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As someone who probably took undergraduate courses more recently than most, I can attest to the fact that applications are necessary. If not given, students very often get lost - not understanding the big picture. They may be able to apply specific operations to specific problems, but it is the applications that allows them to see the forest instead of just ...


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Be it undergraduate or professor, you need hands-on examples to "see" why some concept or technique is worthwhile. Sure, you can take it that more advanced people are better able to come up with their own examples and applications, or have a richer experience to which new material relates. So examples, applications, cross-connections are certainly needed for ...


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You may wish to view the MAA's report Transitions to Proof by Carol Schumacher, Susanna Epp, and Danny Solow: https://www.maa.org/sites/default/files/Transitions%20to%20Proof.pdf It has some suggestions for these kinds of courses, and gives references to some relevant books and articles. Ultimately, the course design is very open-ended, so it's hard to ...


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I teach at community college. I often publish the homework problems at the beginning of the semester, listed by section. I have never had a student work ahead (that I know of). And I have had a few students who loved math, asked deep questions, and were interested in doing extra. I don't think that is likely to happen, except in very rare instances. One ...


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