The course is divided into four sections:
-Module on Algebra and Probability (3 CFC)
-Module on Elements of Mathematical Analysis (Functions, Graphs, Relations) (3 CFC)
-Module on Euclidean Geometry, Analytic geometry, Trigonometry (3CFC)
-Module on Logics and Reasoning(3 CFC)
Module on Algebra and Probability (3 CFC)
Learning outcomes:
Students will be able to manage numerical and algebraic expressions, solve equalities and
inequalities of the first and second order and problems, solve both combinatronics and probability related problems.
Prerequisites
Numerical and algebraic calculus
Teaching methods
•Lectures are carried out using a blackboard.
•Exercises are carried out in the classroom: students will practice the exercises, even in groups, under the supervision of the lecturer.
•Interaction with the teacher is done through interviews (on fixed office hours or by
appointment) and by e-mail.
Syllabus
1.Powers, radicals, logarithms, exponentials and their properties.
2.Linear equalities, linear inequalities and linear systems.
3.Second order equalities and inequalities.
4.Ruffini's rule and resolution of higher order equalities and inequalities.
5.Combinatorial calculus and probability
Bibliography
[1] Israel M. Gelfand, Alexander Shen-Algebra (1993)
[2] Larson R., Boswell L., Kanold T., Stiff L. -
Algebra 1_ Concepts and Skills
[3] Zanichelli: Test your skills, online resources: [a],[b]
[4] High School Math Contests: online resources.
[5] Sheldon Ross, A First Course in Probability, A (5th edition)
–Prentice Hall college (1997)
Assessment methods
Written test consisting of a few problems to be solved in three hours.
Module on Euclidean Geometry, Analytic geometry, Trigonometry(3 CFC)
Learning outcomes:
The students will learn the principal concepts of euclidean
geometry in the plane and of trigonometry,
and will be able to solve geometry problems in the plane and in the space using Euclidean geometry
and analytic geometric methods, to calculate lengths, areas and volumes of geometric sets.
Prerequisites
Numerical and algebraic calculus. Basic concepts of Eulidean geometry (points, lines, line
segments, angles, measures of length, area and volume, measures of angles).
Teaching methods
•Lectures are carried out using a blackboard.
•Exercises are carried out in the classroom: students will practice the exercises, even in groups, under the
supervision of the lecturer.
•Interaction with the lecturer is done through meetings (during fixed office hours or by
appointment) and by e-mail.
Syllabus
1.Principal plane figures
and their elementary properties. Euclidean geometry in the plane.
2.Vectors and operations with vectors.
3.Analytic geometry in the plane and in the space.
4.Trigonometric functions and relations.
Bibliography
[1] Online mathematics school http://onlinemsc
hool.com/math/library/vector/
[2] Online mathematics school http://onlinemschool.com/math/library/analytic_geometry/
.
[3] Csaba Vincze, Laszlo Kozma.
College Geometry. http://www.freebookcentre.net/maths
-books -download/College-Geometry.html
Assessment methods
Written test consisting of a few problems to be solved in three hours.
Module on Elements of Mathematical Analysis (Functions, Graphs, Relations) (3CFC)
Learning outcomes:
The students will learn the principal concepts of sets, functions and relations, the elementary functions of
real variable and their graphs. Students will also learn to solve problems related to the study of simple
functions of real variable and draw graphs of these functions.
Prerequisites
Numerical and algebraic calculus.
Teaching methods
•Lectures are carried out using a blackboard.
•Exercises are carried out in the classroom: students will practice the exercises, even in groups, under the supervision of the lecturer.
•Interaction with the lecturer done through meetings (on fixed office hours or by
appointment) and by e-mail.
Syllabus
1.Basic language of sets, functions and relations.
2.Elementary functions of a real variable and their properties.
3.Study of the graphs of the simple functions of a real variable. Resolving problems involving the functions of a
real variable.
Bibliography
[1] M. Bramanti, C.D. Pagani, S. Salsa. Analisi Matematica I, Zanichelli, 2008.
[2] N.S. Piskunov.
Differential and Integral calculus, vol. I, chapter I, Mir, 1969.
Assessment methods
Written test, consisiting of a few problems to be solved in three hours.
Module on Logics and Reasoning (3CFC)
Learning outcomes:
Students will learn the syntax and some elementary aspects of the semantics of Propositional
Calculus and First-Order Logic. They will use logic formulas to formalize propositions in the natural
language. They will learn simple but formal proof techniques, and will use them to prove (or
disprove) equivalences among sets and among predicate calculus or first-order logic formulas.
Prerequisites
None
Teaching methods
•Lectures are carried out using slides and a blackboard.
•Exercises are carried out in the classroom: students will practice the exercises, even in groups, under the supervision of the lecturer.
•Interaction with the lecturer is done through meetings (on fixed office hours or by
appointment) and by e-mail.
Syllabus
1.Introduction: relevance of the Mathematical Language in Science
2.Examples of discursive and formal proofs of algebraic identities
3.Notations for sets, comparing sets, composing sets: some laws
4.Discursive, graphical and formal proofs of set equalities
5.Syntax and semantics of Propositional Calculus
6.Syntax and basics of semantics of First Order Logic
7.Formalization of natural language statements and formal proofs of logical equivalence
Bibliography
Teaching material (in Italian) will be distributed at the beginning of the module
Assessment methods
Written test, consisiting of a few problems to be solved.