77904 - 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

Readings/Bibliography

Slides of the lectures
Reviews and web sites provided during the lectures

Teaching methods

Lectures and practical sessions

Assessment methods

Written test

Exercises will assess the ability of the students in tackling basic vector and matrix maniulation, basic calculus, statistical and probabilistic problems.

Teaching tools

Office hours

See the website of Pier Luigi Martelli