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"Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?" --- Paul R. Halmos
For those who are also interested in stochastic systems, optimization, and applied finance, here are some textbooks that I highly recommend:
Mathematical Analysis:
W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976.
Real Analysis/Functional Analysis:
Folland, Real Analysis: Modern Techniques and Their Applications, Wiley, 2007.
W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987.
D. G. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons, 1997.
Probability Theory:
R Durrett, Probability: Theory and Examples, Cambridge University Press, 2010.
P. Billingsley, Probability and Measure, Wiley, 2012.
R. Vershynin, High-Dimensional Probability, Cambridge, 2018.
Mathematical Statistics & Information Theory
G. Casella and R. L. Berger, Statistical Inference, Cengage Learning, 2001.
Hogg, McKean, and Craig, Introduction to Mathematical Statistics, Pearson, 2020.
T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, 2006.
Optimization and Convex Analysis
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004
A. Beck, Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB, SIAM, 2014.
A. Beck, First-Order Methods in Optimization, SIAM, 2017.
R. T. Rockafellar, Convex Analysis, Princeton University Press, 1970.
R. T. Rockafellar and R.J.B. Wets, Variational Analysis, Springer Science & Business Media, 2009.
A. Shapiro, D. Dentcheva, and A. Ruszcynski, Lectures on Stochastic Programming: Modeling and Theory, SIAM, 2009.
Financial Engineering & Applied Finance
D. G. Luenberger, Investment Science, Oxford University Press, 2013.
J. C. Hull, Options, Futures, and Other Derivatives, Pearson, 2014.
J. A. Primbs, A Factor Model Approach to Derivative Pricing, 2016.
J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, 2004.
Time Series and Its Applications
R. S. Tsay, Analysis of Financial Time Series, 2005.
G. E. P. Box, G. M. Jenkins, G. C. Reinsel, and G. M. Ljung, Time Series Analysis: Forecasting and Control, 2015.
Mathematics for Economics and Finance
K. Sydsater, P. Hammond, A. Seierstad, and A. Strom, Further Mathematics for Economic Analysis, Prentice-Hall, 2008.
J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Massachusetts Institute of Technology, 2004
Financial Mathematics & Stochastic Calculus
G. Campolieti and R. N. Makarov, Financial Mathematics: A Comprehensive Treatment, CRC Press, 2014.
S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer Science & Business Media, 2004.
S. Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer Science & Business Media, 2004.
I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1991.
B. Oksendal, Stochastic Differential Equations: Introduction with Applications, Springer Science & Business Media, 2013.
Control Theory
J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design, Nob Hill, 2009.
B. Barmish, New Tools for Robustness of Linear Systems, Macmillan Coll Div, 1993.
Control Cartoons by S. M. Joshi.
Some Relevant Journals/Conferences to Follow
Control and Information Theory
IEEE Conferences on Decision and Control (CDC)
American Control Conference (ACC)
IFAC World Congress
Operational Research and Management Science
Finance:
Financial Engineering:
Statistics
Econometrics & Economics
Machine Learning & Artificial Intelligence
Conference on Neural Information Processing Systems (NeurIPS)
International Conference on Machine Learning (ICML)
Conference on Artificial Intelligence (AAAI)
Conference on Learning Theory (COLT)
Others (Preprints Platforms)
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