After this semester is finished, I plan on studying some more maths over the summer. I’m currently a second year student and my summer is 3 months long. Since this is about the length of 1 full semester, I was thinking of treating it that way.
The books I think I might study are “Topology Without Tears” by Sidney A. Morris, “A first course in abstract algebra” by Fraleigh, “Linear Algebra Done Right” by Axler, and “Differential Geometry of Curves and Surfaces” by Kristopher Tapp.
This amounts to about 1600 pages, which I could get through at a pace of about 4-5 pages per day (per book).
However, after looking at the Fraleigh book, I realised that it is probably intended to be used for a full year course, and this is likely the same for the other books.
Since, at my university, we usually do 6 modules per semester, it would make sense to eliminate one of these 4 books.
And that is my question: which book should I eliminate?
I’ve done a semester of abstract algebra (covered 50-60% of what is in Fraleigh), already done a year long first course in linear algebra, but have never done differential geometry or topology.
Next year my course includes topology, more abstract algebra, but no differential calculus, and no second course on linear algebra.
I suppose this comes down to whether it is better to study something “extra curricular”, or to get early exposure to material I will learn next year.
Thanks for reading this far, and thanks for any advice
Edit: Fixed a calculation