Discrete mathematics
By Gerry Leversha. Synthesis Lectures on Mathematics & Statistics, 2004
717 citations recorded by the source corpus.
The training guide is devoted to the presentation of the foundations of discrete mathematics. The main sections are presented: theories of sets, mathematical logic, relations, formal systems, algorithms, algebras, combinatorics, graphs, fractal sets. The theoretical material is illustrated by a large number of examples. The guide includes not only basic concepts and theoretical results, but also methods and algorithms for solving applied tasks. Addressed primarily to teachers and students of higher technical universities, but it can be useful to those who are wish to study it independently. With this goal, a large number of tasks are included, for the knowledge control and the system of assessing them. In each section there are two-level test tasks. The first level – tests to check the compulsory minimum of knowledge, the second – tasks of full complexity. The historical information about scientists who contributed to the development of discrete mathematics is given.
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Signal Processing
View Paper: https://www.semanticscholar.org/paper/e532d230010363b17aa3b4f113579cd2ee85d68d
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Citations in the corpus
- Nonlinear dynamics of networks: the groupoid formalism (2006, background): “The symmetry group of this system is the permutation group Γ = S 3 with generators σ = (1 2) and τ = (1 2 3) in cycle notation (Biggs [8]).”
- Multiobjective Optimization Using Ideas from the Clonal Selection Principle (2003, neutral): ““Complexity of an algorithm” refers to the amount of time and space required to execute it in the worst case [42], [43].”
- Fixed points of Kannan mappings in metric spaces endowed with a graph (2012, background): “Moreover, we may treat G as a weighted graph (see [[6], p.”
- Fixed point of φ-contraction in metric spaces endowed with a graph (2010, background): “Moreover, we may treat G as a weighted graph (see [[4], p.”
- Graph-Theoretic Independence as a Predictor of Fullerene Stability (2003, neutral): “A conjecture of the conjecture-making program Graffiti [3] [4] [12] and a feature of that program for identifying stability sorting patterns led to the observation that, for the very limited (less than fifty) number of examples of stable and presumed unstable fullerenes known to the program, the sta”