/sci/ - Science & Math

Sophomore here. I want to focus on something related to topology next year, but I don't know exactly what. I thought I'd go for K-theory, since I'm arleady kinda good with basic algebraic topology, although homological algebra is a viscious bitch when it is detached from topology.

Anyways, if you were a young student aiming to get to a good grade school eventually and knows some very basic topology, what would you go for?

Year 1
Stewart - Calculus: Early Transcedentals
Freund - Modern Elementary Statistics
Giancoli - Physics for Scientists & Engineers with Modern Physics

Year 2
Axler - Linear Algebra Done Right
Poole - Linear Algebra: A Modern Introduction
Hungerford - Abstract Algebra: An Introduction
Griffiths - Electricity and Magnetism
Davidson/Donsig - Real Analysis and Applications
Boyce/DiPrima - Elementary Differential Equations and Boundary Value Problems
Freund - Mathematical Statistics with Applications

Year 3
Armstrong - Groups and Symmetry
Cioaba/Murty - First course in Graph Theory and Combinatorics
Saff/Snider - Fundamentals of Complex Analysis with Applications to Engineering, Science
Kolmogorov/Fomin - Introductory Real Analysis
James E. Humphreys - Reflection groups and Coxeter groups
Milnor - Morse Theory
Rotman - Galois Theory
Koblitz - A Course in Number Theory and Cryptography

Year 4
Alan Baker - A Concise Introduction to the Theory of Numbers
O'Neill - Elementary Differential Geometry
Dummit/Foote - Abstract Algebra
Rudin - Real And Complex Analysis
Vinberg - Linear Representations of Groups
Fulton/Harris - Representation Theory
Atiyah/Macdonald - Commutative Algebra
Eisenbud - Commutative Algebra
Matsumura - Commutative Ring Theory
Arnold, Gusein-Zade, Varchenko - Singularities of Differentiable Maps, Volumes 1/2