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I have just began my first year as a math graduate student at a US school. I am having an issue in the fact that

During my undergraduate years, I would only take 2-3 classes a semester, and usually only one or two of them were a math class. This got me used to a particular style of learning; I always had as much time as I wanted to spend on any particular topic; I would read about the topic from different books, read about the history of the topic, etc. I feel like I learned very slowly, but what I did learn, I learned well.

Now I am in grad school, and the atmosphere is completely different. I have 3 math classes which move very fast, and assign a lot of homework. I feel like I do not really have time to learn the material well; I learn the material just barely enough to to do the homework and pass the exams, and then I have to immediately push on to the next topic. I solve the problems and try to understand the theorems/proofs, but then one week later I often retain very little. I always feel like I need 2-3 more passes over the material to learn it well, I never get a chance to do it.

I feel like some of those undergrads who just learn the material to pass the class, not really to use it. But this is terrible to do as a grad student, since math is supposed to be my specialty.

My question is, is this common? I am trying to figure out if this is normal, or if I handicapped myself in undergrad by taking it too easy. It seems to me like there are some students who retain information much better; they study much less than me, and seem to recall information from weeks before, and I can't do that.

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    I'd say pretty common. But you are just starting in a new environment. The assigned exercises are your friends. Hopefully you will settle in after a bit, but grad school can be pretty intense. Not a leisurely pursuit. – Buffy Nov 5 '19 at 1:17
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    What other demands do you have on your time? Outside of school, are you working full-time, part-time, or not at all? Do you have a family? – shoover Nov 5 '19 at 3:19
  • Passing the exams is the test of your knowledge. If you pass them with relative ease (never repeat class) then you are doing great. It is a good sign that you consider this knowledge shallow nevertheless, it means you have a drive to improve. – user3819867 Nov 5 '19 at 13:24
  • @shoover I am a TA, so I guess you could call that a relatively easy part-time job. I don't have a family. – Blue Nov 5 '19 at 16:47
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If you're putting the time in, successfully doing the homework, and passing the exams, then you're doing fine. The first year of grad school in mathematics should be thought of as a horrible bootcamp to get through rather than a deep learning opportunity. How comfortable someone is during their first year is mostly a function of what their undergrad experience was like. So it might be true that your undergrad program was less strenuous than that of some of your fellow students, but if you're keeping up, you're getting the job done.

Depending on your learning preferences, you might find that things percolate better if you work with others. I would also suggest that you keep good, searchable records for what you want to get back to at a later date. This will be especially helpful when it comes to prepping for written exams.

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  • very good point having a summary with key point for each lesson/chapter can really make your life easier. – RomainL. Nov 5 '19 at 12:45
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    "...rather than a deep learning opportunity". Well that depends on if OP is taking any machine learning related classes. I'll see myself out. – user3390629 Nov 5 '19 at 18:42
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There are memory systems that assist many peole in better retaining information. Typically it is recommended that you review material repeatedly woth decreasing frequency. I could dig up links, but, so can you and you will better know what suits you.

That said:

This may be useful Active Recall wikipedia

&

How to Improve Memory for Studying in 27 Ways

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Your intuition that you need multiple passes to learn the material is correct. Retrieving material several times from long term memory (spaced repetition) will keep that material accessible to you for much longer than cramming. Another effective technique is to try to teach the material to someone, even if it's a stuffed animal -- by having to explain what you've learned, you not only retain it better, but you uncover gaps in your knowledge.

Between semesters, I'd recommend reading a book on learning. One I really like is Teach Yourself How to Learn, but there are a number of equally good books on the subject. Find one that focuses more on how to understand material with short, focused sessions rather that just spending more time, because short focused sessions are way more effective.

Also, don't skimp on things like sleep, exercise, and nutrition. I felt I never had time for any of that in grad school, but I found if I did a quick 30 minute run I was so much more focused afterwards (and less stressed!) that I was enough more effective when I got back that it was a net gain for my studies.

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    +1 for the comment about sleep. People tend to skimp on it to study, but you have to sleep in order to keep the memories you created during studying. Maybe the single best thing you can do to help memory retention is to regularly get a good night's sleep. – Kat Nov 5 '19 at 21:16

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