Mathematics and foundations of computer science and statistics
- Overview
- Assessment methods
- Learning objectives
- Contents
- Bibliography
- Teaching methods
- Contacts/Info
Basic knowledge: Natural, integer, rational and real numbers. Basic elements of logic and set theory. Elementary algebra. Powers, logarithmic and exponential functions. Equations and inequalities (polynomial, fractional, irrational, logarithmic and exponential). Systems of equations and inequalities. Plane analytical geometry. Basic notions of trigonometry.
Written exam with the following rules:
Mark less or equal to 11/30: exam failed;
Mark between 12/30 and 17/30: students can attend an oral exam to achieve a pass;
Mark equal or higher than 18/30: exam passed. The student has also the possibility to attend an optional oral exam.
The purpose of the course is to teach the necessary basis for the analytic comprehension of the biological scientific phenomenoms through the acquisition of Mathematical and statistical methods.
At the end of the course the student will be able to correctly understand and interpret the biological datas.
Elements of linear algebra. Vectors and matrices with corresponding operations. Determinant. Inverse matrix.
Real functions of one variable
– Introductory concepts: Domain. Maximum, minimum, upper and lower bounds. Bounded functions, monotonic functions, composition of functions, inverse function. Convex functions.
– Limits and continuity: Limits and related theorems. Operations on limits and indecision forms. Continuity of functions and related theorems. Asymptotes.
– Differential calculus: Incremental ratio and derivative. Differentiable functions. Rules of differentiation. Derivative of composite and inverse functions. Fundamental theorems of differential calculus. Taylor formula. Global and local maxima and minima, points of inflexion. Necessary and/or sufficient conditions for the existence of maxima and minima. Concavity, convexity.
– Integral Calculus: The indefinite integral. The Riemann (definite) integral and related theorems. Some techniques of integration.
Statistical methodology and scientific research. The statistical analysis process: gathering and describing data. Frequency distributions. Graphical representation.
Univariate analysis. Location indices: mode, median and algebraic means. Spread indices: indices of dissimilarity (mutability/heterogeneity) and variance.
Elements of probability theory. Definition of probability and basic theorems. Univariate probability models (normal).
Lessons up-loaded on E-Learning Platform
Face to face lessons
Student appointments: by e-mail request
maurizio.dettoni@uninsubria.it