How to Become a Pure Mathematician (Or Statistician)

Summary

Table of Contents Stage 1 Stage 2 Stage 3 Stage 4 Foundation, Logic, Set Theory, etc, Graph Theory, Combinatorics, Cryptography, Coding and Information Theory. Analysis Functional Analysis, Measure Theory, Hilbert Spaces, Real and Complex Analysis, Fourier and Harmonic Analysis. Algebra Advanced Linear Algebra, Groups and Lie Algebras, Rings, Fields and Galois Theory, Modules and Representation Theory, Commutative Algebra, Homological Algebra and Category. Number Theory Algebraic NT, Class Field Theory, Analytic NT, Riemann Zeta Function and the Hypothesis, Modular Forms, Elliptic Curves, etc. Geometry Algebraic Geometry, Differential Geometry, Riemannian Geometry, Fractals. Topology Geometric Topology, Algebraic Topology, K-theory, Differential Topology. Statistics (optional) Statistical Models and Regression, Multivariate Analysis, Bayesian Statistics, Simulation and the Monte Carlo Method, Nonparametric Statistics, Categorical Data Analysis, Data Mining, Time Series. Biostatistics (optional) Statistical Methods in Epidemiology, Design and Analysis of Clinical Trials, Longitudinal Data Analysis, Survival Analysis. Stage 5