ENGLISH

Math 154 (Discrete Mathematics)

By Steven V. Sam

Book information

Year
2019
Language
english
Format
PDF
Filesize
406 kB (415290 bytes)
Edition
version 2019-03-19
Pages
\47
Time added
2020-04-11 06:25:52

Description

1. Induction 1.1. Weak induction 1.2. Strong induction 2. Elementary counting problems 2.1. Bijections 2.2. Sum and product principle 2.3. Permutations and combinations 2.4. Words 2.5. Choice problems 3. Binomial theorem and generalizations 3.1. Binomial theorem 3.2. Multinomial theorem 4. Inclusion-exclusion 5. Graph theory, introduction 5.1. Eulerian trails 5.2. Directed graphs 5.3. Hamiltonian cycles 5.4. Graph isomorphisms 6. Trees 6.1. Definition and basic properties 6.2. Adjacency matrix 6.3. Deletion-contraction 6.4. Matrix-tree theorem 6.5. Minimum-weight spanning trees 7. Coloring and matching 7.1. Colorings and chromatic polynomials 7.2. Bipartite graphs 7.3. Matchings 7.4. Stable matchings 8. Planarity 8.1. Definitions 8.2. Some equations and inequalities 8.3. Obstructions to planarity 8.4. Chromatic numbers of planar graphs 9. Ramsey theory 9.1. Pigeon-hole principle 9.2. Ramsey's theorem for graphs 9.3. Lower bounds on Ramsey numbers

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