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.

## Definition of normal variable.

he normal random variable, denoted , is described by the distribution density the and are real numbers.

The notation is generally reserved for

 (Standard normal variable)
is called "the standard normal variable".

 Notation. Index. Contents.