>>11544996I highly recommend against this. Knowing the basics is a fantastic backup plan in case you end up disenchanted with the world of academia (as has happened to me).
>>11545185- For Numerical Analysis, check Faires' and Burden's Numerical Analysis. There's also Bulirsch, Stoer.
- For Calculus, instead of Apostol you might also want to check out Spivak.
- For Complex Analysis, Ahlfors is the usual recommendation.
- For Commutative Algebra (Abstract Algebra in the image posted previously), Atiyah-MacDonald is pretty good and exercise heavy.
- For Functional Analysis, check out Alt's Linear Functional Analysis (Brezis's book is also good).
- For Multivariable and Vector Calculus I used Marsden-Tromba, it was fine enough.
- For Algebraic Topology is difficult to make good recommendations, because it depends very heavily on what you want to study more specifically; just read Hatcher, and once you start noticing it's shit, go check out Fomenko-Fuchs.
- For Analysis on Manifolds, there's Jost (this book is tough as fuck).
- For Measure Theory, I remember that Folland's Real Analysis was quite fine; I've also heard good things of Cohn's Measure Theory.
- It's not in the image, but I also want to add that Lee's Riemannian Geometry book is quite a nice extension of his Smooth Manifolds book.
Overall, don't worry too much about which book to follow. Pick one, stick to it, and only once you encounter problems do you start checking others. Also, don't pay much attention to the flowchart's precise order. I agree with the choices made in
>>11545196.
