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Problems in Mathematics
- splike 8y agoI would really like to see something like this for probability
- olooney 8y agohttps://www.statlect.com/fundamentals-of-probability/probability-questions https://www.statlect.com/fundamentals-of-probability/probabi...
- rguzman 8y agotry 50 Challenging Problems In Probability by Mosteller. it starts pretty basic and works up slowly to a good foundation for learning probability theory in a rigorous way using very neat problems. https://www.amazon.com/Challenging-Problems-Probability-Solutions-Mathematics/dp/0486653552/ref=sr_1_1?ie=UTF8&qid=1537816101&sr=8-1&keywords=problems+in+probability https://www.amazon.com/Challenging-Problems-Probability-Solu...
- whatshisface 8y agoFor some reason, all of the links are opening in new tabs. Is there any way for me to configure my browser to ignore the html and not do this? (A way to revert to system default scrolling would also be nice.)
- bytematic 8y agoA link normalizing addon would be cool, add some safe rel tags and a setting to prefer new tab/same tab
- paulpauper 8y agoDon't recall learning Group Theory, Ring Theory, Field Theory, Galois Theory, or Module Theory in my undergrad math classes. Did cover linear algebra though.
- apetresc 8y agoThose were all standard topics, generally in years 2-3, at my undergrad program circa 2006.
- btilly 8y agoI took all of those except module theory in my undergrad math classes back in the early 90s. However some of them (for example Galois theory) were optional courses.
- throwawaymath 8y agoAll of those are typically in a single undergraduate course on abstract algebra. Depending on the specific course you might only touch on Galois theory and modules, but you'll definitely get exposure to both. Most undergraduate textbooks will have a chapter/section devoted to each of those topics.
- omegaham 8y agoIs this going by the quarter system or a semester system? I can't imagine doing groups, rings, and fields in a single quarter with significant rigor. That would suck.
- throwawaymath 8y agoSemester system. The first half of the semester would be groups and rings.
- xyzzyz 8y agoI haven't yet seen an algebra class that would start from scratch, define groups and rings for the first time, and do commutative algebra with modules, and fields with Galois theory in a single semester. Usually these take around 2 semesters.
- gowld 8y agoWere you a math major? Almost every math major covers an intro to Group Theory, Ring Theory, Field Theory. That's just about all you can do in pure math immediately after Linear Algebra (except number theory and some probability), and the foundation for almost everything you'd try. If "applied math" was not separated from "pure math" in your school, and you did non-math electives after the minimum core math classes, then you might avoid these topics in favor of a broad curriculum of differential equations, graph theory, probability, and such. Galois Theory, or Module Theory would be electives or touched on in high-expectations program.
- rfurmani 8y agoThere is also Problems in Analytic Number Theory, which teaches the field as a series of problems and exercises. It's a great way to learn, and one that I haven't seen implemented well in other areas (even the corresponding book for Algebraic Number Theory isn't as good) https://www.amazon.com/Problems-Analytic-Number-Graduate-Mathematics/dp/0387723498 https://www.amazon.com/Problems-Analytic-Number-Graduate-Mat...
- ILMostro7 8y agoAhh, "problems", not problems :) I thought this was going to be about the abc conjecture. https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/ https://www.quantamagazine.org/titans-of-mathematics-clash-o...