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Location: New York CUNY (as education systems might be different in other places)

I started my life studying philosophy and psychology and then at 22 transitions to computer science. It took me a long time to understand the importance of mathematics.

I was placed in calculus1 and while it was hard to remember math I managed to pull a B+.

However there is a recurrent problem I have with math classes I am taking, namely too many topics to really understand everything.

In calculus2 and probability and statistics we covered so many topics that I felt that any attempt to understand the material would only hurt me on the test. Constant new topics without any chance to play around and really grasp the material. Moreover textbooks rarely focus on the WHY of things, nor do professors have the time to explain due to computational emphasized department finals and curriculum requirements. I feel like every class has artificially inflated amount of material and it becomes especially obvious when teachers end up rushing up to two topics a class at the end of the semester.

For example we went over possion distribution and later waiting-time possion distribution and besides showing us how to do the problems 0 emphasis was put on why it works and where it came from. I am VERY frustrated with this frenzy of meaningless formulas.

I lately feel that perhaps I am an idiot or something but I just don't see any of the textbooks explain things properly. When they do attempt at explanation it is just a soup of symbols without any intuition. It is like they just copy pasted proofs to make it seem rigorous. The emperor is naked.

Is it my laziness or stupidity or a known problem in education curriculum in early undergraduate math classes? It is killing my recently gained joy for math and lowering my self esteem.

Perhaps people can advice on some math books that would fill the gaps and actually explain things.

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    $\begingroup$ If you are asking a question, make the question clear in your subject. The only question in your subject is actually asserted as fact in your body. The question is a guide $\endgroup$
    – Thomas Andrews
    Jul 9, 2012 at 18:17
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    $\begingroup$ There doesn't seem to be any question here. $\endgroup$
    – hmakholm left over Monica
    Jul 9, 2012 at 18:22
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    $\begingroup$ I think that the last sentence is implicitly a question, or at least a request. While I sympathise with the OP, there does seem to be too much "soapbox" in the question, that would IMO belong better on a blogpost. $\endgroup$
    – user16299
    Jul 9, 2012 at 18:27
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    $\begingroup$ Yeah, there is a question buried here, it's just that the heart of the question should be in the subject of the question. $\endgroup$
    – Thomas Andrews
    Jul 9, 2012 at 18:29

2 Answers 2

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It is a well-known phenomenon that certain beginning undergrad math classes can be crowded with topics, to the point of making it almost impossible to explain them all with the degree of detail and clarity that one would like (and I am speaking as someone who has been on the other side of it --- i.e. teaching these classes). There are various reasons for this; one is that certain topics must be covered (due to demands of various later courses, both within the math dept. and in other depts. for which these courses acts as service courses), and there aren't enough separate course slots available to separate them out into different courses. Well-designed curricula try to minimize this phenomenon, but it's not easy; courses and curricula have momenta of their own, and are not as easy to change or redirect as you might think.

In any case, given the situation you describe, it is probably not realistic to learn everything in your courses to the degree of precision and understanding you would like; like many other things in college and in life, there will have to be a compromise between the ideal and the realistic in your learning. What is possible, I would think, would be to learn some part of your curriculum more carefully and in greater depth.

To this end, I would suggest that you choose one part of your course that you found the most intriguing, and that you would most like to learn, and ask a specific question about that part of your curriculum. (E.g. based on your complaint about the discussion of the Poisson distribution, maybe you would like to understand better the different probablility distributions, where they come from and why we study them, and you could ask as question about "Resources for a beginner to learn and understand different probablility distributions".)

Try this with one topic at a time, and try to balance your study between "keeping up with current topic in class" and "learning topics of interest for personal development/understanding". As (or if) you move onto more advanced math classes, these two threads of your study will start to become more closely entwined, because the pace of introduction of new topics will slow, and you will get the chance to study each topic in more depth.

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If your goal is to understand mathematics, I wouldn't nessacary reccomend the standard calculus textbooks. These books, like you said, emphasize computation, rather than understanding. However, if you are wanting to have an understanding of, calculus say, you will really have to read a book on real analysis. These textbooks emphasize a theoretical devolopment of the subject, and require you to prove theorems, rather than to calculate things. If you don't have any experiance with proofs, I would suggest Analysis by Lay. It's a fine enough book, but most of the people on this website wouldn't call it an anlaysis book.

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    $\begingroup$ Dear Chris, I don't think that the OP is asking for rigorous foundational treatments as in a real analysis course, but rather for clear explanations of the various concepts appearing in his classes. Regards, $\endgroup$
    – Matt E
    Jul 9, 2012 at 18:45

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