Mathematics
A.Y. 2019/2020
Learning objectives
Present mathematical concepts and methods, with specific attention to the development of issues of interest for the students of the Faculty.
The aim of the course is that students gain a proper theoretical understanding of the topics, together with a good capacity to carry out calculation procedures. Moreover, at the end of the course, the student will be able to use the knowledge to formulate and solve rigourously simple applied problems.
The aim of the course is that students gain a proper theoretical understanding of the topics, together with a good capacity to carry out calculation procedures. Moreover, at the end of the course, the student will be able to use the knowledge to formulate and solve rigourously simple applied problems.
Expected learning outcomes
Expected learning outcomes (nuovo testo da inserire in W4)
Acquire tools and knowledge of basic mathematics and elementary mathematical analysis. In particular, for basic mathematics the student will be able to manipulate formulas containing algebraic expressions, percentages and proportions, radicals, logarithms and exponentials, to solve equations and inequalities, to use the most important tools and techniques of analytic geometry, plane and solid geometry and trigonometry. For elementary mathematical analysis, the student will be able to trace and interpret graphs of functions of a variable in different contents, to calculate limits, derivatives and integrals, and to use these concepts to describe and solve real problems. The student will also be able to understand and autonomously carry out simple mathematical operations commonly used in the scientific literature of his/her domain.
Acquire tools and knowledge of basic mathematics and elementary mathematical analysis. In particular, for basic mathematics the student will be able to manipulate formulas containing algebraic expressions, percentages and proportions, radicals, logarithms and exponentials, to solve equations and inequalities, to use the most important tools and techniques of analytic geometry, plane and solid geometry and trigonometry. For elementary mathematical analysis, the student will be able to trace and interpret graphs of functions of a variable in different contents, to calculate limits, derivatives and integrals, and to use these concepts to describe and solve real problems. The student will also be able to understand and autonomously carry out simple mathematical operations commonly used in the scientific literature of his/her domain.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
Course syllabus
Integer numbers, rational numbers and real numbers. Coordinates systems, element of analytic geometry, straight lines, circumferences, parabolas. Elementary functions and their graphics: exponential, logarithmic and trigonometric functions. Equations and inequalities: of I and II degrees, fractional, logarithmic, trigonometric and exponential, systems of inequalities. Real functions: -Definition of relations and function -Limits -Continuity -Derivatives: geometrical meaning, rules of differentiation, relative maxima and minima, -Asymptotes -The study of a function of one real variable. Integration: -primitives of a function, the indefinite integral -the definite integral and the calculus of plane areas -the fundamental Theorem of Integral Calculus
Prerequisites for admission
As a first semester course in the first year, there are no specific prerequisites other than those required for entrance to the degree course.
Teaching methods
Frontal lessons, exercises, use of e-learning platform associated with the textbook, use of educational software, group work. The course uses the Ariel platform, on which are loaded weekly sheets of exercises and other teaching materials related to the topics covered in the lesson. Attendance at the course, although not compulsory, is strongly recommended.
Teaching Resources
Silvia Annaratone, Matematica sul campo. Metodi ed esempi per le scienze della vita. Pearson
Assessment methods and Criteria
The examination consists of a written test and an oral test. The written test is organized in two parts:
· Part A, lasting 30 minutes, consists of 10 open questions concerning the prerequisites to the course. The extremely simple questions are intended to assess whether the student has the minimum skills to approach a university course of mathematics. Part A will be passed answering correctly at least 8 out of 10 questions. Passing Part A is a necessary (but not sufficient!) condition for passing the written test
· Part B, which lasts 90 minutes, consists of six exercises related to topics of the course. The written test is passed if and only if both parts A and B are passed. The score obtained in Part A does not contribute to the final score of the written test.
The use of calculator if forbidden during the written test.
Particular cases: Laboratorio di Matematica di base
Students who took part to Laboratorio di Matematica di base, performing at least 80% of the scheduled activities in the allotted time and passing the final test in November 2019, are exempted from Part A of the written test for the first 5 sessions.
To attend the written test, students must be enrolled regularly through SIFA and must be in front of the classroom 15 minutes before the beginning of the written test, with photo ID and protocol sheets.
The total duration of the written test is 2 hours. During the written test it is forbidden to consult books, notes, use calculators of any kind, computers and mobile phones. It is also forbidden to communicate with the companions. During all the written test it is also forbidden to leave the classroom: in particular, during the first hour of part B it will not be possible to leave the classroom for any reason. At the end of the first hour, students who wish to do so can either finish or withdraw. The oral test may be taken only if the written test has been passed with a score of 18/30 or more, and only at the same session of the written test. Students who, after passing the written test, did not show up for the oral part will fail the exam.
The oral test will cover all the subjects dealt with in the course. The final grade of the exam will be expressed in thirtieth.
Examples of written tests from past years are available on the Ariel course website.
· Part A, lasting 30 minutes, consists of 10 open questions concerning the prerequisites to the course. The extremely simple questions are intended to assess whether the student has the minimum skills to approach a university course of mathematics. Part A will be passed answering correctly at least 8 out of 10 questions. Passing Part A is a necessary (but not sufficient!) condition for passing the written test
· Part B, which lasts 90 minutes, consists of six exercises related to topics of the course. The written test is passed if and only if both parts A and B are passed. The score obtained in Part A does not contribute to the final score of the written test.
The use of calculator if forbidden during the written test.
Particular cases: Laboratorio di Matematica di base
Students who took part to Laboratorio di Matematica di base, performing at least 80% of the scheduled activities in the allotted time and passing the final test in November 2019, are exempted from Part A of the written test for the first 5 sessions.
To attend the written test, students must be enrolled regularly through SIFA and must be in front of the classroom 15 minutes before the beginning of the written test, with photo ID and protocol sheets.
The total duration of the written test is 2 hours. During the written test it is forbidden to consult books, notes, use calculators of any kind, computers and mobile phones. It is also forbidden to communicate with the companions. During all the written test it is also forbidden to leave the classroom: in particular, during the first hour of part B it will not be possible to leave the classroom for any reason. At the end of the first hour, students who wish to do so can either finish or withdraw. The oral test may be taken only if the written test has been passed with a score of 18/30 or more, and only at the same session of the written test. Students who, after passing the written test, did not show up for the oral part will fail the exam.
The oral test will cover all the subjects dealt with in the course. The final grade of the exam will be expressed in thirtieth.
Examples of written tests from past years are available on the Ariel course website.
MAT/02 - ALGEBRA - University credits: 6
Practicals: 40 hours
Lessons: 28 hours
Lessons: 28 hours
Professor:
Poggioli Daniela
Shifts:
-
Professor:
Poggioli Daniela