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I. Basic math. II. Pricing and Hedging. 1. Basics of derivative pricing I. 2. Change of numeraire. A. Definition of the change of numeraire. B. Useful calculation. C. Transformation of SDE based on change of measure results. D. Transformation of SDE in a two asset situation. E. Transformation of SDE based on term matching. F. Invariant representation for the drift modification. G. Transformation of SDE based on delta hedging. H. Example. Change of numeraire in the Black-Scholes economy. I. Other ways to look at the change of numeraire. 3. Basics of derivative pricing II. 4. Market model. 5. Currency Exchange. 6. Credit risk. 7. Incomplete markets. III. Explicit techniques. IV. Data Analysis. V. Implementation tools. VI. Basic Math II. VII. Implementation tools II. Bibliography.

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