Course topics:
Origins of Ancient Greek architecture: materials, technology and the development of the Doric order; The Ionic order and the relationship with the Middle East; The Panhellenic sanctuaries: Olympia and Delphi; Classical Athens and Attica; Roman architecture at the end of the Republican era in the sanctuaries of Latium and in the City; Augustus and the transformation of the Republic; The Roman Empire and its image: The Imperial Fora; The search for consensus: Theatres, amphitheatres and the thermal structures; The imperial residences; Dome of the Heaven: from Pantheon to Hagia Sophia; From Early Christian architecture to Romanesque architecture in France and Italy; Gothic architecture: tradition and innovation between East and West; Frederick II and Arnolfo di Cambio: Origins of the Renaissance; F. Brunelleschi and L. B. Alberti; Donato Bramante in Milan and Rome; Antonio da Sangallo the Younger and the development of the Roman palace; Mannerism and Michelangelo; The rebuilding of St. Peter's basilica; The church architecture and the Catholic Reformation; The rebirth of the villa in Rome; Andrea Palladio and the Venetian villas.
FOR A CRONOLOGY OF THE MAIN MONUMENTS:

https://www.academia.edu/16882678/Corso_di_Storia_dellArchitettura_1_B_Roma_Tre_University_Department_of_Architecture

C. BOZZONI, V. FRANCHETTI PARDO, G. ORTOLANI, A. VISCOGLIOSI, L’Architettura del mondo antico, ROMA – BARI 2006 (LATERZA);
C. L. FROMMEL, L’Architettura del Rinascimento Italiano, MILANO 2009 (SKIRA).

Si consigliano approfondimenti in rete, soprattutto per visualizzare immagini, ad esempio sul sito Academia.edu:

https://uniroma3.academia.edu/GiorgioOrtolani
https://www.academia.edu/10108262/Origini_dell_architettura_greca_in_Architettura_del_mondo_antico
https://www.academia.edu/403458/Ortolani_Lavorazione_di_Pietre_e_Marmi_nel_Mondo_Antico_in_Marmi_antichi
https://www.academia.edu/6245510/Spazio_funzioni_e_paesaggio_nei_santuari_a_terrazze_italici_di_et%C3%A0_tardo-repubblicana._Note_per_un_approccio_sistemico_al_linguaggio_di_una_grande_architettura
https://www.academia.edu/39095606/Estratto_dal_Fascicolo_N._30_-aprile-giugno_2016_Serie_VII_CAIROLI_FULVIO_GIULIANI_-ALESSANDRA_TEN_SANTUARIO_DI_ERCOLE_VINCITORE_A_TIVOLI_III._LARCHITETTURA?email_work_card=interaction_paper
https://www.academia.edu/9942239/F._G._Cavallero_11._Foro_di_Augusto_in_A._Carandini_P._Carafa_a_cura_di_La_Roma_di_Augusto_in_100_monumenti_pp._73-77
https://www.academia.edu/440373/Il_cantiere_del_Colosseo
https://www.academia.edu/14759478/_Who_Built_the_Pantheon_Agrippa_Hadrian_Trajan_and_Apollodorus_in_Hadrian_Art_Politics_and_Economy_ed._Thorsten_Opper_British_Museum_Research_Publication_175_London_2013_31-49
https://www.academia.edu/346513/INNOVATIVE_SOLUTIONS_IN_THE_ORGANIZATION_OF_CONSTRUCTION_PROCESS
https://www.academia.edu/16339032/Walking_on_Water_Cosmic_Floors_in_Antiquity_and_the_Middle_Ages
https://www.academia.edu/5353212/Rinascit%C3%A0_a_Roma_nell_Italia_Carolingia_e_meridionale_in_S._de_Blaauw_ed._Storia_dellArchitettura_Italiana_Da_Costantino_a_Carlo_Magno_Electa_Milano_2010_pp._322-373
https://www.academia.edu/9827610/Vitruvio_Piero_della_Francesca_Raffaello_note_sulla_teoria_del_disegno_di_architettura_nel_Rinascimento_Annali_di_architettura_14_2002_pp._35-54
https://www.academia.edu/3126385/Palladio
https://www.academia.edu/25458244/Italian_Architecture_from_Michelangelo_to_Borromini_London_T_and_H_2002

WE WILL USE THE PRINCIPLES OF DESCRIPTIVE GEOMETRY TO ILLUSTRATE THE GEOMETRIC MODEL OF AN OBJECT BASED ON THE PREMISE THAT DESCRIPTIVE GEOMETRY IS REQUIRED TO UNDERSTAND THREE-DIMENSIONAL SPACE, TO ANALYSE AND RECREATE AN OBJECT WHETHER IT BE A DETAIL, A BUILDING OR AN URBAN SPACE. THE MAIN AIM OF THE COURSE WILL BE TO TEACH STUDENTS HOW TO UNDERSTAND THE SPACE, DIMENSIONS AND PROPORTIONS OF THE OBJECTS STUDIED USING THE VARIOUS METHODS IN A COMPLEMENTARY MANNER.
DESCRIPTION OF THE COURSE. THE COURSE WILL BE DIVIDED INTO TWO CLOSELY-RELATED PARTS: A THEORETICAL PART WHERE STUDENTS WILL BE PROVIDED WITH INFORMATION AND TAUGHT THE PRINCIPLES AND RULES GOVERNING ARCHITECTURAL REPRESENTATION AND DESIGN, AND A PRACTICAL PART WHERE THEY WILL CARRY OUT AD HOC AND EXTEMPORE EXERCISES AND EXAMINE THE GEOMETRIC AND PROJECTIVE CHARACTERISTICS OF SEVERAL DRAWINGS. USING REPRESENTATION METHODS, ORTHOGONAL PROJECTIONS, AXOMETRIC PROJECTIONS AND PERSPECTIVE WE WILL DESCRIBE GEOMETRIC PROPERTIES, PARALLELISM, INTERSECTION AND DETERMINE THE REAL DIMENSION AND FORM OF PLANE FIGURES. SPECIAL ATTENTION WILL BE GIVEN TO SECTIONS AND THEIR GEOMETRIC CONSTRUCTION AS WELL AS THE PLANE DEVELOPMENT OF THREE-DIMENSIONAL FIGURES SO THAT THEY CAN BE MANUALLY RECREATED. A BRIEF HISTORY OF REPRESENTATION METHODS WILL BE PROVIDED AND THE DRAWINGS OF SEVERAL AUTHORS WILL BE ANALYSED. IN PARTICULAR THE FOLLOWING WILL BE STUDIED: DOUBLE ORTHOGONAL PROJECTION METHOD, (CONSTRUCTION OF BASIC GEOMETRIC ELEMENTS) – REPRESENTATION OF POINTS, STRAIGHT LINES AND PLANES – PROJECTION AND INTERSECTION, THE MEASUREMENT OF SLOPE ANGLES AND THE TRUE FORM OF A PLANE FIGURE – PLANE DEVELOPMENT –SOLIDS OF REVOLUTION – THE SECTIONS OF VOLUMES AND SIMPLE ARCHITECTURAL BODIES AND THE INTERSECTION BETWEEN DIFFERENT VOLUMES, THE THEORY OF SHADOWS. THE REPRESENTATION OF MAJOR GEOMETRIC ELEMENTS IN AXONOMETRIC PROJECTION: POINTS, STRAIGHT LINES AND PLANES, OBLIQUE, MILITARY AND CAVALIER PROJECTIONS – RELATIONSHIP OF HOMOLOGICAL RELATIONSHIPS, ESTABLISHMENT OF THE TRUE FORM OF A FIGURE, ORTHOGONAL AXONOMETRIC PROJECTION DIRECT CONSTRUCTION – REFERENCE ELEMENTS – PROBLEMS OF INTERSECTION – AXONOMETRY OF SOLIDS – GRAPHIC CONSTRUCTION OF VAULTED CEILINGS: CROSS VAULTS AND CLOISTER VAULTS.
SPATIAL GENESIS OF REFERENCE ELEMENTS IN PERSPECTIVE – REPRESENTATION OF BASIC GEOMETRIC ELEMENTS – POINTS, STRAIGHT LINES, PLANES – GEOMETRIC PROPERTIES, PARALLELISM, PERPENDICULARITY – POINTS OF MEASUREMENT OF STRAIGHT LINES, ANGLES – CONCLUSIVE PROCEDURES OF PERSPECTIVE – VERTICAL, HORIZONTAL AND OBLIQUE PLANE PERSPECTIVE – PROBLEMS OF INTERSECTION AND TRUE FORM CONSTRUCTION AND MEASUREMENT OF ANGLES PERSPECTIVE RESTITUTION.

CANCIANI M., I DISEGNI DI PROGETTO, COSTRUZIONI, TIPI E ANALISI, DE AGOSTINI, TORINO, 2009.
CANCIANI M., IL DISEGNO IN PROSPETTIVA, ANALISI, ELEMENTI FONDAMENTALI, METODI RISOLUTIVI E TIPI, KAPPA, ROMA 2005.
DOCCI M., MAESTRI D., SCIENZA DEL DISEGNO, UTET, TORINO 2000.

quantifiers. Numbers: natural, integers, rational and real. Axioms of real numbers.
Cartesian coordinates in the plane. Points and vectors. Distance: formal definition. Absolute value. Density of Q in R.
Linear algebra: vector sum, scalar product. Matrices. Matrix operations of sum and product, determinant, rank of a matrix.
Matrix representation of linear transformations. Geometric meaning of the determinant.
Rotation matrices and omotethy. Parametric equation of the line. Orthogonality conditions.
Introduction to real functions. Graphs.Q
Working with graphics, absolute value of a graph. Exponential, logarithm of a function for which you know the plot.
Accumulation points. Limits. Operations with limits. Comparison theorem. Continuous functions. Theorems on continuous functions.
Asymptotes. Derivatives: definition, geometric meaning. Operations: sum, product, quotient, scalar product. Main rules of derivation. Equation of the tangent line at a point to the graph.
Derivative of a composite function and inverse functions. Stationary points.
Fermat's theorem. Theorems of Rolle and Lagrange. Monotony and sign of the first derivative.
Second derivatives, concavity, inflections. Plotting graphs of functions. Theorems of Cauchy and De l'Hopital. Word problems.
Taylor polynomial. Formula of the rest of Lagrange. Hyperbolic functions, conic sections as geometric loci. Classification of conic sections.
Introduction to the problem of calculating the area of a flat region. The fundamental theorem of calculus, definite integrals.
The theorem of the average. Integration by parts and substitution. Integration of rational functions.
Definition of parametric curve. From parametric to cartesian equations and viceversa.
Examples: circumference cycloid, conical. Vector and unit vector tangent vector and the unit vector normal. Length of a curve. Curvature

G.B. THOMAS, R.L. FINNEY ELEMENTI DI ANALISI MATEMATICA E GEOMETRIA ANALITICA ED. ZANICHELLI

Bramanti, Pagani, Salsa “Analisi Matematica 1. Con elementi di geometria e algebra lineare”, Zanichelli

Naldi, Pareschi, Aletti “calcolo differenziale e algebra lineare”, Ed. Mc Graw-Hill

ROBERT A. ADAMS CALCOLO DIFFERENZIALE IED. CEA (CASA EDITRICE AMBROSIANA)

COURANT, ROBBINS "CHE COS' È LA MATEMATICA?" ED. BORINGHIERI

Drawing proposes itself as a quest for an individual aesthetics, one which is subjective, which is one’s own and in some sense unique; and hence a conquest of one’s own autonomy, of one’s own freedom of expression. Graphic operations have, as a matter of fact, the quality of indissolubly marrying execution techniques, understood as manual operability, and abstract thought. From this marriage flows the exceptional condition of drawing as concerning all of the arts, and in some way as well, the multidisciplinarity of its teachings which run through all of the professional training or university degrees in the creative disciplines. Drawing should be understood, in keeping with its most ancient academic traditions, as a project metalanguage (shared amongst the arts), namely how to know that which concerns the figurative dimension - and hence communicative (representative) of architectonic construction. Learning how to draw contributes, in the didactic process, to the formation of a precise figurative culture of architecture and is inescapably situated between design and history. This course proposes to deepen, to experiment with techniques of representation, aimed at the knowledge, reading, direct surveying, analysis, and conception of architecture. One shall not be able to draw flawlessly in the little time at our disposal; the practice of drawing and the learning of this is an absorbing and constant effort which one must do on one’s own and which should accompany us throughout our entire life; the course shall however seek to lay the groundwork which shall allow you to understand and strengthen your own expressive modalities through drawing: and to apply the various techniques, thanks to the direct and practical indications given during the supervised practice sessions, by means of the study, observation and the redrawing of the emblematic cases of both classical as well ascontemporary architecture and art. Through these practice sessions, the definition of your own graphic expressivity shall be furthered, thus helping you to grasp how crucial drawing is in order to express your own ideas as well as for the project. Studying texts dedicated to the masters of architecture, from
Palladio to Aldo Rossi, from Leonardo to Le Corbusier, our running from sketches to the more aseptic computerized renderings, is a kind of knowledge, which is absolutely indispensable for the architect in order to carry out the precise rendering of his or her own ideas. That architecture is learnt and communicated by drawing architectures is for all intents and purposes obvious, but not at the same time the consciousness of drawing as the expression of the mind and soul. The first part of the course shall therefore deepen knowledge of free hand drawing, a procedure which alludes to the past but which has also has illustrious contemporary admirers, and a particular space shall be dedicated to drawing from reality, to the sketches, to prospective drawing and on-sight relief. In the second part we shall experiment with the various techniques of contemporary representation and not, as a complex exercise in the interpretation of reality, we shall pass from ink to pencil, from charcoal crayon to watercolours, from sanguines to pantones on supports which differ from time to time. Every lesson shall be preceded by practice sessions conducted in the classroom or outside in the presence of a teacher who shall provide practical clarifications on the execution. Intermediate verifications will take place and attendance in the lessons and in the practice tasks is required.

- G. De Fiore, Storia del disegno, Milano 1997
- M. Docci e D. Maestri; Scienza del disegno, Torino 2000
- aa.vv., Il disegno dell' architettura fra tradizione e innovazione, Roma 2002

Students (individual or in groups of two) will be involved in the project of a small public building - a museum - in the former slaughterhouse in Testaccio. The museum architecture, beyond its specialized aspects, appears particularly well qualified to experience the first approach to a complex building, for its aesthetic and functional constraints, for the presence of different uses, and for his close relationship with public space. From this point of view, locating in the former slaughterhouse is focusing on familiarity that students have with the place, in order to implement the project with the experience already acquired in terms of measures and use of space, as well as relationships with the urban context.
We will alternate lectures, focus upon individual design aspects, laboratory work, exercises on specific issues, with the aim to advance the student's architectural skills and the representation / presentation of their ideas. There will be periodic connections and shared experiences with the two parallel courses.

- Patricia Cummings Loud, Louis I. Kahn. I musei, Electa, Milano 1997.
- Giovanni Longobardi, Musei. Manuale di progettazione, Mancosu, Roma 2007.

Students (individual or in groups of two) will be involved in the project of a small public building - a museum - in the former slaughterhouse in Testaccio. The museum architecture, beyond its specialized aspects, appears particularly well qualified to experience the first approach to a complex building, for its aesthetic and functional constraints, for the presence of different uses, and for his close relationship with public space. From this point of view, locating in the former slaughterhouse is focusing on familiarity that students have with the place, in order to implement the project with the experience already acquired in terms of measures and use of space, as well as relationships with the urban context.
We will alternate lectures, focus upon individual design aspects, laboratory work, exercises on specific issues, with the aim to advance the student's architectural skills and the representation / presentation of their ideas. There will be periodic connections and shared experiences with the two parallel courses.

- Patricia Cummings Loud, Louis I. Kahn. I musei, Electa, Milano 1997.
- Giovanni Longobardi, Musei. Manuale di progettazione, Mancosu, Roma 2007.

THE PURPOSE OF THE WORKSHOP ARE INTENDED FOR THE STUDENTS TO ACQUIRE ESSENTIAL CONCEPTS AND KNOWLEDGE TO CHECK THE DESIGN OF THE ELEMENTS OF THE BUILDING, TO DEVELOP THE BEST EXPERTISE IN CRITICAL ASSESSMENT TO IDENTIFY THE MOST PROPER CONSTRUCTION CHOICES.
THE ACTIVITIES OF THE LABORATORY IS AIMED TO DEVELOP CRITICAL AWARENESS TO THE INTERACTIONS BETWEEN THE FUNCTIONAL SUITABILITY, THE EXPRESSIVE COHERENCE, THE RELATIONSHIP WITH THE CONTEXT, BOTH FROM THE POINT OF VIEW OF THE ENVIRONMENT, THAT FROM THE POINT OF VIEW OF ENERGY, AND THE CHOICES OF BUILDING MATERIALS AND CONSTRUCTION TECHNIQUES.
STUDENTS ARE DRIVEN TO THE IDENTIFICATION OF DESIGN STRATEGIES TRADITIONAL OR INNOVATIVE DESIGN STRATEGIES, AIMED TO THE DEFINITION OF A SYNERGY BETWEEN THE SHAPE OF THE BUILDING AS AN EXPRESSION OF THE ARCHITECTURAL CULTURE AND THE OPTIMIZATION OF ITS ENERGY BEHAVIOR, ALWAYS KEEPING THE CONTROL OF THE MORPHOLOGY, OF THE ORIENTATION AND OF THE MATERIALS.

LA MIA CASACLIMA, PROGETTARECOSTRUIRE E ABITARE NEL SEGNO DELLA SOSTENIBILITÀ, NORBERT LANTSCHNER, RAETIA

COSTRUIRE IN LEGNO, CRISTINA BENEDETTI, UNIVERSITY PRESS BOLZANO
MATERIALI E PROGETTO: IL FUTURO DELLA TRADIZIONE, CRISTINA BENEDETTI E VINCENZO BACIGALUPI, KAPPA