Algebra
Course objectives
General goals: To provide basic knowledge on topics of group theory and linear algebra which are commonly used in computer science. Specific goals: Basic algebra concepts Introduction to algebraic structures Development of the language of linear algebra: vector spaces and their homomorphisms; vector spaces, numbers, and matrix algebra; endomorphisms, determinants and diagonalization; applications. Knowledge and understanding: A successful student will be able to make computations in small groups of easy structure and understand the meaning and use of matrices in the study of linear phenomena. Application of knowledge and understanding: Use of diagonalization of linear operators to get geometrical interpretation of a linear problem and gather relevant information. Use of the group concept in the study of finite combinatorial problems. Critiquing and judgmental skills: Students will be able to choose the appropriate algebraic setting for the description of a problem. Communication skills: Students will learn the linear algebra and group language, along with basics of complexity theory. Learning ability: Understanding the language of linear algebra and groups will allow students to learn topics that employ them.
Channel 1
GABRIELE VIAGGI
Lecturers' profile
Program - Frequency - Exams
Course program
Sets, partitions, applications, equivalence relations, order relations, permutations.
Natural numbers, the principle of induction. Classes remainder modulus an integer. Congruences and equations in Zn.
Algebraic structures: Groups, rings and fields.
Rings of polynomials. Euclid's algorithm.
Systems of linear equations: Gauss algorithm, determinant of a square matrix. Inverse matrix. Rank of a matrix: Cramer's theorem and Rouche-Capelli's theorem. Solving homogeneous linear systems.
Vector spaces: linear dependence and independence, basis. Matrices. Linear maps and their representation: changes of basis, diagonalization of a linear operator. Characteristic polynomial and relative invariance.
Elements of group theory: Cyclic groups, period of an element of a group. Classification of cyclic groups. Lateral classes form a subgroup. Lagrange's theorem, normal subgroups. The fundamental theorem of homomorphism between groups.
Books
Lang, Linear Algebra
Frequency
Three lessons a week, a main theoretical lesson and two containing applications, examples and exercises.
Exam mode
The exam consists of a written test and an oral test.
There will be five sessions: two between January and February, two between June and July and one in September. For official information on dates, times and places of exam sessions (written, oral and recorded), always refer to the calendar published by the teaching secretariat on the Computer Science degree course web pages.
Lesson mode
1 ongoing test to obtain a bonus, and 5 exam sessions with written exam and optional oral exam. The complete modality is written here https://sites.google.com/uniroma1.it/modalita-esame/home-page
GABRIELE VIAGGI
Lecturers' profile
Giacomo Cherubini
Lecturers' profile
Program - Frequency - Exams
Course program
Sets, partitions, applications, equivalence relations, order relations, permutations.
Natural numbers, the principle of induction. Classes remainder modulus an integer. Congruences and equations in Zn.
Algebraic structures: Groups, rings and fields.
Rings of polynomials. Euclid's algorithm.
Systems of linear equations: Gauss algorithm, determinant of a square matrix. Inverse matrix. Rank of a matrix: Cramer's theorem and Rouche-Capelli's theorem. Solving homogeneous linear systems.
Vector spaces: linear dependence and independence, basis. Matrices. Linear maps and their representation: changes of basis, diagonalization of a linear operator. Characteristic polynomial and relative invariance.
Elements of group theory: Cyclic groups, period of an element of a group. Classification of cyclic groups. Lateral classes form a subgroup. Lagrange's theorem, normal subgroups. The fundamental theorem of homomorphism between groups.
Books
Lang, Linear Algebra
Frequency
Three lessons a week, a main theoretical lesson and two containing applications, examples and exercises.
Exam mode
The exam consists of a written test and an oral test.
There will be five sessions: two between January and February, two between June and July and one in September. For official information on dates, times and places of exam sessions (written, oral and recorded), always refer to the calendar published by the teaching secretariat on the Computer Science degree course web pages.
Lesson mode
1 ongoing test to obtain a bonus, and 5 exam sessions with written exam and optional oral exam. The complete modality is written here https://sites.google.com/uniroma1.it/modalita-esame/home-page
Giacomo Cherubini
Lecturers' profile
Channel 2
FEDERICO PELLARIN
Lecturers' profile
Program - Frequency - Exams
Course program
Sets, partitions, applications, equivalence relations, order relations, permutations.
Natural numbers, the principle of induction. Classes remainder modulus an integer. Congruences and equations in Zn.
Algebraic structures: Groups, rings and fields.
Rings of polynomials. Euclid's algorithm.
Systems of linear equations: Gauss algorithm, determinant of a square matrix. Inverse matrix. Rank of a matrix: Cramer's theorem and Rouche-Capelli's theorem. Solving homogeneous linear systems.
Vector spaces: linear dependence and independence, basis. Matrices. Linear maps and their representation: changes of basis, diagonalization of a linear operator. Characteristic polynomial and relative invariance.
Elements of group theory: Cyclic groups, period of an element of a group. Classification of cyclic groups. Lateral classes form a subgroup. Lagrange's theorem, normal subgroups. The fundamental theorem of homomorphism between groups.
Books
Lang, Linear Algebra
Frequency
Three lessons a week, a main theoretical lesson and two containing applications, examples and exercises.
Exam mode
The exam consists of a written test and an oral test.
There will be five sessions: two between January and February, two between June and July and one in September. For official information on dates, times and places of exam sessions (written, oral and recorded), always refer to the calendar published by the teaching secretariat on the Computer Science degree course web pages.
Lesson mode
1 ongoing test to obtain a bonus, and 5 exam sessions with written exam and optional oral exam. The complete modality is written here https://sites.google.com/uniroma1.it/modalita-esame/home-page
FEDERICO PELLARIN
Lecturers' profile
Program - Frequency - Exams
Course program
Sets, partitions, applications, equivalence relations, order relations, permutations.
Natural numbers, the principle of induction. Classes remainder modulus an integer. Congruences and equations in Zn.
Algebraic structures: Groups, rings and fields.
Rings of polynomials. Euclid's algorithm.
Systems of linear equations: Gauss algorithm, determinant of a square matrix. Inverse matrix. Rank of a matrix: Cramer's theorem and Rouche-Capelli's theorem. Solving homogeneous linear systems.
Vector spaces: linear dependence and independence, basis. Matrices. Linear maps and their representation: changes of basis, diagonalization of a linear operator. Characteristic polynomial and relative invariance.
Elements of group theory: Cyclic groups, period of an element of a group. Classification of cyclic groups. Lateral classes form a subgroup. Lagrange's theorem, normal subgroups. The fundamental theorem of homomorphism between groups.
Books
Lang, Linear Algebra
Frequency
Three lessons a week, a main theoretical lesson and two containing applications, examples and exercises.
Exam mode
The exam consists of a written test and an oral test.
There will be five sessions: two between January and February, two between June and July and one in September. For official information on dates, times and places of exam sessions (written, oral and recorded), always refer to the calendar published by the teaching secretariat on the Computer Science degree course web pages.
Lesson mode
1 ongoing test to obtain a bonus, and 5 exam sessions with written exam and optional oral exam. The complete modality is written here https://sites.google.com/uniroma1.it/modalita-esame/home-page
- Lesson code1015886
- Academic year2024/2025
- CourseInformatics
- CurriculumMetodologico
- Year2nd year
- Semester1st semester
- SSDMAT/02
- CFU9
- Subject areaAttività formative affini o integrative