MATHEMATICS
MATEMATICA
Mathematics
Matematica
| A.Y. | Credits |
|---|---|
| 2020/2021 | 8 |
| Lecturer | Office hours for students | |
|---|---|---|
| Giovanni Molica Bisci |
| Teaching in foreign languages |
|---|
|
Course with optional materials in a foreign language
English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language. |
Assigned to the Degree Course
| Date | Time | Classroom / Location |
|---|
| Date | Time | Classroom / Location |
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Learning Objectives
Aim of the course is to give to the students some basic tools and topics in mathematical analysis, for functions of one variable.
Program
01. Elements of Set Theory:
01.01 Fundamental notions.
01.02 Operations between sets.
01.03 Cartesian product.
01.04 Applications.
01.05 Order relations.
01.06 Equivalence relations.
01.07 Mathematical induction.
01.08 Cardinality in the sense of Frege.
02. Algebraic structures:
02.01 Operations.
02.02 Closed sets.
02.03 Induced laws.
02.04 Associative (commutative) laws.
02.05 Neutral element.
02.06 Simmetrizable elements.
02.07 Regular elements.
02.08 Compatibility and quotient set.
02.09 Relations between compositions laws.
02.10 Algebraic structures: groups, rings, corps, fields.
03. Elements of Lattice Theory:
03.01 Lattices.
03.02 Sublattices.
03.03 Diagrams (Hasse).
03.04 Distributive lattices.
03.05 Complements.
03.06 Boolean lattices.
03.07 Boolean rings.
03.08 Boolean algebras.
03.09 Structures of the power set.
03.10 Stone's theorems.
04. Numerical sets:
04.01 The semiring of naturals.
04.02 The ring of integers.
04.03 The field of rationalas.
04.04 Dedekind completeness.
04.05 The real field.
04.06 The rational field is not complete.
04.07 Completeness: different versions.
Bridging Courses
There are no mandatory prerequisites. It is recommended to take the exam of Mathematics during the first year of the Laurea Degree Program in Biothecnology.
Learning Achievements (Dublin Descriptors)
Knowledge and understanding:
At the end of the course the student will learn the basic notions of mathematical analysis for the study of functions of one variable.
Applying knowledge and understanding:
At the end of the course the student will learn the methodologies of mathematical analysis and will be able to apply them to the study of various problems.
Making judgements:
At the end of the course the student will be able to apply the techniques of mathematical analysis in order to solve new problems, also coming from real-world applications.
Communications skills:
At the end of the course the student will have the ability to express the fundamental notions of mathematical analysis using a rigorous terminology.
Learning skills:
During the course the student will learn the ability to study the notions of mathematical analysis, also in order to use it in solving different kind of problems.
Teaching Material
The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it
Teaching, Attendance, Course Books and Assessment
- Teaching
Theorical and practical lessons.
- Attendance
Although strongly recommended, course attendance is not mandatory.
- Course books
Adams, Calcolo Differenziale 1, Casa Editrice Ambrosiana
Adams - Essex, Calculus: a complete course, Pearson Canada
Bramanti - Pagani - Salsa, Analisi matematica 1, Zanichelli
Bramanti - Pagani - Salsa, Analisi matematica 1 con elementi di geometria e algebra lineare, Zanichelli
Salsa - Squellati, Esercizi di Analisi matematica 1, Zanichelli
- Assessment
The exam of Mathematics consists of a written exam and an oral one, both of them mandatory.
The written exam, to carry out in two hours, consists of exercises related to the topics of the course. The written exam is passed if the mark is, at least, 15/30. During the written exam it is not allowed to use textbooks, workbooks or notes. Moreover, it is not allowed to use scientific calculators and mobile phones, under penalty of disqualification.
The oral exam consists of a discussion related to the topics of the course. The oral exam can be taken only if the written one has been passed. If so, the oral exam can be taken only in the same call in which the written exam has been passed or in the other calls of the same session.
The final mark of Mathematics is the average of the marks of the written exam and the oral one.
- Disability and Specific Learning Disorders (SLD)
Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.
To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.
Additional Information for Non-Attending Students
- Teaching
Theorical and practical lessons.
- Attendance
Although strongly recommended, course attendance is not mandatory.
- Course books
Adams, Calcolo Differenziale 1, Casa Editrice Ambrosiana
Adams - Essex, Calculus: a complete course, Pearson Canada
Bramanti - Pagani - Salsa, Analisi matematica 1, Zanichelli
Bramanti - Pagani - Salsa, Analisi matematica 1 con elementi di geometria e algebra lineare, Zanichelli
Salsa - Squellati, Esercizi di Analisi matematica 1, Zanichelli
- Assessment
The exam of Mathematics consists of a written exam and an oral one, both of them mandatory.
The written exam, to carry out in two hours, consists of exercises related to the topics of the course. The written exam is passed if the mark is, at least, 15/30. During the written exam it is not allowed to use textbooks, workbooks or notes. Moreover, it is not allowed to use scientific calculators and mobile phones, under penalty of disqualification.
The oral exam consists of a discussion related to the topics of the course. The oral exam can be taken only if the written one has been passed. If so, the oral exam can be taken only in the same call in which the written exam has been passed or in the other calls of the same session.
The final mark of Mathematics is the average of the marks of the written exam and the oral one.
- Disability and Specific Learning Disorders (SLD)
Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.
To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.
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