08234 - Elements of Mathematics

Learning outcomes

MATHEMATICS and STATISTICS - 8CFU

At the end of the course the student knows the technical mathematical tools and their use, as well as the main methods and basic tools for the quantitative study of collective phenomena. The student is then able to set up and solve problems and to assimilate new concepts from the experience and previous knowledge, to produce and process statistical data independently, developing the ability of interpretation and critical assessment of statistical information.

Course contents

Matematics

The Mathematics module is part of the STAAF Degree Course and the EMSA Degree Course. - Presentation of the course: contents, study materials, exercises, exams (0.5h) - Review of algebra: monomials, polynomials, algebraic fractions. (2,5h). - Elements of combinatorics: factorial, permutations, arrangements, binomial coefficients, combinations (3h) - Powers with integer and rational exponent. Study of simple algebraic equations and inequalities. Systems of equations and inequalities (4h). - Cartesian plane. Functions: definition; graphic; linear function; domain and codomain; reverse function; compound function; increasing/decreasing function; even/odd function (5h). - Analytical geometry: straight line, parabola, circle, ellipse, hyperbola; functions studied and represented by bringing them back to the previous curves (4h). - Exponential and logarithmic functions. Integer or fractional rational equations and inequalities, of higher degree than the first, irrational, exponential, logarithmic (4h). - Goniometry-trigonometry: measurement of an angle in radians, trigonometric functions and related properties, graphs of trigonometric functions, trigonometric equations and inequalities; relationships between measure of sides and angles of triangles (4h). - Limits: definition, geometric meaning, asymptotes, continuity, calculation techniques (5h). - First derivative. Definition and geometric meaning. Calculation rules (3h). - Derivability; growth; extremants; concave, flexed (5h). - Study of functions of one variable with analytic and geometric methods (5h). - Integration: definition; geometric meaning; calculation rules (3h). - Summary exercises on the study of functions of one variable (4h).

The Basic of Statistics teaching unit is part of the STAAF Degree Course but not of the EMSA Degree Course.

Descriptive statistics

One-dimensional variables: Absolute frequencies, relative frequencies, cumulative frequencies. Location measures. Variability measures. Graphical representation of data. Two-dimensional variables: Bivariate frequency distributions. Marginal distributions, conditional distributions. Relationships between two variables: dependence, linear regression, linear correlation

Readings/Bibliography

Teacher booklet available on teacher website.

Possible in-depth study reference books:

- Statistica, Murray R. Spiegel; Ed. Mc Graw Hill

- Bergamini, Trifone, Barozzi: Moduli blu di Matematica; Ed. Zanichelli

- Thomas' Calculus; Ed. Pearson

-Mecatti, F. (2015), Statistica di base. Come, quando e perché. (II edizione)

Teaching methods

Room lessons and practice on PCs.

Assessment methods

Final examination made by a multiple choice test (https://eol.unibo.it).

Subscription to examination list is made by Almaesami services (https://almaesami.unibo.it).

Considering the Statistics test, the student will be asked ten questions regarding the topics covered during the course.

Teaching tools

Blackboard; video projector; PC; Internet access; computer lab; software [particularly Excel (Microsoft)].

Office hours

See the website of Silvia Foschi