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 I. Basic math.
 1 Conditional probability.
 2 Normal distribution.
 A. Definition of normal variable.
 B. Linear transformation of random variables.
 C. Multivariate normal distribution. Choleski decomposition.
 D. Calculus of normal variables.
 E. Central limit theorem (CLT).
 3 Brownian motion.
 4 Poisson process.
 5 Ito integral.
 6 Ito calculus.
 7 Change of measure.
 8 Girsanov's theorem.
 9 Forward Kolmogorov's equation.
 10 Backward Kolmogorov's equation.
 11 Optimal control, Bellman equation, Dynamic programming.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Normal distribution.

ormal distribution arises in the central limit theorem. By the nature of its origin the set of normal variables is closed with respect to multivariate linear transformations. Standard independent normal variables act like a normal basis. Mathematical expectation acts like a scalar product.

 A. Definition of normal variable.
 B. Linear transformation of random variables.
 C. Multivariate normal distribution. Choleski decomposition.
 D. Calculus of normal variables.
 E. Central limit theorem (CLT).
 Notation. Index. Contents.