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I'm taking a discrete math course. The textbook we use is such a pain to read because the amount of material is very overwhelming. For example, chapter 1 alone is 115 pages. And every subsection, 1.1-1.8, is very important to the coursework (from propositional logic to intro to proofs), so it's not like I can just skip a couple sections.

I'm trying to read everything and then summarize all of chapter 1 into one short chapter, but doing this feels like I'm neglecting a lot of the nuance that fills up the pages.

How do I approach overwhelming course material without neglecting nuance and without burning myself out?

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    $\begingroup$ A textbook that has more than 200 pages per semester is most likely garbage with tons of useless pictures and watered down information. Instead of wading through it looking for gold nuggets, get a syllabus of the course and find a better, leaner and meaner book that covers it without beating around the bush. $\endgroup$ – Rusty Core Oct 23 '20 at 4:24
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    $\begingroup$ Are you sure summarizing each section is worth the time? is it possible that the sections build on each other so you don't need to summarize 1.11 - 1.15 because 1.16 ties it all together and if you mastered 1.16 you are done. As an example from grade school - if you can subtract 5 digit numbers with regrouping, you don't really need the info on subtracting 3 digits without regrouping. $\endgroup$ – Amy B Oct 23 '20 at 6:55
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    $\begingroup$ @RustyCore: That's a fairly strong blanket statement: "A textbook that has more than 200 pages per semester is most likely garbage with tons of useless pictures and watered down information.", even though your advice in the following sentence may be useful. I think that the variability in textbooks is higher than you seem to imply. Also, there are those who benefit from information presented visually. $\endgroup$ – J W Oct 23 '20 at 9:49
  • $\begingroup$ You might want to take into consideration things you mostly already know, and not feel you need to dissect and verify everything stated. For example, you probably had some logic in high school geometry (truth tables, if-then is true except for the F->T case, etc.), some abstract function exposure in high school algebra or precalculus (or in a college algebra course) such as a function is a set of ordered pairs, and other things that you can hopefully just read over for a higher mathematical maturity level treatment, rather than something requiring totally new skills and practice. $\endgroup$ – Dave L Renfro Oct 23 '20 at 16:25
  • $\begingroup$ give yourself permission to ignore much/some of the nuance. try to get the main ideas in the first go, you’ll pick up more of the nuance when reviewing, when taking subsequent courses, and even later in life if you teach the course. its like shoveling the driveway after a blizzard - sometimes you just want to clear enough to just to get the car out of the garage. more concrete answer: start by recording the definitions ... like definition of and, or, etc. Also try to say what are the main ideas in the section. Or the big theorems. you could also find someone elses lecture notes.. $\endgroup$ – usr0192 Nov 8 '20 at 1:09
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I've never done this myself, but what you could do is make a some sort of tiered summarization where the major topics have blue tabs, then subtopics have red tabs, and then minor subtopics have green tabs. And as you do notes, the major ideas will be on the blue, the examples could be on red, and proofs and nuance could be green.

This way, if you look at all blue tabs, for example, you can see all the major topics and have an idea of how things work, but if you want examples then you'll have to look at the red, and so on Here, I never sacrificed anything in the course summary overall, but the summary is tiered in regards to depth for how I'd want to study.

Unfortunately, study habits differ so much that what works for me may or may not work for you, but consider if the only thing overwhelming is sheer amount of content. Could it be complexity of the content? The amount of new vocabulary? The nuance and caveats? The arithmetic and algebraic manipulation? etc.. I've always found compartmentalization of overwhelming too-big topics into smaller manageable topics to be the best strategy.

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I recommend to do some analysis of the situation. Telling us how the long the chapter is means nothing if we don't know how fast you have to cover things. Try to look at the situation as pages per day.

Recommendations:

  1. Work every day and do the required pages every day, to stay on track.

  2. (Perhaps) just chalk this up as a course that is going to take more time than others. And give it the time.

  3. (This runs counter to the others, but you have to consider alternate strategies): Find the minimum you need to do, by talking to people who took the course before. There is a tendency I've noticed in academia of wanting to assign tomes, but then really not giving the time to cover them. This is pretty different from high school or lower level uni courses, where you cover most of the material and really learn the topic. The thing is you find people wanting the prestige of coverage without the work. (Combined with the lack of attention to pedagogy, i.e. TEACHING, in colleges.) This is sort of an unfortunate situation, but you need to at least identify if this is the case in your course (they don't really expect mastery). In which case, you can usually find out what are the critical things to learn if you talk to the grapevine.

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