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Teaching GuideTerm Faculty of Computer Science |
| Grao en Enxeñaría Informática |
 Subjects |
| Algebra |
| Contents |
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| Identifying Data | 2020/21 | |||||||||||||
| Subject | Algebra | Code | 614G01010 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | Basic training | 6 | ||||||||||
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| Topic | Sub-topic |
Chapter 1: Modular arithmetic: application to Cryptography. |
Basic concepts from elementary number theory. Euclides' algorithm. Prime numbers. Linear diophantine equations. Congruences. Modular arithmetic. Definition of cryptosystem. Classical cryptography. Symmetrical and asymmetrical cryptography. Examples of cryptosystems. Numeration systems. Divisibility criteria. |
| Chapter 2: Systems of Linear Equations, Matrices and Determinants. | Definition and properties of systems of linear equations. Echelon row form of system. Gauss method. Matrices. Operations with matrices. Invertible matrix. Determinant of a square matrix, properties. Cramer's rule. |
| Chapter 3: Vector Spaces. | Definition and properties of a vector space. Bases and coordinates. Dimension. Rank of a set of vectors and matrix rank. Computation of the rank. Change of basis. Rouché-Frobenius theorem. |
| Chapter 4. Linear maps. | Definición e propiedades das aplicacions lineais. Núcleo e imaxe de unha aplicación lineal. Matriz asociada a unha aplicación lineal. Teorema da dimensión. Definition and properties of linear maps. Kernel and image of a linear map. Matrix associated to a linear map. Dimension theorem. |
| Chapter 5. Linear Codes | Definition of linear codes. Parameters of a linear code. Hamming distance and Hamming weight. Generator matrix and parity-check matrix of a code. Error correction in linear codes. Binary Hamming codes. |
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