Study plan

The reason why the ECTS requirement for the degree exam ranges from 36 to 45 is due to the need to slightly reshape year by year the educational weight of such exam. The threshold of 15 ECTS may be exceeded only whether at least one of the elective programmes is qualifying to acquire some of the ECTS required to be admitted to public competitions for secondary school teaching.

Curriculum unico

First year

Orientamento unico
Course		Semester	CFU	SSD
1012161 - ASTROPHYSICAL PROCESSES AND PLASMAS	1 Knowledge and understanding: Knowledge and understanding of the physical phenomena of major interest in astrophysics, at a level higher than that of the first cycle. 2 Applying knowledge and understanding: Ability to apply the class topics in the context of the next exams of the Laurea, with particular regards to those with phenomenological character. 3 Making judgements: Ability to integrate the plasma physics basics, with advanced radiation emission mechanisms. Ability to understand the connections between different topics treated in the class. 4 Communication Ability to communicate in clear and unambibuous way the topics developed in this course, and to autonomously draw conclusions from the arguments studied. 5 Learning skills Ability to develop personal study, and to independently deepen some aspect of the course.	First semester	6	FIS/05
1012186 - GENERAL RELATIVITY	Aim of the course is to introduce the basic notions of the modern theory of gravity, and of its more important conceptual and astrophysical implications. At the end of the course the student should: 1) have acquired the instruments of differential geometry which allow to formulate Einstein's equations and derive its predictions. 2) Have understood what is the role of the equivalence principle between gravitational and inertial mass in the formulation of the theory, and why the gravitational field modifies the spacetime geometry. 3) Have understood how to use the symmetries of a physical problem to simplify Einstein's equations and find solutions. 4) Be able to derive the solution describing the gravitational field external to a non rotating, spherically symmetric body (the Schwarzschild solution), and to show that this solution can also represent a non rotating black hole. 5) Have understood how some of the main predictions of General Relativity can be obtained by solving the geodesic equations, which describe the motion of free particles in a gravitational field. 6) Have understood how to solve Einstein's equations in the weak field limit, to show that spacetime perturbations propagate as gravitational waves. Therefore, at the end of the course the student should: 1) be able to compute how vectors, one-forms and tensors transform under a coordinate transformation; to compute the covariant derivative of these geometrical objects and to solve exercises which involve these operations in tensor equations. 2) Be able to compute how does a vector change when parallely transported along a path in curved spacetime, and to derive the curvature tensor using this operation. 3) Be able to derive Einstein's equations. 4) Be able to derive and interpret some of the most interesting predictions of General Relativity: the gravitational redshift, light deflection near massive bodies, precession of Mercury perihelion, existence of gravitational waves. This course introduces the fundamental concept of a curved spacetime due to the existence of a gravitational field, and discusses the more important aspects of the scientific revolution introduced by Einstein's theory. As such, it is a basis course for the laurea magistrale in Astronomy and Astrophysics, and it is also a matter which should be part of the cultural background of a modern physicist.	First semester	6	FIS/02
1012178 - SUPERIOR PHYSICS	The aim of this course is to give a first introduction to nuclear and particle physics. At the end, the student will be able to make by himself simple calculations of tree-level cross sections in QED and in the electroweak theory.	First semester	6	FIS/02
1051847 - Astrophysics Laboratory	To acquire advanced measurement methods in astrophysics and cosmology. To be able to carry-out an advanced astronomical observation or a laboratory experiment related to astronomy, and to be able to analyze the data and provide physical insight of the results.	First semester	6
Astrophysics Laboratory		First semester	6	FIS/05
1044601 - PHYSICAL COSMOLOGY	The main goal of this course is to provide the student with all the necessary information tounderstand and analyze the latest observational results in modern cosmology. This "information" is extremely relevant not only for the student that plans a career inthe field of astrophysics but also for students interested in particle physics from theexperimental or theoretical point of view.	Second semester	6	FIS/05
1012131 - STELLAR ASTROPHYSICS	The course aims at describing the structure and evolution of stars in the more general context of galaxy evolution. At the end of the course, students will gain a deep knowledge of physical processes governing the structure and evolution of stars of different masses from the pre-main sequence phase to their final evolution. In the second part of the course, an introduction on the fundamental physical processes driving the properties of the interstellar medium and the process of star formation will be given. The aim is to apply the competences acquired in the first part of the course to a more general context, allowing the students to confront with frontier fields of research and stimulating their ability as independent learners and their critical sense through individual research plans.	Second semester	6	FIS/05
1044553 - THEORETICAL ASTROPHYSICS	Give the student the mathematical ability to understand in full the classic potential theory that, in its application to gravitation, will allow to face with problems of stellar and galactic dynamics.	Second semester	6	FIS/05
1051847 - Astrophysics Laboratory	To acquire advanced measurement methods in astrophysics and cosmology. To be able to carry-out an advanced astronomical observation or a laboratory experiment related to astronomy, and to be able to analyze the data and provide physical insight of the results.	Second semester	6
Astrophysics Laboratory		Second semester	6	FIS/05
- A SCELTA DELLO STUDENTE		Second semester	6
AAF1901 - English Language	To provide students with the basic linguistic skills needed to deal with written scientific communication.	Second semester	4
GRUPPO A AFFINI INTEGRATIVI		Go to group		FIS/05
GRUPPO B ASTRONOMICO OSSERVATIVO SPERIMENTALE		Go to group
GRUPPO C CARATTERIZZANTE ASTRONOMICO TECNOLOGICO		Go to group

Second year

Orientamento unico
Course		Semester	CFU	SSD
- A SCELTA DELLO STUDENTE		First semester	6
AAF1036 - FINAL EXAM	The final exam consists of the discussion of an advanced thesis, comprising a written document, possibly in English, which presents the results of an original study on a problem of an applicative, experimental or research nature.The preparation of the thesis is carried out under the guidance of an advisor (who can be a teacher of the advanced degree program, or of other Italian or foreign degree programs, or of an Italian or foreign research center) usually during the second year, requiring approximately half of the overall time effort.	Second semester	38
GRUPPO A AFFINI INTEGRATIVI		Go to group		FIS/05
GRUPPO B ASTRONOMICO OSSERVATIVO SPERIMENTALE		Go to group
GRUPPO C CARATTERIZZANTE ASTRONOMICO TECNOLOGICO		Go to group

Optional Groups

**GRUPPO A AFFINI INTEGRATIVI: The student must acquire 6 CFU from the exams below**
Course		Year	Semester	CFU	SSD
1044551 - OBSERVATIONAL COSMOLOGY	To know modern observational methods in cosmology. To be able to understand, elucidate and use specilisitic papers in observational cosmology. To know the main infrastructures available to obtain cosmological data. To know basic analysis techniques in observational cosmology.	First year	Second semester	6	FIS/05
1012184 - ASTRONOMICAL OPTICS	The course is aimed to review with the student the basics of geometrical optics and then to complete them with the introduction of fundamental optical parameters to define and so to quantify the characteristics and the quality of every astronomical telescope. The constraints on the final performance of a telescope will be verified within the physical optics and a few merit functions will be quantified to allow to comparisons of optical systems. The course will provide the student with the capabilities to analyse the current operating telescopes devoted to observing the sky at different spectral wavelengths, integrating the course of Astrophysics Laboratory. Moreover the introduction of a code for optical design and optimization enables the student to put into practice what has been studied during the lessons. In this way the student can start to work on an optical design from a paraxial approximation and than to analyse a telescope configuration among the existing ones. The student is motivated to work in a team and to report the results to his fellow students. This technical knowledge of optical design will be useful to find employment both in the private sector and in research.	First year	Second semester	6	FIS/05
1012137 - DYNAMICS OF STAR SYSTEMS	Providing a knowledge of astrophysical problems connected to the study of the gravitational potential. Such knowledge will leads the students to understand the calculation of a density profile starting from the gravitational potential and viceversa. Particular attention will be addressed to calculation of gravitational potential of a generic distribution of matter by a development in series of Legendre Polynomials.	First year	Second semester	6	FIS/05
1012136 - TEORICAL COSMOLOGY	The course aims to teach to the student mainly the theory of structures formation, both in the early stages of linear evolution and in the most advanced phases. At the same time, statistical methods will be analyzed to compare theoretical predictions with observational data. Finally, the student will learn the main elements of gravitational lensing, either the theoretical aspects, either its use in astrophysics and cosmology. At the end of the course the student should be able to place any topic of research in extragalactic astrophysics and in cosmology in a general framework that constitutes its scientific background. The course completes the knowledge provided by the course of Physical Cosmology, in which the student learns mainly the Big Bang theory that is the global evolution of the Universe, with the knowledge of the standard theory of formation of galaxies and clusters by gravitational instability. Together, these two courses should provide the future researcher in Cosmology with all the basics to tackle research in this field.	Second year	First semester	6	FIS/05
1012165 - SELF-GRAVITATING SYSTEMS	Providing a knowledge of astrophysical problems connected to equilibrium and stability of selfgravitating systems. Knowledge of basic statistical mechanics forstudying distribution functions to apply to gravitational equilibrium models. Analysis of formation and dynamical evolution of some astrophysical systems and calculation of equilibrium configurations with particular attention to stability problem in dynamic and thermodynamic regime. Analysis of gravothermal catastrophe by Lynden-Bell and Wood model and relationship with evolution of globular clusters.	Second year	First semester	6	FIS/05
1056018 - Chemical Evolution of the Universe	The main aim of these lectures is to address the main principles at the base of the origin and evolution of the elements in the Universe	Second year	First semester	6	FIS/05

**GRUPPO C CARATTERIZZANTE ASTRONOMICO TECNOLOGICO: The student must acquire 6 CFU from the exams below**
Course		Year	Semester	CFU	SSD
1012184 - ASTRONOMICAL OPTICS	The course is aimed to review with the student the basics of geometrical optics and then to complete them with the introduction of fundamental optical parameters to define and so to quantify the characteristics and the quality of every astronomical telescope. The constraints on the final performance of a telescope will be verified within the physical optics and a few merit functions will be quantified to allow to comparisons of optical systems. The course will provide the student with the capabilities to analyse the current operating telescopes devoted to observing the sky at different spectral wavelengths, integrating the course of Astrophysics Laboratory. Moreover the introduction of a code for optical design and optimization enables the student to put into practice what has been studied during the lessons. In this way the student can start to work on an optical design from a paraxial approximation and than to analyse a telescope configuration among the existing ones. The student is motivated to work in a team and to report the results to his fellow students. This technical knowledge of optical design will be useful to find employment both in the private sector and in research.	First year	Second semester	6	FIS/05
1012137 - DYNAMICS OF STAR SYSTEMS	Providing a knowledge of astrophysical problems connected to the study of the gravitational potential. Such knowledge will leads the students to understand the calculation of a density profile starting from the gravitational potential and viceversa. Particular attention will be addressed to calculation of gravitational potential of a generic distribution of matter by a development in series of Legendre Polynomials.	First year	Second semester	6	FIS/05
1012152 - ADAVANCED LABORATORY OF COMPUTING	This course is focused on the most important techniques adopted in order to solve system of ordinary differential equations that describe the physical processes at the base of most of the astrophysical systems. The students, continuosly followed by the professor, have the opportunity to develope, by themselves, numerical codes on linux based PC in order to test one, or more, numerical schemes described during the lectures.	Second year	First semester	6	INF/01
1044550 - METHODS OF SPACE ASTROPHYSICS	Give the student the basic knowledge to operate in the field of space astrophysics, with respect to theoretical, experimental and operative environment aspects. Give the students the basic knowledge from the point of view of measurements feasibility, activities planning, procedures and opportunities.	Second year	First semester	6	FIS/01

**GRUPPO B ASTRONOMICO OSSERVATIVO SPERIMENTALE: The student must acquire 6 CFU from the exams below**
Course		Year	Semester	CFU	SSD
1012129 - HIGH ENERGIES ASTROPHYSICS	The course is aimed at the comprehension and study of high energy emission from cosmic sources, compact objects in particular (i.e. white dwarfs, neutron stars and black holes of alla masses). An astrophysically-oriented approach is adopted in introducing and presenting themes at the forefront of research in this area. Topics of relevance to the study of gravitation in the strong field regime and of the properties of matter under extreme conditions (e.g. of density or magnetic field strength) are introduced and presented. Students acquire skills in the solution of problems through approximate calculations and estimates that are assigned to them. The preparation of a short essay and its presentation during the exam are aimed at fostering the students’ development of organisation and communication skills, as well critical thinking and independent judgment. The course teaches students how to carry out independent bibliographic searches and comprehend original publications on current research themes.	First year	Second semester	6	FIS/05
1012130 - EXTRAGALACTIC ASTROPHYSICS	To provide a complete view on the physical properties of extragalactic objects, like Galaxies, Active Galactic Nuclei, Clusters of Galaxies, Inter Galactic Medium, both in the local and in the high redshift Universe. To provide the skill needed to interpret the spectral emission and the morphological properties of these objects, in particular when observations from latest-generation telescopes are available. These issues will be discussed in the framework of the current cosmological scenario of structure evolution.	First year	Second semester	6	FIS/05
1044551 - OBSERVATIONAL COSMOLOGY	To know modern observational methods in cosmology. To be able to understand, elucidate and use specilisitic papers in observational cosmology. To know the main infrastructures available to obtain cosmological data. To know basic analysis techniques in observational cosmology.	First year	Second semester	6	FIS/05
1012184 - ASTRONOMICAL OPTICS	The course is aimed to review with the student the basics of geometrical optics and then to complete them with the introduction of fundamental optical parameters to define and so to quantify the characteristics and the quality of every astronomical telescope. The constraints on the final performance of a telescope will be verified within the physical optics and a few merit functions will be quantified to allow to comparisons of optical systems. The course will provide the student with the capabilities to analyse the current operating telescopes devoted to observing the sky at different spectral wavelengths, integrating the course of Astrophysics Laboratory. Moreover the introduction of a code for optical design and optimization enables the student to put into practice what has been studied during the lessons. In this way the student can start to work on an optical design from a paraxial approximation and than to analyse a telescope configuration among the existing ones. The student is motivated to work in a team and to report the results to his fellow students. This technical knowledge of optical design will be useful to find employment both in the private sector and in research.	First year	Second semester	6	FIS/05
10589158 - PLANETS AND EXOPLANETS	This module provides an introduction to the topics of detection and characterisation of planets orbiting stars other than the Sun. Current theories of planetary formation and evolution are also reviewed. Until 20 years ago, planets of our Solar System were the only known bodies orbiting a star. Today we know that on average every star in the Galaxy has at least one planet. Exoplanets present a diversity in their physical parameters that it is not observed in the Solar System. This present new challenges to modern Astrophysics in order to answer questions about planet formation and evolution, and about the uniqueness of our Solar System in the Galaxy. This module is for those students interested in acquiring an understanding of the field through the knowledge of observational and data analysis techniques used, the interpretation of the experimental evidences, and by reviewing current theories of planet formation and evolution. Aims: To introduce the theoretical concepts of planet formation and evolution To describe our Solar System as a reference case To discuss current research in exoplanetary science To describe the main challenges arising from exoplanetary observations To introduce observational and statistical methods applied to the detection of exoplanets and remote sensing of their atmospheres To describe the current and future astronomical facilities for the detection and characterisation of the exoplanet population in the Solar System neighbourhood	First year	Second semester	6	FIS/05
1012136 - TEORICAL COSMOLOGY	The course aims to teach to the student mainly the theory of structures formation, both in the early stages of linear evolution and in the most advanced phases. At the same time, statistical methods will be analyzed to compare theoretical predictions with observational data. Finally, the student will learn the main elements of gravitational lensing, either the theoretical aspects, either its use in astrophysics and cosmology. At the end of the course the student should be able to place any topic of research in extragalactic astrophysics and in cosmology in a general framework that constitutes its scientific background. The course completes the knowledge provided by the course of Physical Cosmology, in which the student learns mainly the Big Bang theory that is the global evolution of the Universe, with the knowledge of the standard theory of formation of galaxies and clusters by gravitational instability. Together, these two courses should provide the future researcher in Cosmology with all the basics to tackle research in this field.	Second year	First semester	6	FIS/05
1055885 - PARTICLE AND ASTROPARTICLE PHYSICS	- Achieve a thorough and updated understanding of the problems related to the physics of Cosmic Rays of high energy; - Thorough knowledge of the basic problems of astroparticle physics, the purposes of the scientific experiments currently underway or under construction; - Knowledge of modern instrumentation and observational techniques for experiments in astroparticle physics; - Knowledge of specific technical-scientific lexicon.	Second year	First semester	6	FIS/01
1055363 - EXPERIMENTAL GRAVITATION	The Physics Department of our university has a long tradition in the domain of the experiments in Gravitation. At present the main effort is represented by the construction the interferometric detector of Gravitational Waves Advanced VIRGO and the exploitation of the data already collected with the VIRGO detector. Other activities concerning the isolation of the equivalence principle, the setting of new limits for the PPN parameters or the astrophysical study of new sources of gravitational waves are carried on in the whole research area of Rome. We will discuss the experimental bases of the present theory of Gravitation complementing the course of General relativity and discussing one of the main topic of the Astroparticle Physics. In practice, by presenting the most important experiments of Gravitation carried on in the past and proposed for the future, the course permits to illustrate the most relevant strategies for the measurement of small forces.	Second year	First semester	6	FIS/01
1041552 - INTRODUCTION TO QUANTUM GRAVITY	Students will acquire a broad perspective on the research lines that compose the study of the quantum-gravity problem and will acquire the most basic techniques of analysis of each approach.	Second year	First semester	6	FIS/05
1044550 - METHODS OF SPACE ASTROPHYSICS	Give the student the basic knowledge to operate in the field of space astrophysics, with respect to theoretical, experimental and operative environment aspects. Give the students the basic knowledge from the point of view of measurements feasibility, activities planning, procedures and opportunities.	Second year	First semester	6	FIS/01
1012165 - SELF-GRAVITATING SYSTEMS	Providing a knowledge of astrophysical problems connected to equilibrium and stability of selfgravitating systems. Knowledge of basic statistical mechanics forstudying distribution functions to apply to gravitational equilibrium models. Analysis of formation and dynamical evolution of some astrophysical systems and calculation of equilibrium configurations with particular attention to stability problem in dynamic and thermodynamic regime. Analysis of gravothermal catastrophe by Lynden-Bell and Wood model and relationship with evolution of globular clusters.	Second year	First semester	6	FIS/05
1056018 - Chemical Evolution of the Universe	The main aim of these lectures is to address the main principles at the base of the origin and evolution of the elements in the Universe	Second year	First semester	6	FIS/05

Educational regulations

General rules

NG1 Admission requirements

To be admitted to the Master’s Degree in Astronomy and Astrophysics, students must have obtained the degree, the Bachelor’s Degree or any other suitable title of study got abroad. A good knowledge of classical and modern physics, of basic chemistry and of the necessary mathematical and IT tools is required. At all events, to be admitted to the Master’s Degree in Astronomy and Astrophysics, graduates must have acquired at least:

• overall 20 ECTS in mathematics and/or IT subjects (MAT/01-MAT/08, INF/01, ING-INF/05)

• 5 ECTS in chemistry subjects (CHIM/01-03 and CHIM/06),

• overall 65 ECTS in physics subjects (FIS/01-FIS/08), out of which at least

• 40 ECTS in Experimental physics (FIS/01),

• 12 ECTS in Theoretical physics, mathematical models and methods (FIS/02),

• overall 5 ECTS in Physics of matter and/or in Nuclear and subnuclear physics (FIS/03, FIS/04),

• a certificate attesting at least a B-1 English level (according to the QCER, the Common European Framework of Reference for Languages) or equivalent. The achievement of an English language qualification in a university study programme (Bachelor’s or Master’s Degree) that equals at least 3 ECTS is considered as an equivalent qualification.

Students who do not have such curricular requisites may enrol in single programmes, as provided for by the University Programme Manifesto, and sit the relating exams before enrolling in the Master’s Degree.

Also Sapienza students and those coming from different universities who have not graduated yet may apply to enrol in the Master’s Degree Programme, it being understood that they will have to get the degree within the deadline indicated in the University Programme Manifesto. In addition to the above procedures, such students shall also apply to the Student Office within the deadline indicated in the University Programme Manifesto, in order to be enrolled after graduation.

NG2 Test for incoming students

The skills of incoming students will be tested by a special committee, that will assess any similarities among scientific disciplinary sectors and/or automatically approve the students’ admission to the Master’s Degree in Astronomy and Astrophysics, provided that they have acquired at least:

• 25 ECTS in mathematics subjects (MAT/01-MAT/08),
• 5 ECTS in chemistry subjects (CHIM/01-03 and CHIM/06),
• 50 ECTS in Experimental physics (FIS/01),
• 20 ECTS in Theoretical physics, mathematical models and methods (FIS/02),
• 5 ECTS in Physics of matter or in Nuclear and subnuclear physics (FIS/03 or FIS/04),
• 12 ECTS in Astronomy and Astrophysics (FIS/05).

Such special committee will interview the other students to assess their possession of the required skills.

NG3 Changes of degree programmes, transfers from other universities, programme shortening, ECTS recognition

NG3.1 Changes of degree programmes and transfers from other universities

The applications to change a degree programme, submitted by students coming from other Sapienza master’s degree or single-cycle degree programmes and the applications for transfers from other universities, military academies or other higher education military institutions, are subject to the approval of the Programme Area Council that:

• resolves upon the total or partial recognition of the student’s academic records and validates the entirety or part of the exams passed and the ECTS acquired, if any, with the relating marks; in the event of changes from study programmes belonging to the same class pursuant to former Ministerial Decree no. 270, at least 50% of the ECTS acquired in each scientific disciplinary sector shall be recognised (art. 3, paragraph 9, of Ministerial Decree of Master’s Degree classes);

• indicates the academic year which the student is enrolled in;

• establishes the additional learning requirements, if any, to be fulfilled;

• formulates the study plan for the achievement of the degree.

If students, according to the recognised academic records, are admitted to a year following those provided for by the current academic system, they may opt to enrol either in the corresponding year of the old academic system or in the most advanced year then existing of the current academic system (art. 33, paragraph 5, of the University Educational regulations).

Applications for transfers to the Master’s Degree in Physics shall be submitted within the deadline and according to the modalities specified in the University Programme Manifesto.

NG3.2 Programme shortening

Students who have already achieved a four-year, five-year or single cycle degree according to the old academic system, or a master’s degree according to the current academic system and intend to get an additional degree, may request from the Programme Area Council to be enrolled in an academic year subsequent to the first one.

Such applications are assessed by the Programme Area Council, that:

resolves upon the total or partial recognition of the student’s academic records and validates the entirety or part of the exams passed and the ECTS acquired, if any, with the relating marks; in the event of changes from study programmes belonging to the same class pursuant to former Ministerial Decree no. 270, at least 50% of the ECTS acquired in each scientific disciplinary sector will be recognised (art. 3, paragraph 9, of Ministerial Decree of Master’s Degree classes);
indicates the academic year which the student is enrolled in;
establishes the additional learning requirements, if any, to be fulfilled;
formulates the study plan for the achievement of the degree.

Students cannot enrol in a Master’s Degree Programme falling within the same class of the master’s degree they have already achieved.

Applications shall be submitted within the deadline and according to the modalities specified in the University Programme Manifesto.

NG3.3 Criteria for ECTS recognition

All the already acquired ECTS may be recognised if they concern courses, substantiated by the course programmes, whose contents are consistent with any of the curricula provided for by the Master’s Degree Programme. For changes from study programmes of the same class, minimum 50% of the ECTS acquired in each scientific disciplinary sector will be recognised.

The Programme Area Council may resolve upon the equivalence among scientific disciplinary sectors to recognise ECTS according to the contents of courses and in compliance with the Educational regulations of the Master’s Degree Programme.

The already acquired ECTS relating to courses whose contents, though with a different name, are clearly equivalent to any courses of the Master’s Degree Programme, may be recognised as relating to the courses typical of the master’s degree programme which a student wishes to enrol in. In this case, the Programme Area Council resolves upon the recognition according to the following modalities:

- if the number of ECTS corresponding to the course for which the recognition is requested coincides with that of the recognised course, they are directly awarded;

- if the number of ECTS corresponding to the course for which the recognition is requested is different from that of the recognised course, the Programme Area Council will award ECTS according to the student’s academic records, also for groups of exams belonging to the same scientific disciplinary sector, and after some additional interviews, if required.

The Programme Area Council may recognise as ECTS the knowledge and professional skills certified pursuant to the regulations in force on the matter, as well as other kinds of knowledge and skills accrued in academic-level training whose planning and implementation the University has contributed to. Such ECTS are included in the 12 ECTS relating to the students’ elective courses. At all events, 12 are the maximum recognisable ECTS in such fields. The activities already recognised as ECTS-awarding in the degree programme cannot be recognised also for the Master’s Degree Programme.

NG4 Curricular study plans and individual study plans

Students have to obtain the official approval of their study plan by the Programme Area Council (by means of an on-line procedure to be used both to submit the application and to obtain the receipt of the notice of approval) before having recorded the exams relating to courses that are not mandatory for all students.

Students may obtain such approval by opting between two alternatives:

1. either choosing one of the curricular study plans established every year by the Programme Area Council; or

2. submitting an individual study plan that shall be assessed by the Programme Area Council for approval.

NG4.1 Curricular study plan

A curricular study plan has to abide by the regulations of the Degree Programme Manifesto. The webpage relating to a curricular study plan includes the list of all the courses of the curriculum chosen by students and a special box where they must indicate the courses relating to their elective 12 ECTS (an increase up to maximum 15 ECTS is allowed). The elective ECTS may be chosen among all those included in the Sapienza Course Catalogue.

The enrolment form must be submitted online, according to the new IT enrolment procedure provided by Sapienza University and by the Programme Area Council. For further information please contact the Educational Affairs Office.

The enrolment form has to be submitted online on the dates indicated by Sapienza University. Such form will be forwarded by the Educational Affairs Office to the Director of the Programme Area Council and to the person in charge of approval, so that the consistency of the elective courses with the curriculum may be assessed. Should this check be successful, the curricular study plan is approved; otherwise, students are invited by the Educational Affairs Office to amend the list of the elective courses.

From the day following the approval of the Programme Area Council, students are allowed to sit all the mandatory and non-mandatory exams listed in the study plan of choice and to have them recorded.

The choice of a curricular study plan may be made only once in an academic year, starting from the second year.

NG4.2 Individual study plan

The individual study plan has to abide by the regulations of the Degree Programme Course Catalogue.

The form to enrol in an individual study plan has to be submitted online on the dates decided by Sapienza University and by the Programme Area Council. Such form will be forwarded by the Educational Affairs Office to the Director of the Programme Area Council and to the person in charge of approval in order to be assessed. Should this check be successful, the individual study plan is approved; otherwise, students are invited by the Educational Affairs Office to amend it.

From the day following the approval of the Programme Area Council, students are allowed to sit all the mandatory and the non-mandatory exams listed in the approved study plan and to have them recorded.

The submission of an individual study plan may be made only once in an academic year, starting from the second year.

If students come from other degree programmes, from a programme shortening or transfer from other universities, they have to submit an individual study plan by means of a special online form. For further information please contact the Educational Affairs Office.

NG4.3 Change of curricular study plans and of individual study plans

Students whose study plan, either curricular or individual, has been already approved, may submit a new one, either curricular or individual, in a following academic year.

At all events, the exams already recorded cannot be changed and the consistency of the new individual study plan will be previously assessed by the Programme Area Council.

NG5 Educational activities

Educational activities are conventional and divided in semesters.

Teaching activities include lectures, classroom exercises and lab activities, all organised according to a timetable that enables students to have sufficient time to devote to individual study.

The nominal duration of a Master’s Degree Programme is 4 semesters, equal to two years.

NG5.1 University ECTS

The university ECTS measure the student’s workload needed to achieve a learning outcome. ECTS are acquired by students after passing exams or obtaining qualifications, if provided.

The European Credit Transfer System adopted in the Italian and European universities provides that one ECTS is equivalent to 25 hours of work, divided between institutional collective educational activities (i.e., lectures, exercises and lab activities) and individual study.

In the Astronomy and Astrophysics Master’s Degree Programme, in compliance with art. 23 of the University Educational regulations, one ECTS equals 8 hours of lecture or 12 hours of laboratory or of exercises supported by a teacher.

The syllabus of each course, that is available on the Degree Programme website, indicates the apportionment of ECTS and hours of lecture according to the different activities, together with the requirements, learning outcomes and general programmes.

The overall workload to achieve the degree is 120 ECTS.

In the Astronomy and Astrophysics Master’s Degree Programme, the individual study or other individual educational activities shall account for at least 50% of the student’s overall workload.

NG5.2 Academic calendar

The usual schedule is the following:

• first semester: end of September - January;
• first session of exams: February;
• second semester: March - June;
• second session of exams: July;
• third session of exams: September.

Further details about the start and end dates of lectures in each semester and of each session of exams are available on the Degree Programme website. Terms devoted to lectures and to exams cannot overlap.

NG5.3 Exams

The assessment of the students’ acquired skills is made by means of oral exams, sometimes preceded by a written or an individual lab test. The assessment is expressed per each course by assigning students a mark, given in thirtieths, ranging from 18 (minimum) to 30 (maximum).

NG6 Attendance, mandatory preliminary exams, admission to following years

Regular attendance to all courses is essential to help students’ profitable integration in the Degree Programme organisation and is therefore highly recommended. Attendance to lab activities provided for the Astrophysics Laboratory course is mandatory.

No mandatory preliminary exams are provided in the study programme. At all events, the arrangement of courses in the curriculum is a clear indication of the most recommended sequence with which to attend them and sit the relating exams.

NG7 Part-time learning

Terms and modalities to apply for part-time learning as well as the relating rules are established in the University Programme Manifesto and are available on Sapienza website.

NG8 Irregular students and validity of the acquired ECTS

In compliance with the University Programme Manifesto, that is available on Sapienza website, students are deemed as being irregular when, though having attended all the educational activities provided for by these Educational regulations, they have not passed all the exams and have not acquired the number of ECTS required for the achievement of the degree within two years.

In compliance with the University Programme Manifesto:

- full-time students who are irregular will have to pass the exams still lacking to complete their university career within six years after enrolment;

- part-time students who are irregular will have to pass the exams still lacking to complete their university career within twice as many years as those agreed upon for part-time students.

Regardless of the above terms, the Programme Area Council may request from students to undergo an interview in which the skills relating to the ECTS acquired more than 9 years before the expected date of degree will be assessed.

NG9 Tutorship

Students of the Master’s Degree Programme in Astronomy and Astrophysics may benefit from the tutorship provided by the teachers indicated by the Programme Area Council, by submitting any time a special request to the Educational Affairs Office. The name of any further teachers available as tutors and the tutorship modalities will be published each academic year at the Educational Affairs Office and on the Degree Programme website.

NG10 Honours Programmes

The Programme Area Council in Physical sciences and technologies, Physical sciences and Sciences of the universe institutes an Honours Programme for the Master’s Degree Programme in Astronomy and Astrophysics aimed at enhancing the skills of the most deserving students.

The Honours Programme provides students with educational activities additional to the standard study programme which they are enrolled in. Such activities are curricular and cross-curricular studies, seminars and internships chosen within the courses of the relating degree class, according to a programme that will be tailor-made and agreed upon with each of them. Students admitted to the Honours Programme will be assigned to a teacher or a tutor appointed by the Director of the Programme Area Council, who will support and will cooperate with them in the organisation of the agreed upon activities. The students’ maximum annual workload will be 200 hours and will include the drawing up of a final report.

The Erasmus students who perform part of their curriculum at a foreign university and are admitted to the Honours Programme may attend part of such Programme at the hosting university.

Students may be admitted to the Honours Programme by applying to the Programme Area Council after publication of the call, upon completion of the first year of the Degree Programme. The essential requirements are:

• acquisition of all the ECTS required for the first year within November 30;

• attainment of a weighted average of the examination marks not lower than twenty-seven/thirtieths (27/30).

In order to go on with the Honours Programme, students have to acquire all the ECTS required for the year of attendance within October 31 with a weighted average of marks not lower than twenty-seven/thirtieths (27/30). The Programme Area Council will check the above mentioned requirements at the end of the reference academic year based on a report issued by the teacher. Upon achievement of the Master’s Degree, students who have completed the Honours Programme will be awarded a certificate issued by the Faculty Dean, according to the modalities provided for all the other certificates, that will be recorded on the students’ academic records. Together with the above certificate, the University will award students a prize equal to the amount of the tuition fees paid in the last academic year.

Terms and modalities to apply for an Honours Programme and further information about the call are available on the Degree Programme website, from which the facsimile of the application form may also be downloaded.

NG11 Degree exam

To be admitted to the degree exam, students must have acquired all the ECTS provided for by the academic system for activities other than the degree exam and must have abode by the administrative formalities provided for by the University Educational regulations and the University Programme Manifesto.

The degree exam consists in the preparation and discussion of a thesis, preferably written in English, either theoretical or experimental, to be presented to the examination committee. A thesis is assigned to students at the beginning of the second year of the study programme, is drawn up under the guidance of a supervisor (a teacher of the Degree Programme, of other Italian or foreign degree programmes or a researcher of an Italian or foreign research institution) and is submitted by the candidates to the examination committee upon completion of their study programme.

The final mark is awarded by taking into account the candidate’s academic records, the thesis work and its presentation as well as any further elements aimed at considering the candidate’s getting through the exams in the due times established by the academic system. The examination committee gives the final mark in one hundred tenths and may unanimously award the candidate the highest mark magna cum laude.

NG12 Application of art. 6 of the Student Regulations (Royal Decree of June 4, 1938, no. 1269)

Students enrolled in the Master’s Degree Programme in Astronomy and Astrophysics may enrol, each academic year, in two additional courses of a different faculty and sit the relating exams in order to enrich their study plan, pursuant to art. 6 of Royal Decree of June 4, 1938, no. 1269. Students have to send in the application together with a self-certification of the exams passed to the Educational Affairs Office, that in turn will submit it to the Programme Area Council. The same application may be then submitted to the Student Office of the Faculty of Mathematical, Physical and Natural Sciences within January of each year. Such exams must not be included in the study plan.

Considering the scientific and cultural meaning of such rule, the Programme Area Council resolved that such application may be filed only by students who have acquired at least 21 ECTS in the first year courses of the Master’s Degree Programme in Astronomy and Astrophysics.

Description of curriculum

Educational activities are conventional and are distributed in semesters. The usual schedule is the following:

• first semester: end of September - January;
• first session of exams: February;
• second semester: March - June;
• second session of exams: July;
• third session of exams: September.

Further details of the start and end dates of the lectures of each semester and of each session of exams are available on the Degree Programme website.

Teaching activities include lectures, classroom exercises and lab activities, all organised according to a timetable that enables students to have sufficient time to devote to individual study. The nominal duration of the Master’s Degree Programme is 4 semesters, equal to two years, during which students have to acquire 120 ECTS, equal to 3,000-hour overall workload. Knowledge will be usually assessed by means of oral exams and, for some courses, by means of written or practical (lab) tests, according to the modalities indicated in the syllabus of each course.

Regular attendance to all courses is essential to help the students’ profitable integration in the Degree Programme organisation and is therefore highly recommended. Attendance to lab activities provided for the Astrophysics Laboratory course is mandatory.

No mandatory preliminary exams are provided. At all events, the arrangement of courses in the curriculum is a clear indication of the most recommended sequence with which to attend them and sit the relating exams.

The Master’s Degree students submit their study plan at the beginning of the first year, by choosing the optional exams in a provided group and the elective exams (12 ECTS). The rules governing curricula are set forth in the University Educational regulations of the study programme. Upon completion of their curriculum, students shall also obtain an English language qualification to demonstrate that they have a fluent knowledge of both written and oral English.

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