamura3449]

4am…. That’s Nathan….. 😅

[@CHALKND]

Thanks Diego!

[@CHALKND]

Yeah I thought we would have had at least another 6 months of edits and revisions before we would be good to go if we got positive feedback from the referee. So I was very surprised!

[@CHALKND]

I must beat the sun to rise 😄

[@dhickey5919]

Good luck, Nathan. And yes, at some point it feels like your own goals are delayed by necessary but peripheral events, tests, etc. I know too I wonder sometimes why people around me aren't doing something academically hard/rewarding too. Instead of living large, they live 'small'. Frustrating world. Anyway, you've got this!

[@mmariokart231]

You’re doing great man!

[@CHALKND]

🤓

[@fuzzylogic2737]

You are doing great man! Keep up the great work!!!

[@CHALKND]

🤓

[@3zrv]

Though I don't know you, but I feel the efforts you've put into your goals. You are 3 standard deviations above the average, and I'm so proud of you, proud that there are people like you in this world! Keep grinding 👏

[@faressoufan1308]

Go Nathan!!

[@CHALKND]

I going Fares I going 😄

[@garrettdyess1110]

In the majority of cases, do you feel like people get burnt out during their educational journey because of the learning/topic, itself - or, do you feel like it is the context in which we must learn? The context being the constant, overhanging stress/pressure of how grades tend to determine the future for students wanting to pursue further academics. Your discussion on being tired of being tested on material is very relatable and I was wondering if you share the view I just mentioned.

[@CHALKND]

The latter but usually grades in courses aren’t seen as a huge road block. I’ve witnessed more people burn out because they just don’t want to take a qualifying exam - or that the studying process for a qual was too stressful. However aside from quals I have seen this play out with students in particular graduate courses under specific professors. In most cases these were people who were excited to talk about the subject matter and enjoyed engaging with mathematics before beginning the process of studying for quals or taking a certain professor’s course. For me in particular, I really enjoy research and learning about different mathematical structures and working to communicate them with others and the qual process has really destroyed a large chunk of my motivation to work on those things by way of “gatekeeping” my ability to do so in the future should I not pass quals within a certain timeframe. While not actually being a good metric for if I am good at what I would like to work on (qual subject areas are usually too surface level in comparison to the hyper-specialization that comes with research, and sometimes the material is wholly unrelated to ones desired research field. That in conjunction with the only real metric for being a good researcher is being able to successfully contribute to research projects/papers) so the process if very frustrating beyond the general academic stress of studying for a big exam. Being that my qualifying exam is tomorrow morning, this is all very fresh on my mind so this take is hot right out of the mental pressure cooker. Hopefully it goes well and I can stop worrying about such things. This was a great question thanks for asking it!!

[@tomijantunen9992]

Thanks for the update! It is fun to hear about your journey.

[@LucasDimoveo]

I hope you're doing okay. Take care of yourself to the best of your ability. It seems that your approach to Analysis and Dynamical Systems is very algebra and topology heavy. I'm more interested in the scientific computing side, and I'm still only in community college, so a lot of the pure math topics outside of Analysis seems mysterious to me

[@CHALKND]

I am doing alright 😅 At least that particular theorem from that talk is more abstract algebra heavy, most of the stuff I look uses much more analysis and topology than abstract algebra. Speaking of scientific computing, the leading example I used in that talk was Conway's Game of Life.

[@jmw1500]

You are very fortunate

[@Kinghercules]

So question; why do you repeat the same classes in grad school from undergrad? Like you've taken Complex Analysis and Topology in undergrad but yet those and others are repeated in grad school. With some much math out there why are the classes repeated? Please explain. Thank you

[@CHALKND]

@Kinghercules there is a significant difference in material between undergraduate and graduate math courses in much the same way that there is a difference between taking algebra for the first time in middle school in the states as opposed to taking algebra/precalculus in highschool in the states. Although some of the basics of the material may be repeated, there is usually a much greater depth reached for a larger overall breadth of material within the subject area which also in turn requires more detailed arguments and more advanced/nuanced proof methods are used as well in grad classes as opposed to their undergrad counterparts. At least that is my take on your question, I am sure others have different analogues or distinct ways in which they find grad courses different from their undergraduate counterparts.

[@Kinghercules]

@@CHALKND Thank you and keep up the videos sir!!

[@dehnsurgeon]

why does the topology exam only cover point-set topology? what would someone going into differential, geometric or algebraic topology take?

[@CHALKND]

Great question! I thought about this quite a bit when I was applying to schools. So the contents of PhD qualifying exams vary quite a bit from school to school. From what I know from my own institution, and comparing those exams with others and looking at the CV's of professors at each institution the contents of what may be tested is highly dependent on the expertise of the professors in the department and especially for those on committee for that exam. So, as you note, there is not really any differential geometry or algebraic topology on the topology qualifying exam where I am, and if you then look at areas of expertise of professors on the committee, they work on topics related to Model Theory, Set Theory, Logic and Topological Dynamical Systems. Each of these areas requires a good working knowledge of the topology of metrics spaces, compactness, and just working with other set-family objects aside from topologies that come up across mathematics (like filters, sigma-algebras, ordinals, the borel hierarchy, etc.) amongst other things which fall in the realm of point-set topology. Some places have a "Topology and Geometry" or a "Topology and Algebra" qualifying exam where differential geometry and algebraic topology come up respectively too so it all just depends on where you look.

[@dehnsurgeon]

@@CHALKND that's really interesting - I'll have to think about that when I'm done with undergrad and ready for the next step

[@PresDonaldTrump]

Do it, forget about it, and progress.

[@CHALKND]

well hopefully not forget about it, Topology is core to my research area(s) of interest. but aside from that, this is the plan lol 😅

[@PresDonaldTrump]

@@CHALKND 🤪