Advanced¶
Graduate Books¶
Logic
- Introduction to Mathematical Logic and Type Theory - Andrews `[pdf] <>`__
- Symbolic Logic - Copi `[pdf] <>`__
- A Mathematical Introduction to Logic - Enderton `[pdf] <>`__
- Logic for Mathematicians - Hamiltion `[pdf] <>`__
- Introduction to Mathematical Logic - Mendelson `[pdf] <>`__
- Mathematical Logic - Shoenfield `[pdf] <>`__
Set Theory
- Set Theory - Jech `[pdf] <>`__
- Set Theory - Kunen `[pdf] <>`__
Graph Theory
- Modern Graph Theory - Bollobas `[pdf] <>`__
Functional Analysis
- Functional Analysis - Riesz F. and Sz.-Nagy B `[pdf] <>`__
- Functional Analysis - Yoshida `[pdf] <>`__
Real and Complex Analysis
- Real and Complex Analysis - Baby Rudin `[pdf] <>`__
- Complex Analysis - Ahlfors `[pdf] <>`__
Fourier and Harmonic Analysis
- Harmonic Analysis - Stein `[pdf] <>`__
Algebra
- Topics in Algebra - Herstein `[pdf] <>`__
- Algebra - Hungerford `[pdf] <>`__
- Lectures in Abstract Algebra I, II, III - Jacobson `[pdf] <>`__
- Basic Algebra II - Jacobson `[pdf] <>`__
- Algebra - Serge Lang `[pdf] <>`__
Groups and Lie Algebra
- An Introduction to the Theory of Groups - Rotman `[pdf] <>`__
Rings and Galois Theory
- Galois Theory - Stewart `[pdf] <>`__
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
- An Introductory to the Theory of Numbers - Hardy G.H. and Wright E.M. `[pdf] <>`__
- Number Theory - Hasse `[pdf] <>`__
- A Course in Arithmetic - Serre `[pdf] <>`__
Algebraic Number Theory
- Algebraic Number Theory - Neukirch `[pdf] <>`__
Class Field Theory
- Basic Number Theory - Weil `[pdf] <>`__
Analytical Number Theory
- A Primer of Analytic Number Theory: From Pythagoras to Riemann - Stopple `[pdf] <>`__
Partial Differential Equations
- Partial Differential Equations - Evans `[pdf] <>`__
Mathematical Physics
- Feynman Lectures On Physics - Feynman `[pdf] <>`__
Probablity Measure Theory
- Probability and Measure - Billingsley `[pdf] <>`__
- A Course in Probability Theory - Chung `[pdf] <>`__
- An Introduction to Probability Theory and Its Applications Vol. 2 - Feller `[pdf] <>`__
- Foundations of Modern Probability - Kallenberg `[pdf] <>`__
- Probability Theory I, II - Loève `[pdf] <>`__
- Probability - Shiryaev `[pdf] <>`__
Stochastic Processes
- Stochastic Processes - Doob `[pdf] <>`__
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
- Categorical Data Analysis - Agresti `[pdf] <>`__
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] <>`__
Calculus¶
Abstract Algebra¶
Combined¶
Other Topics to cover¶
Analysis (real/complex/functional)
Complex Variables
Statistics (frequentist v. bayesian)
Probablity theory
Optimization
Information theory
Other Links¶
References
| [1] | How to become a pure Mathematician - http://hbpms.blogspot.com/ |
| [2] | Data Science Masters - http://datasciencemasters.org/ |
| [3] | https://honglangwang.wordpress.com/2014/12/30/machine-learning-books-suggested-by-michael-i-jordan-from-berkeley/ |