DISCRETE STRUCTURES AND LINEAR ALGEBRA
MATEMATICA DISCRETA
Discrete Structures and Linear Algebra
Matematica Discreta
| A.Y. | Credits |
|---|---|
| 2012/2013 | 6 |
| Lecturer | Office hours for students | |
|---|---|---|
| Devis Abriani | Tue-Wed from 4 pm to 5 pm. |
Assigned to the Degree Course
| Date | Time | Classroom / Location |
|---|
Learning Objectives
The objective of this Course is to provide knowledge of the language and of the main structures of algebra and familiarity with some of the most common techinques of combinatorial mathematics and linear algebra.
Program
01. Sets and their relations:
01.01 Sets, equivalences and partitions.
01.02 Applications.
01.03 Composition of applications and inverse.
01.04 Cardinality: countable and uncountable sets.
01.05 Elements of combinatorics.
01.06 Total and partial order.
02. Matrices:
02.01 Definitions.
02.02 Addition of matrices and properties.
02.03 Product of matrices and properties.
02.04 Transpose.
02.05 Square matrices.
03. Theory of groups:
03.01 Semigroups.
03.02 Monoids.
03.03 Groups.
03.04 Homomorphisms.
03.05 Subgroups.
03.06 The group of permutations.
04. Theory of rings:
04.01 Rings and commutative rings.
04.02 Rings with identity.
04.03 Zero divisors.
04.04 Integral domains and fields.
04.05 Polynomials rings.
05. Linear algebra:
05.01 Vector spaces.
05.02 Linear dependence and independence.
05.03 Basis and dimension.
05.04 Subspaces.
05.05 Linear applications.
05.06 Kernel and image.
05.07 Matrices and linear applications.
05.08 Changes of basis.
05.09 Rank.
05.10 Linear Systems and Rouche'-Capelli's Theorem.
05.11 How to solve a linear system in practice.
05.12 Determinant and Cramer's theorem.
05.13 Minors and Rank.
05.14 Eigenvalues and Eigenvectors.
05.15 Diagonalization.
Bridging Courses
None.
Teaching, Attendance, Course Books and Assessment
- Teaching
Theory lectures and exercises, both face to face and online.
- Attendance
Although recommended, course attendance is not mandatory.
- Course books
Facchini, "Algebra e Matematica Discreta", Decibel Editrice, 2000.
S. Lang, "Linear Algebra" (second edition), UTM Springer-Verlag, 1989.
- Assessment
Written and oral exam.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
Notes
The course is offered both face to face and online within the Laurea Degree Program in Applied Computer Science.
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