Advanced

Books

  • Introductory Real Analysis - Kolmogorov A.N. and Fomin S.V. [pdf]
  • Principles of Mathematical Analysis - Baby Rudin [pdf]
  • Algebra - Artin [pdf]
  • Basic Algebra I - Jacobson [pdf]

Graduate Books

Logic

Set Theory

Graph Theory

Functional Analysis

Real and Complex Analysis

Fourier and Harmonic Analysis

Algebra

Groups and Lie Algebra

  • An Introduction to the Theory of Groups - Rotman `[pdf] <>`__

Rings and Galois Theory

Commutative Algebra

  • Introduction to Commutative Algebra - Atiyah M.F. and MacDonald I.G. `[pdf] <>`__

Homological Algebra

  • Homological Algebra - Cartan H. and Eilenberg S. `[pdf] <>`__
  • Categories for the Working Mathematician - Mac Lane S. `[pdf] <>`__

Number Theory

Algebraic Number Theory

Class Field Theory

Analytical Number Theory

  • A Primer of Analytic Number Theory: From Pythagoras to Riemann - Stopple `[pdf] <>`__

Partial Differential Equations

Mathematical Physics

Probablity Measure Theory

Stochastic Processes

Statistics(Inference)

  • Statistical Inference - Casella G. and Berger R.L. `[pdf] <>`__
  • Kendall’s Advanced Theory of Statistics, Volume 1: Distribution Theory - Kendall M. Stuart A. and Ord J.K. `[pdf] <>`__
  • Theory of Point Estimation - Lehmann E.L. and Casella G. `[pdf] <>`__
  • Testing Statistical Hypotheses - Lehmann E.L. and Romano J.P. `[pdf] <>`__

Statistic Models and Regression

  • Kendall’s Advanced Theory of Statistics: Volume 2A -Classical Inference and and the Linear Model - Kendall M. Stuart A., Ord J.K. and Arnold S. `[pdf] <>`__
  • Applied Linear Statistical Models - Kutner M.K., Nachtsheim C.J., Neter J. and Li W. `[pdf] <>`__

Multivariate Analysis

  • An Introduction to Mulrivariate Statistical Analysis - Anderson T.W. `[pdf] <>`__
  • Applied Multivariate Statistical Analysis - Johnson R.A. and Wichern D.W. `[pdf] <>`__

Bayesian Statistics

  • Bayesian Theory - Bernardo J.M. and Smith A.F.M. `[pdf] <>`__
  • Bayesian Data Analysis - Gelman A., Carlin J.B., Stern H.S. and Rubin D.B. `[pdf] <>`__
  • Kendall’s Advanced Theory of Statistics: Volume 2B: Bayesian Inference - Kendall M. and O’Hagan A. `[pdf] <>`__

Categorical Data Analysis

Statistics Methods in Epidemiology)

  • Epidemiology: Study Design and Data Analysis - Woodward `[pdf] <>`__
  • Statistics for Epidemiology - Jewell `[pdf] <>`__

Longitudinal Data Analysis

  • Analysis of Longitudinal Data - Diggle P., Heagerty P., Liang K.-Y. and Zeger S. `[pdf] <>`__
  • Applied Longitudinal Analysis - Fitzmaurice G.M., Laird N.M. and Ware J.H. `[pdf] <>`__

Survival Analysis

  • Survival Analysis: A Self-Learning Text - Kleinbaum D.G. and Klein M `[pdf] <>`__

Other Topics to cover

Analysis (real/complex/functional)

Complex Variables

Statistics (frequentist v. bayesian)

Probablity theory

Optimization

Information theory