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I'm a sophomore studying computer science. I have the option of finishing up my degree, or switching to math and taking my minor in CS. I'm contemplating switching for a variety of reasons - don't like sitting in front of the computer, not interested in computer "science", not particularly fond of the professors or my classmates in CS, and not fond of the I'm-in-it-for-the-money atmosphere.

I really like math, but I haven't taken a single upper division course. In high school and for the only math class I've taken in college (linear algebra) I could breeze through by studying off the textbook. Is this true for upper division math classes - could I do well by focusing primarily on textbook studying? I prefer reading textbooks, as listening to someone lecture bores me and it's never at quite the right pace for me, either too fast or too slow.

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    $\begingroup$ The important part of the lectures, in my experience, is to get context, particularly as you reach the upper undergraduate level. For example, you could easily read a textbook about commutative algebra and have no idea that one of the main motivations and guiding principles comes from geometry! There are less extreme examples, but basically when you hit that boundary between education and research, it's good to learn from a practitioner to get their colour. $\endgroup$ – Callus - Reinstate Monica May 28 '14 at 18:59
  • $\begingroup$ I view the teacher as a very experienced tour guide. They point out the interesting parts, explain the difficult parts, show what is important. But it is (always) up to you to do the work. $\endgroup$ – PeterR May 28 '14 at 19:11
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    $\begingroup$ It depends (on the school you're at, on the course you're taking, on the lecturer you're taking it from...). $\endgroup$ – Qiaochu Yuan May 28 '14 at 19:44
  • $\begingroup$ ...as well as your own aptitude for the material in the course. $\endgroup$ – oxeimon May 28 '14 at 19:46
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I take this as an advice question: I will explain my experience in regards to what you're discussing, but I will leave it to you to make the decision of whether or not you should switch your concentration to mathematics. Usually (note that this distinction is important and many professors have different ways of conducting their courses), in upper-level math courses, there is definitely a component that is lecture-focused. In other words, lectures are important in some ways: professors are typically very knowledgeable in what they are teaching and can point out the highlights, or the topics and examples that are worth noting in your study of the subject of the course. Professors go through the process of determining what is really crucial to understanding the content before they even begin lecturing, reinforced by their expertise. Thus, attending lecture and focusing on the professor's approach and examples is a powerful resource. However, ultimately in a mathematics course, the learning and work is largely left to the student with the professor as a guide. Often, homeworks serve as an outlet for students to work through the motivation and heart of content - this is where most of your effort and subsequent reward (understanding) will come from. In summary, the lectures and the textbook are considered more of resources in a mathematics course in comparison with courses in other disciplines. However, weighing the benefit of these resources, lectures come out on top because the professor goes through the process of figuring out what you need to know (in his/her class) beforehand. In the end, though, you should evaluate the relative benefit of these on a specific course/professor combination basis. This is only a general discussion based on my experiences.

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