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Courses Regarding the Difficulty of Math Graduate Courses

  1. Aug 18, 2016 #1
    Dear Physics Forum personnel,

    I will be taking my first graduate course (as an undergraduate) in mathematics starting on this Fall Semester. The course is about the algebraic topology (Hatcher, Spanier, Massey, etc.), which I am very excited to take as I love the topology. I am curious about the typical difficulty and pace of graduate courses. Could you give me some of your experience about them in mathematics? Do graduate level courses assume all undergraduate backgrounds (analysis, algebra, topology, combinatorics, set theory, logic, etc.) from the students?

    My learning style is to keep asking why and doubt everything in the book and try to reason and resolve them by myself. I also like to formulate my own problem sets and try to work on them, rather than the chapter problems I still solve them, but not everything). As such, I usually move very slow.

    Also, I am suffering from a severe case of OCD, which have been haunting me since my freshman year (resulted in a bad GPA)...I am receiving medical treatment, and I am curious if I need to talk to the instructor to accommodate my difficulty.
     
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  3. Aug 18, 2016 #2

    Krylov

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    That is nice, I hope you will enjoy it a lot.

    I am just a simple applied mathematician and I did not take algebraic topology. My own graduate courses were almost exclusively in analysis. As such they did rely heavily on the undergraduate courses in that discipline, but not that heavily on those in other disciplines such as algebra. There was some time to recall and re-read the undergraduate material, but not a lot.

    So did I. I think it is important to know when to move on and keep the bigger picture in mind. I still find this difficult myself. Try to distinguish between something that positively interests you and an obsession.

    Yes, I strongly believe so. If you had been paralyzed, for example, your handicap would have been immediately obvious to your instructor, but now it is not. If you think it will play a role in how you work through the course, discuss this well in advance.
     
  4. Aug 18, 2016 #3
    Thank you very much for your insights and advice! My problem is that I found everything to be very interesting and lead me to investigate more about them. For example, I researched intensively about the importance of empty sets and why the union of empty collection of sets does not exist after encountering the union and intersection of the collection of sets. I learned quite a lot, including the basics of set theory and model theory, but I know such investigation will consume a lot of time, which actually interfered with my effort to focus on most important topics of the courses. The OCD played a role in a sense that I become very uncomfortable and cannot move forward if I cannot resolve every details of my curiosity and questions.....I know it is important to acquire an ability to when to move on, but my brain strongly tells me that I cannot get a bigger picture without knowing the details that are painted.

    Perhaps I should take very few math courses and do more reading courses with professors. I actually have four opportunities to do reading courses, and I am thinking of choosing two of them to learn more about my interest.
     
  5. Aug 18, 2016 #4

    Krylov

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    You are welcome :smile:
    Yes, and I hope that as your OCD symptoms will become less severe, you may also be able to acquire that ability.
    Are "reading" courses also about mathematics? Are they like self-study courses on a specific topic, where you meet every now and then to discuss? This is how I did a number of advanced courses, because where I studied the audience was too small to warrant formal lectures.
     
  6. Aug 18, 2016 #5
    The reading courses can be as general as set-theoretic topology or specific as dimension theory, depending on professor and my tastes. At this point, I would like to study general topic like set-theoretic topology than focus more on the specificities.

    The reading course is one-to-one meeting with a professor, one-two meetings per week to discuss my reading and debating about my knowledge. I personally think the reading courses are an excellent opportunity for me to study some branches of mathematics that I cannot learn through official courses (I need to take 1-2 courses per semester, as recommended due to OCD).

    I have one question....Is it okay to mention that I was suffered past years with OCD to explain that I am taking fewer courses and some of my bad grades that resulted form the OCD? I know I can do much, much better from now as I have been receiving the medical treatment and learning some life techniques to counter the OCD attacks, but I am afraid that graduate programs will see me as a student with weak mentality and fainted heart who cannot even handle mental disorder by himself.
     
  7. Aug 18, 2016 #6

    Krylov

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    Excellent, I would certainly take this opportunity. It fits your interests and your personal situation.

    I would mention it without lamenting. Bring it as a very factual thing, no need to dwell on it.

    Nobody can handle a serious mental illness by himself. It requires professional medical care. Would people accuse patients with a serious physical condition of "weak mentality" and "fainted heart"? No, I do not think so. So, no need to be apologetic.
     
    Last edited: Aug 18, 2016
  8. Aug 18, 2016 #7

    micromass

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    The union over an empty collection does exist, it's the intersection that doesn't exist.

    Anyway, I'm an instructor of mathematics, but I'm also an OCD sufferer. So even though I know the debilitating nature of the disease, I also know that instructors will not take it into account. That is, unless you have a doctor writing you a note. If you want special "privileges" then you should ask this from your university through the official channels. The instructor would and should not give you and privileges just because you mention that you have some disease. So get proof from your doctor, and then research in what ways the university can accommodate you.

    A grad class will move fast, so you have the habit of thinking things through endlessly, this will be a challenge for you.
     
  9. Aug 18, 2016 #8
    Thanks for the correction; I meant the intersection. I can ask my psychiatrist for a letter and proofs of my OCD. I think my university has a program for people with disabilities (I believe mental disorder also count), where they accommodate those students in the classroom by corresponding with instructors too. I can also meet with the instructor to discuss possible ways to make a best use of the course with OCD.

    Just curious, what symptoms of OCD do you have?
     
  10. Aug 18, 2016 #9

    Krylov

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    Without wishing to go into more detail, my experience is different.

    However, I do agree with micromass that it is probably best to hand over a medical attest to your university. This way there can be no misunderstandings and you can always refer to the attest whenever the issue comes up during a course.
     
  11. Aug 18, 2016 #10

    micromass

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    You should try the official channels first. Once you got that in order, you could meet with the instructor.

    I don't wish to talk about this, sorry. Just know that it is a very big part of my life, sadly.
     
  12. Aug 18, 2016 #11
    By "official channels", do you mean the university personnel who run the programs for students with disability, and my psychiatrist? Please let me know if I am not correct. I am going to meet the dean of my college and major adviser on tomorrow.
     
  13. Aug 18, 2016 #12

    micromass

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    I don't know how your university arranges this, so I can't tell you. You need to do some searching on the site of your university on how to apply for accommodation for illnesses and what proof you need. The advisors will probably also be able to tell you what to do for that.
     
  14. Aug 18, 2016 #13
    I am very sorry to keep interrupting you, but I have one more question! Do you think it is a good idea to ask my instructor, after presenting the proofs of OCD, if my habits will be destructible for the course? I really would like to take that graduate course as I love topology very much, but very fast pace worries me.
     
  15. Aug 18, 2016 #14

    micromass

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    I don't know how the instructor can possible know how your OCD would interfear with the course. You can ask him for accommodation, but the instructor is not your psychologist and hardly knows anything about you. So I'm not sure how he could possibly help you with this.
     
  16. Aug 18, 2016 #15

    Krylov

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    It seems to me that you are in fact obsessing over this now.

    Instead, follow the official route offered by your university and inform your instructor that the university is aware of your handicap whenever this is relevant during his course.

    Apart from that, try to concentrate on the course(s) you love to take, as well as your treatment. It is very good that in spite of your illness you are able to feel joy for something such as topology.
     
  17. Aug 18, 2016 #16
    You are correct. I almost fell to it again.

    I am very excited to start the new semester. I will be taking very interesting courses and closely interacting with my professors and research mentors. I am also participating in many interesting campus activities too (good way to keep myself out of isolation, which is a huge driving factor for OCD).

    Once again, thank you very much for all of your help!
     
  18. Aug 18, 2016 #17
    I am sorry for one more intrusion....Is it true that the graduate-level courses are less dependent on the assigned textbooks? The officially required textbook is Hatcher, but I like Spanier, Singer/Thorpe, and Bredon. I think they appeal to either algebraic or geometric aspects more strongly than Hatcher, which I feel like trying to introduce both aspects but did not present well.
     
  19. Aug 19, 2016 #18

    micromass

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    There's not much you can say in general. It depends on the instructor.
     
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