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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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I am going to be taking a year off from my studies and would like to self study abstract algebra as it is right now the biggest gap in my math background.
I have a copy of Dummit and Foote from which I would like to study, however I realize that it contains quite a large amount of material! I would thus like to put together a list of essential topics to cover so that at the end I would have covered a similar content to a third year undergraduate course for mathematicians. One thing I would like to do if possible is get an introduction to Galois theory, it is quite mysterious to me and I would love to get acquainted to the subject.
I am (quite unfortunately) in electrical engineering, although I am directing myself to do a masters in math or perhaps control theory on the mathematical side of things. As such I have taken as many math course as I could and have done some self studying so that I think I now have a reasonable degree of mathematical maturity (real analysis, topology, differential geometry, linear algebra of course, probability and stats, discrete math, etc). Unfortunately I can't take as many pure math courses an as a math undergrad which is why I want to self-study abstract algebra.
I know this is an ambitious project but I am quite motivated so any tips are very appreciated!
I actually did this, and so I have some experience with Dummitt and Foote that I'd like to share. First, if you're not committed to D&F, but just to getting some good basis in modern algebra, I might be inclined to recommend a different book. Let me just tell you some pros and cons about this bible of algebra.
Pros:
Tons of examples worked out. Every chapter has some general theory, followed by usually about a half dozen explicit examples. It's really good to do these examples by yourself, and then read how the book does them, or read them in the book and then try modified examples for yourself and see if you can follow the same deas">ideas. Another useful thing to do is to try to work some examples as you read through theorems. None of this is unique to D&F but rather just good dvice">advice for reading any math book, but it goes double for D&F for reasons I'll explain below.
A billion and two exercises. This is a must for algebra, for the same reason. Practice practice practice. The problems range from routine to difficult (but none are so hard I could never work them out, if you like to be
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