MATEMATICA E METODI STATISTICI

The course has a dual objective: on the one hand it intends to provide basic calculation tools, useful for the specific disciplines; on the other hand, it intends to train or consolidate the aptitude for reasoning and problem solving, activities typical of a mathematical education and of transversal usefulness.
We will always start from a practical problem and then provide the mathematical knowledge useful for solving the problem posed.
The exercises will be aimed, in particular, at developing the ability to solve problems. 
Expected Learning Outcomes (AAR) according to the Dublin descriptors:
to. Knowledge and understanding: knowledge of functions, goniometry and trigonometry, differential calculus, basics of integral calculus, basics of statistics.
b. Applied knowledge and understanding: knowing how to work with the fundamentals of goniometry, knowing how to work with functions, knowing how to interpret graphs of functions.
c. Making judgements: knowing how to give a mathematical interpretation of real problems, knowing how to deduce information relating to real problems starting from mathematical data, knowing how to make judgments on real facts starting from mathematical considerations. 
d. Communication skills: knowing how to rigorously communicate the mathematical concepts studied, knowing how to effectively communicate the mathematical meanings being studied.
And. Ability to learn: being able to study and understand both in a group and independently, being able to connect topics covered during the course, grasping connections between the mathematical topics covered and other disciplines (lateral transfer), being able to understand even more complex mathematical topics that are not treated during the course (vertical transfer).

The course includes a double number of hours of exercises compared to the number of frontal lessons, to be precise 42 hours of exercises and 21 of frontal lessons, for a total of 63 hours.

If the course will be used in mixed mode (distance - in person), the in-person lessons will be mainly dedicated to practical exercises (RAA b.).

The mathematical concepts will be introduced starting from real problems (RAA c. ​​and e.) through a visual and practical approach, also using software with a high educational impact (RAA a. and b.), to then arrive at a real formalism (RAA d.), through participatory lessons (RAA d.).

If the teaching is taught in mixed or remote mode, the necessary variations may be introduced with respect to what was previously declared, in order to respect the planned program and reported in the syllabus.

Information for students with disabilities and/or DSA

To guarantee equal opportunities and in compliance with current laws, interested students can request a personal interview in order to plan any compensatory and/or dispensatory measures, based on the educational objectives and specific needs.

It is also possible to contact the CInAP (Centre for Active and Participated Inclusion - Services for Disabilities and/or DSA) professor of our Department, prof.  Anna De Angelis.

Essential basic mathematics cultural requirements:
• Arithmetic (numbers, operations, percentages, approximations);
• Geometry (polygons, Pythagorean theorem);
• Algebra (polynomials, first degree equations and inequalities, second degree equations and inequalities).

Attendance at the course is strongly recommended, especially for the exercises, which will actively involve students, promoting their learning.
Attendance will be recorded only for statistical and course evaluation purposes.

Detailed Course Content

Learning assessment methods
During the course, ongoing tests (multiple choice) will be administered. 
Methods for those who take advantage of ongoing tests: 
The ongoing tests are worth 10 points each out of 30 and the final written test (with exercises) is worth 10 points out of 30. Those who score at least 18 between the ongoing and written tests can decide to confirm the written grade in the oral exam.
Those who, having passed the ongoing tests (at least 18 out of 30), decide to also take the oral exam, will have the possibility, by correctly answering the questions asked, to obtain a further 3 points.
Methods for those who do not take advantage of the ongoing tests:
The final exam consists of a written test (with exercises) and an oral test. 
Verification of learning can also be carried out electronically, should conditions require it.
Evaluation grid: 
Not suitable
Knowledge and understanding of the topic: Important deficiencies. Significant inaccuracies
Applied knowledge: Poor ability to manipulate mathematical objects.
Making judgements: Poor or absent ability to make judgments on real or realistic facts starting from mathematical considerations.
Communication skills: Deficiencies in communicating mathematical meanings. Absent or improper use of mathematical language.
Ability to learn: Poor ability to connect studied topics together. Poor ability to solve problems.

18-20
Knowledge and understanding of the topic: Sufficient. Obvious inaccuracies.
Applied knowledge: Just sufficient ability to manipulate mathematical objects.
Making judgements: Sufficient ability to make judgments on real or realistic facts starting from mathematical considerations.
Communication skills: Sufficient ability to communicate mathematical meanings. Sufficient use of appropriate mathematical language.
Ability to learn: Sufficient ability to connect studied topics together. Sufficient ability to solve problems if guided.
21-23
Knowledge and understanding of the topic: Good. With inaccuracies.
Applied knowledge: Ability to manipulate mathematical objects.
Making judgements: Ability to make judgments on real or realistic facts starting from mathematical considerations.
Communication skills: Ability to communicate mathematical meanings. Appropriate use of mathematical language.
Ability to learn: Ability to connect topics studied together. Ability to solve problems with partial guidance.

24-26
Knowledge and understanding of the topic: Good. With a few inaccuracies.
Applied knowledge: Good ability to manipulate mathematical objects.
Making judgements: Good ability to make judgments on real or realistic facts starting from mathematical considerations.
Communication skills: Good ability to communicate mathematical meanings. Appropriate use of mathematical language.
Ability to learn: Good ability to connect studied topics together. Ability to solve problems independently.
27-29
Knowledge and understanding of the topic: Excellent. Without inaccuracies.
Applied knowledge: More than good ability to manipulate mathematical objects.
Making judgements: More than good ability to make judgments on real or realistic facts starting from mathematical considerations and to make mathematical considerations starting from real facts.
Communication Skills: More than good ability to communicate mathematical meanings. Appropriate and rigorous use of mathematical language.
Ability to learn: More than good ability to connect studied topics together. Ability to solve problems independently.
30-30 with honors
Knowledge and understanding of the topic: Excellent. With insights.
Applied knowledge: Excellent ability to manipulate mathematical objects. Ability to solve problems according to correct non-standard procedures.
Making judgements: Excellent ability to make judgments on real or realistic facts starting from mathematical considerations and to make mathematical considerations starting from real facts.
Communication skills: Excellent ability to communicate mathematical meanings. Appropriate and rigorous use of mathematical language.
Ability to learn: Excellent ability to connect studied topics together. Ability to pose problems and solve problems independently.

Examples of frequently asked questions and/or exercises
EXAMPLES OF WRITING EXERCISES
	Find the domain of the following function: f(x)= ln(4-x2)
	Calculate the limit as x tends to infinity of the function f(x)= (x3-1)/(x3)
	Study the trend and represent the graph of the function f(x) = xex
	A population of bacteria follows the trend of the logistic function p(t)= 1000/(1 +e(-2t) ), with t>=0, where the variable t expresses the time in days and p(t) the numerousness of the bacterial colony.

Compute the limit lim┬(t→+∞)⁡〖p(t)〗. What do we deduce from the calculated limit?

EXAMPLES OF ORAL QUESTIONS
• Define the trigonometric functions sine, cosine, tangent.
• State the theorem of sines.
• How do you solve a right triangle?
• How can a phenomenon with a linear trend be represented on the Cartesian plane? What type of equation will be associated with the representation on the plane?
• How do you define a function? In which cases is it appropriate to use a function to model a real phenomenon? Provide examples
• What phenomenon might an exponential function describe? Is it a logarithmic function?
• Give the definition of finite limit of a real function with a real variable 
• What is the use of calculating an infinite limit for a real function with a real variable? 
• Give the definition of derivative of a real function of a real variable and explain its geometric meaning
• What is the use of understanding the behavior of the derivative of a function? Give examples
• What is integral calculus for?
• Tell what the mean and median of a set of data are. When is it better to use one or the other?
• What is the standard deviation (or standard deviation)?
	Describe the behavior of the function p(t) = 1 / [1+ e -2t] which expresses the trend of a population.
	In the first three partial mathematics tests, Giovanni's grades were 25, 20, 26. The grade of the fourth and final test did not change the average (arithmetic). What is the score for the fourth test? 
	What can be deduced from a set of data if the arithmetic mean is less than the median? 
	Write a set of data whose arithmetic mean is greater than the median.
	Determine the mean and median of the following data set: 1, 2, 4, 4, 7, 7, 8, 15.