How may one start?

Some students and coleagues are always asking about the place to start studying some topic! On the page bellow, I provide the best references I know for this purpose!

Mathematics

Real Analysis

Análise Real 1 and 2 by Ellon Lages Lima

Analysis in Euclidean Space by Kenneth Hoffman

Principles of Mathematical Analysis by Walter Rudin

Functional Analysis

Introductory Functional Analysis with Applications by Erwin Kreyszig (see my opinion about this book in Amazon)

Applied Functional Analysis by D.H. Griffel

Introductory Real Analysis by A. N. Kolmogorov and S. V. Fomin

Measury theory

The Elements of Integration by Robert G. Bartle

Optimization

Optimization by Vector Space Methods by David G. Luenberger

Convex Optimization by Stephen Boyd and Lieven Vandenberghe (this book is free-downloadable at the author's home-page)

Dynamic Programming and Reinforcement Learning

Dynamic Programming and Optimal Control by Dimitri P. Bertsekas

Markov Decision Processes: Discrete Stochastic Dynamic Programming by Martin L. Puterman

Reinforcement Learning: An Introduction by Richard S. Sutton and Andrew G. Barto

Calculus of Variations

Introduction to the Calculus of Variations by Hans Sagan

Numerical methods

Analysis of numerical methods by E. Isaacson. and H. B. Keller

Numerical methods in economics by K. L. Judd (This is a good guide for finding applications of numerical methods in Economics, but it is not a good place to start. It is just here because its popularity and the fact that everybody asks about this book)

Economics

Microeconomics

Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green

Econometrics

Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J. Bierens

Time series

Time Series Analysis by James Douglas Hamilton

Applied Econometric Times Series by Walter Enders

Panel data

Analysis of Panel Data by Cheng Hsiao

Finance

Principles of Financial Economics by Stephen F. LeRoy, Jan Werner, and Stephen A. Ross (This book is an amazing introduction to Financial Economics and Asset Pricing). See my review about this book in Amazon)

Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange by Keith Cuthbertson and Dirk Nitzsche (This is for Financial Econometrics)

The Econometrics of Financial Markets by John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, and Andrew Y. Lo (This is also for Financial Econometrics.)

Theoretical Foundations of Corporate Finance. by Joao Amaro de Matos (This is clearly for corporate finance)

The Theory of Corporate Finance by Jean Tirole (This is also for corporate finance)

Complex systems

Self-Organized Criticality

Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems by Professor Henrik Jeldtoft Jensen

Complexity And Criticality by Kim Christensen and Nicholas R. Moloney

Chaos

An Introduction to Chaotic Dynamical Systems by Robert Devaney and Robert L. Devaney (The mathematics of chaotic systems!)

Thermodynamics of Chaotic Systems: An Introduction by Christian Beck and Friedrich Schögl (Characterizing chaos!)

Caos - Uma Introduçao Nelson Fiedler-Ferrara and Carmen P. Cintra (A very nice Brazilian book dealing with both with mathematics and characterization of complex systems!)

Fractals

Fractals by Jens Feder

Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer

Última atualização (Dom, 29 de Novembro de 2009 21:17)