B5806 - ELEMENTS OF COMPUTATIONAL BIOLOGY

Learning outcomes

At the end of the course the student will acquire the basic knowledge of computational methods necessary for analysing biological data in the omic era.

Course contents

Basics concepts of Linear Algebra

-) Vectors and matrices: basic definitions and operations.

-) Linear transformations in vector spaces.

-) Inverse matrix, Invertibility, Determinants.

-) Eigenvalues and Eigenvectors: applications to Principal Component Analysis.

Basics concepts of Calculus

-) Functions in R. Inverse functions.

-) Derivatives. Maximization and minimization,

-) Integrals.

-) Functions in R2.

-) Partial derivatives. Gradient. Maximization and minimization.

-) Constrained Maximization and Minimization: Lagrange's multipliers.

Basic concept of Probability and Statistics

-) Joint probability, conditional probability, Bayes' theorem.

-) Discrete probability distributions: Binomial, Poisson

-) Continuous probability distributions: Normal, Boltzmann, Student, Chi-square, Gumbel (Extreme value)

-) Mean, median, mode, variance.

-) p-value and E-value

-) Tests for statistical significance: Student, Fisher, Chi-square

All topics will be treated in the context of the applications in Computational biology.

Readings/Bibliography

Reviews and usefule onl line resources will be provided during the lectures and will be made available on Virtuale

Teaching methods

Lectures and exercises

Assessment methods

Written test aiming at verifying the ability of the student to apply the learned methods to simple problemes. The test consists of 5-6 problems to be solved in 90 minutes.

Teaching tools

Lectures and exercise sessions

Office hours

See the website of Pier Luigi Martelli