MATHEMATICS
- Academic year
- 2024/2025 Syllabus of previous years
- Official course title
- MATHEMATICS
- Course code
- FOY02 (AF:540327 AR:307724)
- Modality
- On campus classes
- ECTS credits
- 12
- Subdivision
- A
- Degree level
- Corso di Formazione (DM270)
- Educational sector code
- NN
- Period
- 1st Semester
- Course year
- 1
- Where
- VENEZIA
- Moodle
- Go to Moodle page
Contribution of the course to the overall degree programme goals
Expected learning outcomes
-know the main theories required to take a first year university mathematics course;
-be able to solve exercises on all the covered topics and to correctly answer to multiple choice questions similar to those proposed in the university admission tests.
Pre-requirements
Contents
— Logic of propositions.
— Logical connectives.
— Logic of propositional functions.
— Quantifiers.
— Definitions.
— Axioms.
— Theorems.
— The summation symbol.
2. Numbers.
— Natural numbers, whole numbers and their properties. Need to extend the set of natural numbers for applications.
— Integer numbers and their properties.
— Rational numbers. Calculations with fractions. Decimal representations and related calculations. Numerical approximations.
— Real numbers and their properties.
3. Powers and logarithms.
— Powers and properties of powers.
— Why we need logarithms.
— Logarithms properties and calculations with logarithms.
— How to use pocket calculators for logarithms and exponentials.
4. Percentages.
5. Sets
— Elements of sets.
— How to write a set.
— Subsets.
— Operations between sets: union, intersection, difference, cartesian product, in particular the set R2.
— Special sets of real numbers and their representation.
6. Elementary algebra.
— Algebraic expressions and corresponding calculations.
— Factoring an algebraic expression. Special products.
— Simplifying algebraic fractions.
7. Functions.
— Definitions and examples. Examples from economics and other sciences.
— Real functions of one real variable.
— Composite and inverse functions.
— Injective, surjective, one to one functions.
— Monotone functions.
— Periodic functions.
— Even and odd functions.
— The graph of a function.
— Shifting graphs. The importance of units while plotting and comparing graphs.
— Graphs and properties of some elementary functions: linear functions, quadratic functions, the function of inverse proportionality, logarithmic and exponential functions.
— The absolute value and calculations with absolute values.
8. Equations and inequalities.
— Linear equations and inequalities in one or two unknowns.
— Systems of linear equations in two unknowns.
— Second degree equations and inequalities in one variable.
— Irrational equations and inequalities.
— Fractional equations and inequalities.
— Equations and inequalities with absolute values.
— Exponential and logarithmic equations and inequalities.
9. Analytic geometry.
— Cartesian coordinates in the plane and space.
— Distance between two points. Midpoint of a segment.
— The line in the cartesian plane and its various equations. The slope of a line.
— The vertical parabola or quadratic function.
— Conics: horizontal parabola, circumference, standard form of the ellipse and hyperbola.
— Intersection points between curves.
10. Basics of trigonometry.
— Angles and their measure: degrees and radians.
— The unit circle and the definition of the trigonometric functions: sine, cosine, tangent, cotangent.
— Trigonometric functions of the most important angles.
— Graphs of the trigonometric functions.
— Trigonometric relations: functions for the sum and difference of two angles, for the doubleangle and the half-angle.
— Right triangles and trigonometric functions.
— Simple equations and inequalities involving trigonometric functions.
Referral texts
Assessment methods
a) Participation and attendance: 10%
b) Mid-term evaluations: 70%
c) Final exam: 20%
Both mid-term evaluations and the final exam have a written part with the resolution of exercises and on oral part.
Teaching methods
Discussions
Excercises