This lecture is based on the following papers: 1. A. Majda and B. Gershgorin, 2010: Quantifying Uncertainty in Climate Change Science Through Empirical Information Theory, PNAS in press 2. A. Majda, R. Abramov, B. Gershgorin, "High Skill in Low Frequency Climate Response through Fluctuation Dissipation Theorems Despite Structural Instability," PNAS, January 2010, Vol. 107, no. 2, pp 581 - 586. 3. B. Gershgorin, A. Majda, "Filtering A Nonlinear Slow-Fast System with Strong Fast Forcing," Comm. Math. Sci., March 2010, Vol. 8, Issue 1, pp. 67-92 4. A. Majda, B. Gershgorin, Y. Yuan, " Low Frequency Response and Fluctuation-Dissipation Theorems: Theory and Practice," JAS, available electronically, April 2010, Vol. 67, pp. 1186-1201. All papers except the first one can be found on Majda's faculty website.