Is solution-manual type studying as big of a flaw as I think it is?

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I am pretty close to finishing my undergrad degree in math, and I am really starting to realize as my classes get more demanding, conceptual, loaded, whatever, that the style in which I have cultivated studying is not going to keep working. I very, very rarely read the texts. I realize this isn't a good thing. I have done a lot of applied math in my undergrad, but not a lot of pure, and I think that's where I am finding the trouble starting.

How do I condition myself out of looking at solutions or finding ultra-similar problems and replacing things? Really I would call what I do as backward studying. I've never really been in a situation where I approached a question being honest with myself that I wasn't going to just fly for the solution, and I haven't conditioned myself to the whole "problem solving" cycle where you review theorem/definition, find an approach, try question etc. Any tips?
 

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  • #2
lisab
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There was a lively discussion on this some weeks ago in this thread -

https://www.physicsforums.com/showthread.php?t=708986

The consensus was, I think, that it can be a problem but not necessarily. In other words there was no strong consensus :smile:.

Interesting. Thanks that was a good read. As one person pointed out, obviously it's a different thing to be simply copying answers and seeing answers and working backwards. I am definitely trying to back off seeing solutions and give myself a little "thinking" time. But then I get to the issue that made me want to ask this question. I'm doing some low-level set theory stuff, and having generally an applied math background and having only taken a few abstract classes, when I get to some questions, I am just totally stumped.

Ask me to prove something ive seen before and I have no problem doing it, and I know why i'm doing it and how. But if I see a new question, I'm often stumped. Not so much when it comes to similar questions, but for example, when I went from the introductory stuff of set theory into cartesian products then into relations. I still don't know how to approach the relations questions, but I can still go back and prove most of the basic set theory rules and laws by either using arbitrary inclusions or breaking it down through formal logic and boolean algebra.... but I don't know how to harness that "cumulative expansion" into the next topics. I had a very similar problem to this in analysis and I would rather not re-live it.
 
  • #4
UltrafastPED
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The goal in mathematics is to have an intuitive understanding of how things work - this allows you to tackle new kinds of problems. Thus you need to study the text (or lecture notes), and be able to work out for yourself how to do a problem.

Cribbing from solutions manuals is not studying and hardly prepares you for actual work.

How to break these bad habits? Take a course which has not solutions manuals - an upper level proof-based course in abstract algebra, or linear algebra. Or take a course from the physics department - analytical mechanics requires only first year physics but teaches a lot of mathematical techniques.

Course work isn't the only way to learn - if you are self-motivated you can back up and re-teach yourself the material from your earlier courses, working problems and only checking answers after you are done. You can really move pretty fast in such a detailed review - but you won't have any spare time while you are doing this.
 
  • #5
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The goal in mathematics is to have an intuitive understanding of how things work - this allows you to tackle new kinds of problems. Thus you need to study the text (or lecture notes), and be able to work out for yourself how to do a problem.

Cribbing from solutions manuals is not studying and hardly prepares you for actual work.

How to break these bad habits? Take a course which has not solutions manuals - an upper level proof-based course in abstract algebra, or linear algebra. Or take a course from the physics department - analytical mechanics requires only first year physics but teaches a lot of mathematical techniques.

Course work isn't the only way to learn - if you are self-motivated you can back up and re-teach yourself the material from your earlier courses, working problems and only checking answers after you are done. You can really move pretty fast in such a detailed review - but you won't have any spare time while you are doing this.

Ive taken both group theory and abstract linear algebra (arbitrary fields, linear maps, etc etc). Although they didn't have solution manuals, I would say I still studied in a similar way; find a similar problem with fully worked solutions, work it backwards, and learn it like that, as opposed to what I would consider the traditional (better?) method of laying out theorem/definition/lemmas/whatever and trying to build the house brick by brick. I guess the issue is really just discipline and being willing to spend the time. I'd love to take a physics course - sadly that's completely unrealistic for me at this point haha.
 
  • #6
UltrafastPED
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Perhaps yout future career will be in reverse engineering, or fixing problems in other people's code, or as an editor. You do have a useful skill ... you should look into cryptography, especiajjy the code breaking side! :)
 
  • #7
People learn differently. I actually found that I learned best from solutions initially when studying for olympiad level physics - sometimes common techniques come up, and you need to learn to master those. After I had a good grasp of those, it was like my horizons were widened and I could think of new techniques on my own. So solution studying isn't worthless - just don't do it all the time!
 

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