Discrete Mathematics
Spanish version
Program: scripts and bibliography
- Course syllabus in virtual teaching web space.
- Scripts and slides of the units in virtual teaching web space.
Exercise lists (in virtual teaching web space)
- List of problems 1. Logic.
- List of problems 2. Sets and functions.
- List of problems 3. Lattices and Boolean algebras.
- List of problems 4. Introduction to number theory: Modular Arithmetic.
Theory and practice manuals (in Spanish)
Métodos computacionales en álgebra para informáticos. Matemática discreta y lógica. (1)
Ordóñez,C, Ruiz, J.F. y García-Muñoz,M.A. Editorial: Servicio de Publicaciones de la Universidad de Jaén. 2º Edición, 2020
ERRATAS
Matemática discreta para la computación. Nociones teóricas y problemas resueltos. (2)
García-Muñoz, M.A. Eitorial: Servicio de Publicaciones de la Universidad de Jaén. 2º Edición revisada, 2015
| Program | Contents | Chapters |
|---|---|---|
| Previous Mathematica program. | THE WORKING ENVIRONMENT: MATHEMATICA. bASIC ARITHMETIC. VARIABLES AND FUNCTIONS. LISTS: TABLES, MATRICES Y VECTORS. PROGRAMMING IN MATHEMATICA. |
Chapter 1 of the practice manual [1]. Chapter 2 of the practice manual [1]. Chapter 3 of the practice manual [1]. Chapter 4 of the practice manual [1]. |
| Unit 1. Logic. | STATEMENTS, CONECTIVES AND TRUTH TABLES. TAUTOLOGIES, CONTRADICTIONS, NORMAL FORMS. ADEQUATE SET OF CONECTIVES, LOGICAL EQUIVALENCES, LOGICAL IMPLICATIONS AND ARGUMENTATIONS. |
Chapter 5 of the practice manual [1]. Chapter 6 of the practice manual [1]. |
| Unit 2. Sets and functions. | BASIC CONCEPTS, THE POWER SET, FUNCTIONS, BINARY RELATION AND ORDERED SETS. |
Chapter 7 of the practice manual [1]. Chapter 8 of the practice manual [1]. |
| Unit 3. Boolean algebras and Boolean functions. | LATTICES, BOOLEAN ALGEBRAS, BOOLEAN FUNCTIONS: CANONICAL FORMS. APPLICATIONS: BOOLEAN CIRCUITS. |
Chapter 9 of the practice manual [1]. Chapter 10 of the practice manual [1]. |
| Unit 4. Introduction to number theory: Modular Arithmetic. | NATURAL AND INTEGER NUMBERS. DIVISIBILITY AND CONGRUENCES. APPLICATIONS OF THE BEZOUT THEOREM. NUMERAL SYSTEMS. |
Chapter 11 of the practice manual [1]. Chapter 12 of the practice manual [1]. |
| Unit 5. Notions of computational complexity. | ALGORITHMS. GROWTH FUNCTIONS. ALGORITHMIC COMPLEXITY. THE P AND NP CLASS. |