Mathematics Informatics and Biostatistics
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Teaching methods
- Contacts/Info
The following basic knowledge is necessary to fully understand the Mathematics segment: 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. All these topics are however explained during the course. Before attending the Biostatistics Segment, the Mathematics segment needs to be covered.
Segment of Mathematics: at the end of the course a written exam must be passed, aimed at evaluating whether the student has a critical knowledge of the mathematical issues presented and can apply, in different situations, the appropriate mathematical methods, models and tools. According to the grade obtained, the following rules apply:
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 to improve his/her grade.
Segment of Biostatistics: at the end of the module, the student will undergo a written examination. S/he will be presented with three numerical exercises aimed at verifying the knowledge of the logic and methodological tools required for a correct evaluation of experimental data. The allotted time for the exam is 2.5 hours and the exam will be considered passed equal or over the 18/30 mark. During the exam, the use of pocket calculators is allowed.
The final grade will be the weighted average of the marks obtained for both segments.
The Course of Mathematics, Computer Science and Statistics is structured in two segments, over two consecutive semesters. The first segment (Mathematics and Computer Science) teaches the necessary basis for the analytic comprehension of scientific phenomena in Biology through the acquisition of mathematical methods and how to acquire an essential, rigorous language. In particular, students will learn the basis of linear algebra and differential and integral calculus, which are the starting points for the analysis of biological events. In the second segment (Principles of Statistics and Biostatistics), students will learn the theoretical basis of inferential statistics and the statistical tests commonly used in Biology. Particular emphasis will be given to how to correctly apply the tests.
The main goal of this course is to develop the students’ ability to critically apply the mathematical concepts exposed in the course and to stimulate their ability to utilize mathematical models and tools in a variety of cases. The basis of linear algebra and differential and integral calculus learned in the first segment will provide students with the quantitative tools needed to develop and interpret indexes for the analysis of data and characters obtained from biological and clinical experiments. In the second segment the same objectives will be analyzed from a statistical point of view; the laws of probability, how to perform correct sampling and the construction of a formal hypothesis to be tested will be learnt in order to improve the ability of analyzing experimental data, by means of the most common statistical tests. At the end of the course, therefore, students will possess the necessary knowledge to correctly analyze and interpret experimental data in Biology.
SEGMENT OF MATHEMATICS AND COMPUTER SCIENCE (9 CFU):
Elements of linear algebra – 1.5 CFU
• Vectors and matrices with corresponding operations.
• Determinant.
• Inverse matrix.
• Linear systems.
Real functions of one variable - 5 CFU
• 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
• Software utilization (derivative calculus, plotting a graph).
Integral calculus – 2.5 CFU
• The indefinite integral. The Riemann (definite) integral and related theorems.
• Some techniques of integration.
SEGMENT OF PRINCIPLES OF STATISTICS AND BIOSTATISTICS (3 CFU):
Introduction – 0.5 CFU
- Populations and samples. Basics of the laws of probability. Random variables.
- Frequency distributions. The meaning of the statistical test.
- Power and protection of the test, type I and type II errors.
- Parameter estimation; the standard error of the mean; the confidence interval.
Cathegorical variables – 0.5 CFU
- The χ2 test for comparing two proportions. Contingency tables.
Quantitative variables – 2 CFU
- Comparison between two or more means. Student’s t and one-way
Analysis of Variance (ANOVA).
- Two-ways ANOVA.
- Simple regression analysis.
Please refer to section Contenuti
– Segment of Mathematics: the teacher will post the recommended material on the e-learning site.
- Segment of Biostatistics: the teacher will provide students with an updated list of useful textbooks. Class attendance is strongly recommended.
For both segments, traditional classes will be held. In the first segment, exercitations will be held for a total of 3 cfu. In the second segment, some exercises will be taught under the teacher’s guidance.
Teachers will answer questions regarding the topics discussed in the course, following an e-mail. Students are kindly required not to ask bureaucratic/administrative question, if not absolutely necessary and urgent.