The discussion centers on the optimal sequence for studying advanced mathematics topics, specifically complex analysis, differential equations, vector calculus, and topology. The consensus is to begin with linear algebra, followed by vector calculus, and then advance to differential equations and complex calculus. It is also noted that a foundational understanding of real calculus is essential, while set topology can be studied independently or in parallel with other topics.
PREREQUISITESStudents and self-learners aiming to advance their knowledge in mathematics, particularly those interested in complex analysis, differential equations, vector calculus, and topology.
Which topics? The question is so vague that the only possible answer is: get a list of lectures at any university where mathematics can be studied.Santiago Perini said:Hi PF community, i'd like to learn about advanced maths but i don't know what are the requirements to study some topics, so if you can give me a list with the topics that i should learn first i will be very thankfull. :)
I'd like to study complex analysis, differential equations, vector calculus and topology, the problems is that i don't know what topics are in the middle or what study first.fresh_42 said:Which topics? The question is so vague that the only possible answer is: get a list of lectures at any university where mathematics can be studied.
Single variable calculus and linear algebraInfrared said:What math do you currently know?
You should start with linear algebra before vector calculus. Then you can approach differential equations and complex calculus. Set topology is more or less independent of those, although some calculus would be nice to understand the examples. You can do it in parallel. And of course you need all basics in real calculus.Santiago Perini said:I'd like to study complex analysis, differential equations, vectorial calculus and topology, the problems is that i don't know what topics are in the middle or what study first.
Thansk! :Dfresh_42 said:You should start with linear algebra before vector calculus. Then you can approach differential equations and complex calculus. Set topology is more or less independent of those, although some calculus would be nice to understand the examples. You can do it in parallel. And of course you need all basics in real calculus.