Textos
En esta sección se encuentran textos que, en forma completa o fragmentaria, se refieren a limitados segmentos de la asignatura. En cualquier caso pueden servir de complemento a la bibliografía básica del curso, que es la que oficicia como un cubrimiento suficiente de los contenidos básicos completos. La consulta a la bibliografía no es una actividad que pueda ser reemplazada ni soslayada sin pérdida sustancial del aprendizaje.
Este apunte contiene una breve introducción a las proposiciones y las funciones proposicionales. Se definen los conectivos negación, disyunción, conjunción, condicional y bicondicional.
HTML muy breve y de sencilla lectura
Versión electrónica de un libro de lectura sencilla con lo esencial de la mayoría de los temas de la asignatura:Wallis, H. (2012). A Beginner’s Guide to Discrete Mathematics, New York: Springer.
This book consists of six units of study: Boolean Functions and Computer Arithmetic, Logic, Number Theory and Cryptography, Sets and Functions, Equivalence and Order, Induction, Sequences and Series. Each of this is divided into two sections. Each section contains a representative selection of problems. These vary from basic to more difficult, including proofs for study by mathematics students or honors students.
- This note covers the following topics: Introduction to sets, Subsets, power sets, equality of sets, Finite and infinite sets, Set operations, De Morgan rules, distributivity, tables, Ordered pairs, Cartesian products, Introduction to relations, Ordering relations, Equivalence relations and Functions.
Una muy precisa introducción a las relaciones de orden en un conjunto.
De Wolfram, el más completo glosario en la red, con definiciones muy precisas ilustradas con gran calidad y sencillez. Cualquier navegante aprende mucho y bueno pasando un rato recorriendo este sitio casi infinito. Incluye en algunas ocasiones demos y también applets interactivos.
Por el profesor Chris K. Caldwell de la Universidad de Tenesse, un tutorial con múltiples referecnias cruzadas que permite lecturas en distintos niveles, segun las preferencias e intereses. Registrándose, se tienen devoluciones de las acciones introducidas en un ámbito interativo.
Pueden aquí seguirse los artículos que se van publicando y recorrer los antecedentes. Los artículos residen ya en la especialidad y no están destinados a la enseñanza.
Más de un centenar de links hacia textos o sitios con materiales en diversos formatos con múltiples posibilidades. Por ejemplo, el excelente link (The Bridges of Königsberg - Isaac Reed) permite aprender mucho acerca de los grafos eulerianos, se proponen ejercicios cuya solución puede verse con un click. Muy recomendable.
The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. This note covers the following topics: Graphs and Subgraphs, Trees, Connectivity, Euler Tours and Hamilton Cycles, Matchings, Edge Colourings, Independent Sets and Cliques, Vertex Colourings, Planar Graphs, Directed Graphs, Networks, The Cycle Space and Bond Space.
This note contains an introduction to basic concepts and results in graph theory, with a special emphasis put on the network-theoretic circuit-cut dualism.
This note covers the following topics: Modular decomposition and cographs, Separating cliques and chordal graphs, Bipartite graphs, Trees, Graph width parameters, Perfect Graph Theorem and related results, Properties of almost all graphs, Extremal Graph Theory, Ramsey's Theorem with variations, Minors and minor closed graph classes.
This note covers the following topics: Eigenvalues and the Laplacian of a graph, Isoperimetric problems, Diameters and eigenvalues, Eigenvalues and quasi-randomness.
This note covers the following topics: Basic Concepts in Graph Theory , Random Graphs, Equivalence relation, Digraphs, Paths, and Subgraphs, Trees , Rates of Growth and Analysis of Algorithms.
This note covers the following topics: fundamentals of mathematical logic , fundamentals of mathematical proofs , fundamentals of set theory , relations and functions , introduction to the Analysis of Algorithms, Fundamentals of Counting and Probability Theory and Elements of Graph Theory.
This note covers the following topics: Preliminaries, Counting and Permutations, Advanced Counting, Polya Theory, Generating Functions and Its Applications.
The goal of this lecture note is to introduce students to ideas and techniques from discrete mathematics that are widely used in Computer Science. This note covers the following topics: Propositional logic, Induction, Strong induction, Structural induction, Proofs about algorithms, Algebraic algorithms, Number theory, RSA, Basics of counting, basic probability,Conditional probability, Linearity of expectation, variance.
This note covers the following topics: induction, counting subsets, Pascal's triangle, Fibonacci numbers, combinatorial probability, integers divisors and primes, Graphs, Trees, Finding the optimum, Matchings in graphs, Graph coloring.
This note covers the following topics: Sets and Algorithms, Arithmetic of Sets, Number Theory, Graph Theory, Searching and Sorting, Recurrence Relations.
This note covers the following topics: Pseudocode, Proof Methods, Logic, Sets, and Boolean Algebra, Relations and Functions, Number Theory, Enumeration, Sums and Recursions, Graph Theory.
This note explains the following topics: Relations, Maps, Order relations, Recursion and Induction, Bounding some recurrences, Graphs, Lattices and Boolean Algebras.
This note covers the following topics: Logic And Sets, Relations And Functions, The Natural Numbers, Division And Factorization, Computational Aspects: Finite State Machines, Finite State Automata, Turing Machines, Groups And Modulo Arithmetic, Introduction To Coding Theory, Group Codes, Public Key Cryptography, Principle Of Inclusion-exclusion, Number Of Solutions Of A Linear Equation, Recurrence Relations, Weighted Graphs.
This note covers the following topics: Compound Statements, Sets and subsets, Partitions and counting, Probability theory, Vectors and matrices, Linear programming and the theory of games, Applications to behavioral science problems.
This note covers the following topics: Logic and Foundations, Proposition logic and quantifiers, Set Theory, Mathematical Induction, Recursive Definitions, Properties of Integers, Cardinality of Sets, Pigeonhole Principle, Combinatorial Arguments, Recurrence Relations.
This note covers the following topics: Computation, Finite State Machines, Logic, SetsSet Theory, Three Theorems, Ordinals, Relations and Functions, Induction, Combinatorics, Algebra, Cellular Automata and FSRs.
The purposes of this book is, first, to answer the question 'What is a number?' and, of greater importance, to provide a foundation for the study of abstract algebra, elementary Euclidean geometry and analysis. This book covers the following topics: The elements of the theory of sets, The Natural Numbers, The Integers and the Rational Numbers and the Real Numbers.
This note covers the following topics: Background and Fundamentals of Mathematics, De Morgan�s laws, Hausdorff Maximality Principle, Equivalence Relations, Notation for the Logic of Mathematics and Unique Factorization Theorem.
These are notes for a course in math proof: An introduction to writing proofs, the basic types of proofs, and an introduction to important mathematical objects such as functions and relations. The logic and set theory are presented in a naive way.
This note covers the following topics: Ordered sets; A theorem of Hausdorff, Axiomatic set theory; Axioms of Zermelo and Fraenkel, The well-ordering theorem, Ordinals and alephs, Set representing ordinals, The simple infinite sequence; Development of arithmetic, The theory of Quine, Lorenzen's operative mathematics and The possibility of set theory based on many-valued logic. (este texto se halla por encima de nuestro nivel, al trata de teoría no ingenua de conjuntoso).
Texto muy superior al nivel del curso. Published by the American Mathematical Society as volume 155 of the Surveys and Monographs series; to buy it from the AMS.
Texto de nivel muy superior al del curso.
Elements of Boolean Algebra Intended as a Resource for Electrical Engineers and Other Practitioners of the Boolean Arts James M. Cargal
Partial order and lattice theory now play an important role in many disciplines of computer science and engineering. For example, they have applications in distributed computing (vector clocks, global predicate detection), concurrency theory (pomsets, occurrence nets), programming language semantics (fixed-point semantics), and data mining (concept analysis). They are also useful in other disciplines of mathematics such as combinatorics, number theory and group theory. In this book, I introduce important results in partial order theory along with their applications in computer science. The bias of the book is on computational aspects of lattice theory (algorithms) and on applications (esp. distributed systems). Since many books exist on lattice theory, I must justify writing another book on the subject. This book is written from the perspective of a computer scientist rather than a mathematician.
This chapter introduces finite-state machines, a primitive, but useful computational model for both hardware and certain types of software. We also discuss regular expressions, the correspondence between non-deterministic and deterministic machines, and more on grammars. Finally, we describe typical hardware components that are essentially physical realizations of finite-state machines.
This book focuses on key theoretical topics of computing, in particular formal languages and abstract machines. It is intended primarily to support the theoretical modules on a computer science or computing-related undergraduate degree scheme
This book is an introduction to the theory of computation. After a chapter presenting the mathematical tools that will be used, the book examines models of computation and the associated languages, from the most elementary to the most general: finite automata and regular languages; context-free languages and pushdown automata; and Turing machines and recursively enumerable and recursive languages.
- This note covers the following topics: A brief history of computing, Fundamentals, Formal languages and machine models, Computability and undecidability, NP-completeness, Generalized number systems and Cryptography mental poker.
This is a free textbook for an undergraduate course on the Theory of Computation, which we have been teaching at Carleton University since 2002.
Libro de texto completo de teoría de grafos.