Calculus and Computer Laboratory
A.Y. 2026/2027
Learning objectives
To provide the basic method and calculus tools of mathematical analysis and linear algebra which are propaedeutic to a full understanding and correct handling of biological data and information. These tools represent a mandatory cultural element for a modern biologist who wants to comprehend the life in its quantitative aspects.
To teach concepts and tools of Computer Science for an appropriate use of application software. Topics will concern basic introductory notions of informatics, data analysis and management, and introduction to Bioinformatics. The course is offered in e-learning through a dedicated online software platform, with the addition of two frontal lectures and two hands-on in computer laboratory.
To teach concepts and tools of Computer Science for an appropriate use of application software. Topics will concern basic introductory notions of informatics, data analysis and management, and introduction to Bioinformatics. The course is offered in e-learning through a dedicated online software platform, with the addition of two frontal lectures and two hands-on in computer laboratory.
Expected learning outcomes
At the end of the study the students will be able to use computational processes to analyze the biological phenomena. In particular the student: i) will be able to formalize elementary problems by mean of mathematical models; ii) will know the main basic results of differential and integral calculus (for real functions of one real variable) and of the linear algebra; iii) will be able to deal with such a theoretical part and related tools in order to solve problem in sciences of live for which a mathematical approach is suitable.
The students will benefit from this course since they will learn concepts of data representation, hardware, and software. In addition, they will acquire the ability to process data by using spreadsheets, databases, Internet and the web consultation related to biological databases.
The students will benefit from this course since they will learn concepts of data representation, hardware, and software. In addition, they will acquire the ability to process data by using spreadsheets, databases, Internet and the web consultation related to biological databases.
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
Surname A-L
Responsible
Prerequisites for admission
Elementary algebra, analytic geometry, trigonometry. Elementary functions and their graphs. Inequalities.
(see also the MiniMat course material available online at https://myariel.unimi.it/course/view.php?id=5093).
(see also the MiniMat course material available online at https://myariel.unimi.it/course/view.php?id=5093).
Assessment methods and Criteria
Assessment for the General Mathematics module consists of a 150-minute written examination comprising exercises and questions on the theoretical topics covered in the syllabus.
The exercises assess students' ability to apply tools from the theory of elementary functions, differential and integral calculus, and linear algebra; to select appropriate methods; and to carry out the relevant calculations correctly. The theoretical questions assess students' knowledge and understanding of the definitions, statements, and conditions under which the results presented in the syllabus are applicable.
The assessment is based on the following criteria:
* knowledge and understanding of the theoretical content;
* correctness of the approach and results;
* appropriateness of the methods selected;
* completeness, correctness, and logical coherence of the procedures;
* ability to justify the main steps;
* clarity of presentation and command of mathematical language and notation.
The examination is graded on a scale of 30 and is passed with a score of at least 18/30. The examination paper specifies the number of marks awarded for each exercise and each theoretical question. As a rule, students are not permitted to consult any materials or use calculators during the examination.
*Mid-term examinations*
The written examination may be replaced by two mid-term examinations, available exclusively to students enrolled in the first year of the Bachelor's degree programme in Biological Sciences. Each examination assesses knowledge and skills relating to a specific part of the syllabus; taken together, the two examinations provide an assessment equivalent to the final written examination.
The mid-term examinations replace the written examination provided that:
* a score of at least 16/30 is obtained in each examination;
* the average of the two scores, rounded up to the next whole number, is at least 18/30.
In this case, the module grade is the average of the scores obtained in the two examinations, rounded up to the next whole number.
*Award of honours*
To be awarded honours, students must have obtained at least 29/30 in the written test and have to take an additional oral examination during the same examination session. The oral examination covers the definitions, statements, proofs, and any counterexamples included in the detailed syllabus. It assesses command of the subject matter, rigour of argumentation, and clarity of presentation. Failure to obtain honours in the oral examination does not affect the grade obtained in the written examination.
*Final grade for the integrated course*
The examination for the integrated course comprises an assessment for the General Mathematics module, worth 6 ECTS credits, and an assessment for the Computer Laboratory module, worth 3 ECTS credits. The final grade can be officially recorded only after both modules have been passed. Both modules must be successfully completed by December 2027.
The final grade is calculated as the ECTS-weighted average. The result is rounded to the nearest whole number: down when the first decimal digit is between 0 and 4, and up when it is between 5 and 9.
The exercises assess students' ability to apply tools from the theory of elementary functions, differential and integral calculus, and linear algebra; to select appropriate methods; and to carry out the relevant calculations correctly. The theoretical questions assess students' knowledge and understanding of the definitions, statements, and conditions under which the results presented in the syllabus are applicable.
The assessment is based on the following criteria:
* knowledge and understanding of the theoretical content;
* correctness of the approach and results;
* appropriateness of the methods selected;
* completeness, correctness, and logical coherence of the procedures;
* ability to justify the main steps;
* clarity of presentation and command of mathematical language and notation.
The examination is graded on a scale of 30 and is passed with a score of at least 18/30. The examination paper specifies the number of marks awarded for each exercise and each theoretical question. As a rule, students are not permitted to consult any materials or use calculators during the examination.
*Mid-term examinations*
The written examination may be replaced by two mid-term examinations, available exclusively to students enrolled in the first year of the Bachelor's degree programme in Biological Sciences. Each examination assesses knowledge and skills relating to a specific part of the syllabus; taken together, the two examinations provide an assessment equivalent to the final written examination.
The mid-term examinations replace the written examination provided that:
* a score of at least 16/30 is obtained in each examination;
* the average of the two scores, rounded up to the next whole number, is at least 18/30.
In this case, the module grade is the average of the scores obtained in the two examinations, rounded up to the next whole number.
*Award of honours*
To be awarded honours, students must have obtained at least 29/30 in the written test and have to take an additional oral examination during the same examination session. The oral examination covers the definitions, statements, proofs, and any counterexamples included in the detailed syllabus. It assesses command of the subject matter, rigour of argumentation, and clarity of presentation. Failure to obtain honours in the oral examination does not affect the grade obtained in the written examination.
*Final grade for the integrated course*
The examination for the integrated course comprises an assessment for the General Mathematics module, worth 6 ECTS credits, and an assessment for the Computer Laboratory module, worth 3 ECTS credits. The final grade can be officially recorded only after both modules have been passed. Both modules must be successfully completed by December 2027.
The final grade is calculated as the ECTS-weighted average. The result is rounded to the nearest whole number: down when the first decimal digit is between 0 and 4, and up when it is between 5 and 9.
Modulo: Matematica generale
Course syllabus
· Natural, integer, rational, real numbers. The field of real numbers and its operations. The symbols + ∞ and -∞. Complex numbers and application to second order algebraic equations.
· Real functions of real variable. Properties: injectivity, surjectivity, biunivocity, monotony. Inverse functions. Composition of functions. Cartesian representation of the graph of a function.
· Brief review elementary functions: powers, logarithms, exponentials, trigonometric functions, absolute value.
· Linear algebra: vectors, matrices and their operations. Determinant of a square matrix. Inverse matrix. Systems of linear equations and matrix representation; Gauss method. Eigenvectors, eigenvalues .
· Limits of functions: definitions and first properties. Uniqueness of the limit. Limits of monotone functions. Limits of elementary functions. Operations with limits. Indeterminate forms. Asymptotic functions. Comparison theorems.
· The number of Nepero. Special limits. Hierarchy of infinities and infinitesimals. Continuous functions and their properties: zeros theorem and Weierstrass theorem.
· Differential calculus: definition of derivative; geometrical meaning; tangent line. Derivability and continuity. Operations with derivatives. Derivatives of composition of functions and inverse functions. Derivatives of elementary functions. Applications of derivatives. Stationary points.
· Fermat's theorem and Lagrange theorem. Increasing and decreasing functions. Convexity. Taylor expansion and applications.
· Study of the graph of a function. Horizontal, vertical, oblique asymptotes.
· Indefinite integral. Calculus of primitives: integration by sum decomposition, integration by parts, integration by substitution.
· Definite integral. Definition, geometric interpretation, properties. The integral mean value theorem. The fundamental theorem of integral calculus. The formula of integral calculus theorem. Area of plane regions.
· Outline of first order differential equations: separation of variables and qualitative study (autonomous case). Application to biology. In case we have time: second order differential equations with constant coefficients or first order linear systems.
· Real functions of real variable. Properties: injectivity, surjectivity, biunivocity, monotony. Inverse functions. Composition of functions. Cartesian representation of the graph of a function.
· Brief review elementary functions: powers, logarithms, exponentials, trigonometric functions, absolute value.
· Linear algebra: vectors, matrices and their operations. Determinant of a square matrix. Inverse matrix. Systems of linear equations and matrix representation; Gauss method. Eigenvectors, eigenvalues .
· Limits of functions: definitions and first properties. Uniqueness of the limit. Limits of monotone functions. Limits of elementary functions. Operations with limits. Indeterminate forms. Asymptotic functions. Comparison theorems.
· The number of Nepero. Special limits. Hierarchy of infinities and infinitesimals. Continuous functions and their properties: zeros theorem and Weierstrass theorem.
· Differential calculus: definition of derivative; geometrical meaning; tangent line. Derivability and continuity. Operations with derivatives. Derivatives of composition of functions and inverse functions. Derivatives of elementary functions. Applications of derivatives. Stationary points.
· Fermat's theorem and Lagrange theorem. Increasing and decreasing functions. Convexity. Taylor expansion and applications.
· Study of the graph of a function. Horizontal, vertical, oblique asymptotes.
· Indefinite integral. Calculus of primitives: integration by sum decomposition, integration by parts, integration by substitution.
· Definite integral. Definition, geometric interpretation, properties. The integral mean value theorem. The fundamental theorem of integral calculus. The formula of integral calculus theorem. Area of plane regions.
· Outline of first order differential equations: separation of variables and qualitative study (autonomous case). Application to biology. In case we have time: second order differential equations with constant coefficients or first order linear systems.
Teaching methods
Traditional. Support tutoring activities in two phases: from early October to mid-November for alignment and review of prerequisites, and from late December to late February for preparation for the written exams.
Teaching Resources
- Main material: online course "Matematica Assistita", https://myariel.unimi.it/course/view.php?id=5034
Additional material:
- Matematica per le Scienze, Bramanti-Confortola-Salsa, Zanichelli editore.
- Metodi Matematici per le scienze applicate, Bisi-Fioresi, CEA editore (per cap. 5 e 6 sulle EDO).
Additional material:
- Matematica per le Scienze, Bramanti-Confortola-Salsa, Zanichelli editore.
- Metodi Matematici per le scienze applicate, Bisi-Fioresi, CEA editore (per cap. 5 e 6 sulle EDO).
Modulo: Laboratorio di informatica
Course syllabus
The Course program is focused on the following topics:
· Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
· Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
· Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
· Internet and web
o Computer networks
o The Internet network
o Web architecture
o Web standards
o Web contents
o Search engines
o Web evolutions
· Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
· Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
· Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
· Internet and web
o Computer networks
o The Internet network
o Web architecture
o Web standards
o Web contents
o Search engines
o Web evolutions
Teaching methods
The Course provides the basic notions of the computer-science discipline with focus on i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. Furthermore, the Course provides skills about the main functionalities of spreadsheet software tools, with focus on the use of formulae, functions, and chart creation.
The Course is provided as a blended-learning course.
For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.
Examination modality and evaluation criteria
The examination is articulated in two distinct evaluation steps.
The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).
The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.
The Course is provided as a blended-learning course.
For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.
Examination modality and evaluation criteria
The examination is articulated in two distinct evaluation steps.
The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).
The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.
Teaching Resources
Teaching stuff
The teaching stuff is online at https://3cfuinformatica.unimi.it
The teaching stuff is online at https://3cfuinformatica.unimi.it
Modules or teaching units
Modulo: Laboratorio di informatica
INFO-01/A - Informatics - University credits: 3
Computer basics: 18 hours
Modulo: Matematica generale
MATH-01/A - Mathematical Logic - University credits: 3
MATH-04/A - Mathematical Physics - University credits: 3
MATH-04/A - Mathematical Physics - University credits: 3
Exercises: 48 hours
Lessons: 24 hours
Lessons: 24 hours
Professors:
Pasquali Fabio, Penati Tiziano
Surname M-Z
Responsible
Prerequisites for admission
Elementary algebra, analytic geometry, trigonometry. Elementary functions and their graphs. Inequalities.
(see also the MiniMat course material available online at http://ariel.unimi.it/User/).
(see also the MiniMat course material available online at http://ariel.unimi.it/User/).
Assessment methods and Criteria
The exam consists of two parts, one for each of the two modulus of Matematica Generale (6 CFU) and of Laboratorio di Informatica (3 CFU).
To participate to the test of each modulus, the student must register through SIFA to the module itself.
The final grade is obtained after passing the tests related to the two modulus.
The two tests must be passed within the same academic year.
The grade resulting from the weighted average of the grades reported in the two modulus (approximated to the unit by default / excess depending on the decimal number 0-4 / 5-9) will be registered by the professor of the modulus of Matematica Generale.
To pass the exam relating to the modulus of Matematica Generale it is necessary to know the theory (definitions, theorem statements) presented during the lectures and to be able to solve some exercises exploiting what illustrated during the exercises lectures.
The test of the modulus of Matematica Generale consists of exercises and may also contain some multiple choice questions on the contents of the theory. The test is considered passed if at least 18 points are obtained out of a total of 30.
There will be 7 tests distributed during the academic year, dates appearing on SIFA.
Candidates must attend the written tests or in itinere tests with a valid identity document with a photograph; during the written test it is not allowed to consult any type of material, nor the use of calculators.
To participate to the test of each modulus, the student must register through SIFA to the module itself.
The final grade is obtained after passing the tests related to the two modulus.
The two tests must be passed within the same academic year.
The grade resulting from the weighted average of the grades reported in the two modulus (approximated to the unit by default / excess depending on the decimal number 0-4 / 5-9) will be registered by the professor of the modulus of Matematica Generale.
To pass the exam relating to the modulus of Matematica Generale it is necessary to know the theory (definitions, theorem statements) presented during the lectures and to be able to solve some exercises exploiting what illustrated during the exercises lectures.
The test of the modulus of Matematica Generale consists of exercises and may also contain some multiple choice questions on the contents of the theory. The test is considered passed if at least 18 points are obtained out of a total of 30.
There will be 7 tests distributed during the academic year, dates appearing on SIFA.
Candidates must attend the written tests or in itinere tests with a valid identity document with a photograph; during the written test it is not allowed to consult any type of material, nor the use of calculators.
Modulo: Matematica generale
Course syllabus
This is the program for the years 2023/24, 2024/25 and 2025/26; it is expected that the course 2026/27 will follow the same scheme.
A more detailed program is available on the ARIEL page.
Numbers
Functions
Vectors and Matrices
Limits
Derivatives
Integrals
Differential equations and biological applications
A more detailed program is available on the ARIEL page.
Numbers
Functions
Vectors and Matrices
Limits
Derivatives
Integrals
Differential equations and biological applications
Teaching methods
Standard lectures and exercise classes
Teaching Resources
Prerequisites: see Corso online "Matematica Assistita", http://ariel.unimi.it/User/
Any text on introductory Mathematical Analysis will do, and contain more than what the course will provide. An indication of texts (also available in English, here we give the Italian version) is as follows
Theory: V.I. Smirnov, Corso di Matematica Superiore - volume I (Editori Riuniti)
Exercises: B.P. Demodovic: Eserrcizi e Problemi di Nalisi Matematica (Editori Riuniti)
The detailed program provided on ARIEL refers to chapters and sections of the Smirnov text
A text looking at biological applications is
· D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Casa Editrice Ambrosiana
Some notes are also available on the ARIEL page; therein the student will also find collections of exercises with solutions. The exam texts of previous year are also available.
Any text on introductory Mathematical Analysis will do, and contain more than what the course will provide. An indication of texts (also available in English, here we give the Italian version) is as follows
Theory: V.I. Smirnov, Corso di Matematica Superiore - volume I (Editori Riuniti)
Exercises: B.P. Demodovic: Eserrcizi e Problemi di Nalisi Matematica (Editori Riuniti)
The detailed program provided on ARIEL refers to chapters and sections of the Smirnov text
A text looking at biological applications is
· D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Casa Editrice Ambrosiana
Some notes are also available on the ARIEL page; therein the student will also find collections of exercises with solutions. The exam texts of previous year are also available.
Modulo: Laboratorio di informatica
Course syllabus
The Course program is focused on the following topics:
· Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
· Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
· Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
· Internet and web
o Computer networks
o The Internet network
o Web architecture
o Web standards
o Web contents
o Search engines
o Web evolutions
· Foundations of Computer Science
o Introduction to Computer Science
o Information coding
o Computer structure
o Programs and software
o The "Infosphera" risks
· Spreadsheets
o Introduction to spreadsheets
o General functions in Excel
o Statistical functions in Excel
o Chart creation in Excel
· Information management
o Introduction to information management
o Data storing and databases
o Relational databases
o Database creation
o Query composition
o Web databases
· Internet and web
o Computer networks
o The Internet network
o Web architecture
o Web standards
o Web contents
o Search engines
o Web evolutions
Teaching methods
The Course provides the basic notions of the computer-science discipline with focus on i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. Furthermore, the Course provides skills about the main functionalities of spreadsheet software tools, with focus on the use of formulae, functions, and chart creation.
The Course is provided as a blended-learning course.
For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.
Examination modality and evaluation criteria
The examination is articulated in two distinct evaluation steps.
The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).
The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.
The Course is provided as a blended-learning course.
For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.
Examination modality and evaluation criteria
The examination is articulated in two distinct evaluation steps.
The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).
The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.
Teaching Resources
Teaching stuff
The teaching stuff is online at https://3cfuinformatica.unimi.it
The teaching stuff is online at https://3cfuinformatica.unimi.it
Modules or teaching units
Modulo: Laboratorio di informatica
INFO-01/A - Informatics - University credits: 3
Computer basics: 18 hours
Modulo: Matematica generale
MATH-01/A - Mathematical Logic - University credits: 3
MATH-04/A - Mathematical Physics - University credits: 3
MATH-04/A - Mathematical Physics - University credits: 3
Exercises: 48 hours
Lessons: 24 hours
Lessons: 24 hours
Professors:
Gaeta Giuseppe, Tasin Luca
Educational website(s)
Professor(s)
Reception:
to be fixed by email
office num. 1039, first floor, Dep. Mathematics, via Saldini 50
Reception:
Appointment via email.
Dipartimento di Matematica "F. Enriques" - Ufficio 0.007