Author: Simona Ranieri

Linear Algebra and Geometry

Simona Ranieri 1 Year, 2 semester, 9 credits, Subjects
Linear Algebra and Geometry
1 YEAR 2 semester 9 CFU
Prof. Paolo Salvatore 2019-20
SALVATORE PAOLO –
LHOTKA CHRISTOPH HEINRICH		 2020-21
Francesca Tovena – tovena@mat.uniroma2.it
Andrea Santi

2021-22
2022-23

Andrea Santi (6)
Filippo Viviani (3)

 2023-24

Andrea Santi (6)
Francesca Carocci (3)

 2024-25

Andrea Santi (6 cfu) – santi@mat.uniroma2.it
Efthymios Sofos (3 cfu) –  sofos@mat.uniroma2.it

 2025-26
  Code: 8037949
SSD: MAT/03

LEARNING OUTCOMES

The course aims to provide an introduction to linear algebra and Euclidean analytical geometry.

KNOWLEDGE AND UNDERSTANDING: At the end of the course, the student is supposed to know the notions of vector space, linear combination, generated vector subspace, linear dependence and independence, basis, solution of a linear system, matrices and their rank, linear applications, kernel and image, diagonalisation of linear applications and quadratic forms, geometric subspaces and their position, conics and their classification criteria.

APPLYING KNOWLEDGE AND UNDERSTANDING:
At the end of the course, the student is supposed to be able to determine the rank of a matrix, to discuss the solvability and to solve linear systems with a finite number of indeterminates, to determine the dimension and a basis of subspaces of numerical spaces or geometric vectors, to apply the Gauss method of reduction, to represent linear applications between vector spaces of finite dimension and to determine their kernel and image, to discuss the diagonalisation of square matrices and to diagonalise them, to represent linear geometric subspaces and their intersections/subspaces in parametric and Cartesian form, to classify plane conics, to represent and classify quadratic forms, to apply the notions of linear algebra to the study of geometric situations and vice versa.

MAKING JUDGEMENTS: The student will be able to discuss and verify the correctness of reasoning involving the studied notions of linear algebra and Euclidean analytic geometry. The student will also be able to apply linear algebra in solving problems in affine and Euclidean geometry.

COMMUNICATION SKILLS: The student will be able to explain and discuss the solution of problems; he/she will also be able to discuss and correctly reproduce definitions and demonstrations of results related to vector spaces, affine and Euclidean spaces.

LEARNING SKILLS: The student will be able to read and learn by himself more advanced topics of linear algebra related to solving linear systems and matrix decompositions useful for numerical applications.

Syllabus – Linear Algebra and Geometry

Part I – Linear Algebra

  1. Vector Spaces and Subspaces

    • Vector spaces and subspaces.

    • Linear dependence and independence.

    • Steinitz’s theorem.

    • Bases and dimensions.

    • Sum and intersection of vector subspaces.

    • Grassmann formula.

  2. Linear Applications

    • Linear applications.

    • Image, kernel and rank of a linear application.

    • The group of automorphisms of a vector space.

  3. Matrices and Rank

    • Matrices and rank of a matrix.

    • Gauss method for calculating the rank.

  4. Linear Systems

    • Linear systems.

    • Compatible systems.

    • Rouche–Capelli theorem.

    • First and second uniqueness theorems.

    • Parameter dependent systems.

    • Solving a linear system with Gauss elimination.

    • Reduced systems.

  5. Matrices and Linear Applications

    • Relation between matrices and linear applications.

    • Invertible matrices.

    • Orthogonal matrices.

    • Change of basis.

  6. Determinants

    • Definition, calculation methods, and applications.

    • Binet’s theorem.

    • Kronecker’s theorem.

    • Cramer’s theorem.

  7. Complex Numbers

  8. Diagonalization and Orthogonality

    • Diagonalization of matrices.

    • Positive definite scalar products.

    • Gram–Schmidt orthogonalization algorithm.

    • Spectral theorem.

Part II – Geometry

  1. Affine and Euclidean Spaces

    • Dimensions of an affine space.

    • Free and applied vectors.

    • Affine subspaces of a Euclidean space and their positions.

    • Parametric and Cartesian equations of an affine subspace.

    • Dependence and independence of points.

    • Mutual position of affine subspaces.

    • Systems of subspaces: bundles and stars.

    • Affinity.

    • Orientation.

  2. Euclidean Geometry

    • Orthonormal references.

    • Vector product.

    • Areas and volumes.

  3. Conics

    • Metric classification of conic curves.

Note

  • The exercises performed are considered an integral part of the program.

 

 

Fundamentals of Computing

Simona Ranieri 1 Year, 2 semester, 9 credits, Subjects
Fundamentals of Computing
1 YEAR 2 semester 9 CFU
Flavio Lombardi 2018-19
Enrico Simeoli 2019-20

Walter Liguori

since 2020-21
Gianluca ROSSI 2023-24

Cesare ROSETI

Mauro DE SANCTIS

Tommaso ROSSI

 2024-25
  Code: 8037947
SSD: ING-INF/05

OBJECTIVES

LEARNING OUTCOMES:
The course aims to provide students with knowledge and skills for effectively using computer methodologies and tools in the engineering field, especially for developing algorithms.

KNOWLEDGE AND UNDERSTANDING:
Acquire knowledge of the internals of computer architectures.
Acquire knowledge of data structures and algorithms.
Acquire knowledge of the principles of programming languages, including the object-oriented paradigm and tools and techniques for software development.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Acquire the ability to analyze problems and design and implement software artifacts addressing them.
Acquire the capability of a group working on software development and documentation.

MAKING JUDGEMENTS:
Being able to choose appropriate languages and tools for software development.
Being able to evaluate the correctness and efficiency of a software implementation.

COMMUNICATION SKILLS:
Be able to describe and document software artifacts correctly and effectively.

LEARNING SKILLS:
Using the technical documentation and the reference manuals of systems, products and languages effectively.

COURSE SYLLABUS

  • “Introduction to the computational method. Von Neumann architecture. Programming languages: assembler, compiled, and interpreted languages. Basic concepts of programming languages: variables; data types and assignment; control structures (loops, conditional selection); basic data structures; input and output. Functions and recursion. Searching and sorting algorithms. Computational complexity. Dynamic data structures: array; linked lists; trees; hash tables. Object-oriented programming.

     

    The programming languages taught are Python and C.”

Mathematical Analysis I

Simona Ranieri 1 semester, 1 Year, 12 credits, Subjects
Mathematical Analysis I
1 YEAR 1 semester 12 CFU
Prof. Fabio Ciolli e Prof. Roberto Longo 2018-19
Prof. Sebastiano Carpi 2019-20

Yoh TANIMOTO – hoyt@mat.uniroma2.it

 2020-21 to 2023-24

Yoh TANIMOTO  – hoyt@mat.uniroma2.it (9 cfu)

Oliver James BUTTERLEY (3 cfu) –

 2024-25
  Code: 8037944
SSD: MAT/05

LEARNING OUTCOMES:
One learns real numbers, limits and continuity of functions, derivative of functions, their properties and examles, Taylor series and some applications, Riemann integral, complex numbers, real numerical series and separable differential equations. One obtains the ability to calculate various limits, derivatives and integrals of functions, to discuss the convergence numerical series and improper integrals, to solve basic differential equations and to calculate complex numbers. One develops the theoretical basis to be applied to the problems of engineering.

KNOWLEDGE AND UNDERSTANDING: 
To know the definitions of basic conepts (limit, continuity, derivative, integrale, convergence of series, differential equations) and apply various theorems to execute concrete computations.

APPLYING KNOWLEDGE AND UNDERSTANDING:
To Identify the theorems and techniques to apply to the given problems and execute computations correctly.

MAKING JUDGEMENTS: 
To understand mathematical concepts for the given problems and to divide them into smaller problems that can be solved with the knowledge obtained during the course.

COMMUNICATION SKILLS:
To frame the problems in the obtained concepts, express the logic and general facts that are used during the computations.

LEARNING SKILLS:
To know precisely basic mathematical concepts and apply them to some simple examples in physics.

PROGRAMME:

– real numbers
– sequences of real numbers and their limits
– real functions of one real variable
– limits and continuity of functions
– properties of continuous functions
– differentiability and first derivative
– properties of derivative
– higher order derivatives and Taylor series
– Riemann integral
– fundamental theorem of calculus
– real numerical series
– basic differential equations
– complex numbers

Fundamentals of Chemistry

Simona Ranieri 1 semester, 1 Year, 9 credits, Subjects
Fundamentals of Chemistry

 

1 YEAR 1 semester 9 CFU
Prof. Roberto Paolesse 2019-20 to 2020-21
2021-22
PAOLESSE ROBERTO – LVOVA LARISA 2021-22
LVOVA LARISA

since 2022-23
 

larisa.lvova@uniroma2.it

Code: 8037945
SSD: CHIM/07

Scheda di Insegnamento: Fundamentals of Chemistry – LVOVA 1.0

LEARNING OUTCOMES:
To provide students with basic chemical skills, in order to facilitate the understanding of the subsequent class of the course. To provide a solid basic knowledge of chemistry, preparatory to the understanding of a wide range of phenomena. To provide the tools for a proper interpretation of matter and its transformations, both at a microscopic (atomic/molecular) and macroscopic (phenomenological) level.

KNOWLEDGE AND UNDERSTANDING:
At the end of the lectures, the student must have acquired the knowledge necessary to understand and apply general chemistry concepts, in particular concerning reactivity and structure of matter in its different states of aggregation, with specific regard to relevant issues of Engineering Science. The acquired skills will be employed by the student to carry out more advanced studies.

APPLYING KNOWLEDGE AND UNDERSTANDING:
At the end of the teaching period the student must have matured the ability to apply the theory of basic chemistry to the resolution of exercises and problems, with specific reference to engegneering science.

MAKING JUDGEMENTS:
Judgment skills are developed through individual or group works. The student will have to self-evaluate (self assessment-test) and compare with colleagues.

COMMUNICATION SKILLS:
At the end of the teaching sessions the student will be able to use a rigorous chemical language, both in written and oral form, together with the use of graphic and formal languages to represent the descriptive models of the matter.
Inoltre lo studente avrà la possibilità di dimostrare di saper operare efficacemente nel gruppo di pari utilizzando supporti informatici per raccogliere e divulgare informazioni.
In addition, the student will have the opportunity to demonstrate that he / she can work effectively in the peer group using IT support to collect and disseminate information.

LEARNING SKILLS:
At the end of the teaching sessions the student will be able to understand and predict the outcome of the most common inorganic reactions, as well as correlate structure-reactivity properties of the fundamental inorganic compounds and of selected simple organic molecules

COURSE SYLLABUS

  • The scientific method. Elements and compounds. Chemical formulas. The balancing of chemical reactions. Chemical nomenclature (notes). Stoichiometric calculations. The principal chemical reactions. Atomic Theory. Sub-atomic particles. Isotopes. Quantum Theory. Particles and waves. Quantum numbers. Atomic orbitals. Pauli and Hund principles. Electronic structures of atoms. The periodic system and periodic properties.
  • Chemical bonds. Ionic and covalent bonds. Valence bond theory: hybridization and resonance. Determinationof meolecular structuresbased on the repulsion of the valence electron pairs (VSEPR). Molecular orbitals theory (LCAO-MO). Application of MO theory for homo- ed heteronuclear diatomic molecules of the I and II period. Dipolar interactions. Hydrogen bond. Metallic bond. Band theory. Structure and conductivity.
  • Solid state. Crystal and amorphous solids. Metals. Ionic crystals and lattice energy. Insulators and semiconductors.
  • The gaseous state. Ideal gas laws. Ideal gas equation. Dalton law. Real gases: van der Waals equation.
  • First principle of thermodynamics. State functions: Internal Energyand Enthalpy. Thermochemistry. Hess law. Secondand third principleofthermodynamics. Entropyand Free Energy. Equilibrium and spontaneity criteria. Molar free energy: activityand standard states.
  • Vapour pressure. Clapeyron equation.
  • Solutions: Phase equilibria. State diagrams. Fractional distillation.Colligative properties for ideal solutions.
  • Chemical equilibrium: Le Chatelier principle. Equilibrium constant. Law of mass action. Gaseous dissociation equilibria.
  • Electrolytic systems: electrolytic dissociation equilibria, electric conductivity. Colligative properties of electrolytic solutions. Low soluble electrolytes: solubility product.
  • Acid-base equilibria. Autoionizationof water: pH. Monoprotic and polyprotic acids and bases. Buffer solutions. Indicators. Titrations. pH dependent solubility.
  • Chemical kinetics: Chemical reactions rate, activation energy, catalysis.
  • Red-ox systems: electrode potentials. Galvanic cells: Nernst equation. Electrolysis: Faraday law; electrode discharge processes.
  • Electrochemical applications: Fuel cells, batteries. Metal corrosion.
  • Nuclear Chemistry. Notes of Organic chemistry. Polymers.

International English for Scientific Studies

Simona Ranieri 1 Year, Subjects
International English for Scientific Studies
1 YEAR 1 semester 3 CFU (APTITUDE TEST)
Dr. Carlotta Dell’Arte 2019-20 to 2023-24
Prof. Marianna Nacchia 2024-25
  2025-26
  Code: 8038849
SSD: L-LIN/12

International English for Scientific Studies – A.Y. 2025-26

 

LEARNING OUTCOMES:
The course aims at (i) providing 1st-year international students with the language skills, critical thinking and learning strategies required to attend a University degree held in English (ii) providing students with the basic vocabulary in the field of mathematics, physics and chemistry (iii) providing students with the basic knowledge in Academic English (iv) raise students’ awareness on English as a Global Language and English as a Lingua Franca (v) developing students’ listening and reading skills.

KNOWLEDGE AND UNDERSTANDING:
By the end of the course, students will able to (i) recognise specific vocabulary in the fields of maths, physics and chemistry (ii) have a general understanding of spoken and written texts on engineering and science (iii) recognise different pronunciations of English (iv) interact appropriately with administrative staff and professors.

APPLYING KNOWLEDGE AND UNDERSTANDING:
By the end of the course, students will be able to (i) use specific vocabulary accordingly (ii) identify key ideas and supporting ideas in spoken and written texts (iii) discuss the contents analysed in the texts (iv) address administrative staff and professors appropriately.

MAKING JUDGEMENTS:
By the end of the course, students will be able to (i) assess the coherence of spoken and written texts (ii) classify key ideas and supporting ideas (iii) make conclusions and deduce implications.

COMMUNICATION SKILLS:
By the end of the course, students will be able to (i) summarise key ideas of a text (ii) highlight the logical reasoning behind a test (iii) use specific vocabulary in the field of maths, physics, chemistry and engineering.

LEARNING SKILLS:
By the end of the course students will be able to (i) use online language resources efficiently (ie. dictionaries, word references) (ii) search for and assess new online language resources.

Students are required to have a B1+ level of English to attend the course.
Students who do not have that level, would need to prepare individually in order to attend the course effectively.
Students may use the book below for personal study: Murphy R., English Grammar in Use, with answers, Intermediate, Fourth Edition, Cambridge University Press.

  • English as a Global Language and English as a Lingua Franca
  • Implications of English language learners
  • Native Speakers and Non-Native Speakers
  • Phonology and Phonetics of English as an International Language
  • Register (formal, informal, neutral, colloquial)
  • Specific vocabulary: maths, physics, chemistry, engineering, academic English, communications, statistics and social sciences
  • Summary writing, for and against essays, opinion essay and abstract