Program and Organisation - Crest

Mathias André Maxime Tô

M1 EPP 2011 Maths Summer Camp

Program and Organisation Master Economics and Public Policies, Maths Summer Camp

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Formalisation and Basic Tools Maxime Tô : 1 Session (S1), Friday 1, 8 am to 10 am 1. Sets, Notations 2. Demonstrations : Implications, Equivalences, Induction See Simon and Blume (1994) (Appendix 1), Wooldridge (2008) (Appendix A).

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Real Analysis : One Variable Function Maxime Tô : 1 Session (S2), Friday 1, 10 :15 am to 12 :15 pm Maxime Tô : 2 Sessions (S3, S4), Friday 1, 2 :45 pm to 7 pm 1. Limit, continuity, Derivation, Graphics : Studying a Function 2. Convexity, Concavity 3. Usual Functions See Simon and Blume (1994) (Chapters 2, 3, 27), Mas-Colell et al. (1995).

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Real Analysis : Complements Mathias André : 2 Sessions (S5, S6), Monday 4, 10 :15 am to 2 :30 pm 1. Composition, Derivation 2. Bijection 3. Rolle’s Theorem, Mean-value Theorem 4. Taylor’s expansions See Simon and Blume (1994) (Chapters 4, 5, 30), Mas-Colell et al. (1995).

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Integration Mathias André : 2 Sessions (S7, S8), Monday 4, 5 pm to 9 :15 pm See Simon and Blume (1994) (Appendix 4).

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Vectorial Analysis Mathias André : 2 Sessions (S9, S10), Tuesday 5, 5 pm to 9 :15 pm 1. Euclidean Spaces, Scalar product 2. Generalization of Real Tools 3. 2 Variables functions : Gradient, Derivation 4. Theorem : Envelope, Fixed Point, Implicit Function 5. Euler’s equation and homogeneous function See Simon and Blume (1994) (Chapters 6, 8, 9, 22, 23, 25, 26), Mas-Colell et al. (1995). 1

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Matrix Algebra Maxime Tô : 2 Sessions (S11, S12), Wednesday 6, 8 am to 12 :15 pm Maxime Tô : 2 Sessions (S14), Friday 8, 8 am to 12 :15 pm 1. Linear Systems 2. Matrix 3. Projections

See Simon and Blume (1994) (Chapters 10 to 16), Wooldridge (2008) (Appendix D), Greene (2007), Barro and i Martin (1999), Davidson and MacKinnon (2004). McMahon (2006) gives a complete approach.

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Basic Optimization and Constrained Optimization Maxime Tô : 1 Session (S15), Tuesday 12, 10 :15 am to 12 :15 pm Maxime Tô : 1,5 Sessions (S16,S21a), Tuesday 12, 2 :45 pm to 6 pm 1. Lagrangian 2. First and Second Orders Conditions

See Simon and Blume (1994) (Chapters 21, 24, 25, 30), Barro and i Martin (1999), Mas-Colell et al. (1995).

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Introduction to Probabilities (Or Exercices’ Solutions) Mathias André : 1 Session (S17), September 6, 7 :15 pm to 9 :15 pm Mathias André : 1 Session (S18), September 7, 7 :15 pm to 9 :15 pm Mathias André : 2,5 Sessions (S19, S20, S21b), September 9, 8 am to 1 pm 1. Random Variables 2. Independence 3. Distributions 4. Conditional Expectations 5. Asymptotics

See Simon and Blume (1994) (Appendix 5), Wooldridge (2008) (Appendix B), Greene (2007), Cameron and Trivedi (2005), Davidson and MacKinnon (2004).

Références Barro, R. J. and X. S. i Martin (1999) : Economic Growth, MIT Press. Cameron, A. C. and P. K. Trivedi (2005) : Microeconometrics : Methods and Applications, Cambridge University Press. Davidson, R. and J. G. MacKinnon (2004) : Econometric Theory and Methods, Oxford University Press. Greene, W. (2007) : Econometric Analysis : 6th Ed., Pearson Education. Mas-Colell, A., M. D. Whinston, and J. R. Green (1995) : Microeconomic Theory, Oxford University Press. McMahon, D. (2006) : Linear Algebra Demystified, McGraw-Hill. Simon, C. P. and L. Blume (1994) : Mathematics for Economists, W. W. Norton & Company.

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Sydsaeter, K. and P. Hammond (2008) : Essential Mathematics for Economic Analysis, Prentice Hall. Sydsaeter, K., A. Strom, and P. Berck (2005) : Economists’ Mathematical Manual, Springer. Wasserman, L. (2005) : All of Statistics, Springer. Wooldridge, J. M. (2002) : Econometric Analysis of Cross Section and Panel Data, MIT Press. ——— (2008) : Introductory Econometrics : A Modern Approach, South-Western College Pub.

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