This module gives the learner a first impression of what discrete mathematics is about, and in which ways its "flavor" differs from other fields of mathematics.
It introduces basic objects like sets, relations, functions, which form the foundation of discrete mathematics.
We prove Cayley's formula, stating that the complete graph on n vertices has n^(n-2) spanning trees.
We prove Hall's Theorem and Kőnig's Theorem, two important results on matchings in bipartite graphs.
Each policy consists of a number of component parts separated by dots.
The first figure to the far left and preceding the first dot (.), refers to the chapter number.Inside the "docker" directory can be used by a course administrator to update all of the assignment graders.Feedback on how to improve this test-and-build processing is encouraged.Please fork this repository and share your contributions to the master with pull requests.The assignments presented here were inspired by those used in "Solving Hard Problems in Combinatorial Optimization" (i.e.We also welcome other classes to use this code as a basis for developing their own customer grading framework.Community-driven development and enhancement of these assignments is welcomed and encouraged.With the machinery from flow networks, both have quite direct proofs.Finally, partial orderings have their comeback with Dilworth's Theorem, which has a surprising proof using Kőnig's Theorem.Graphs are arguably the most important object in discrete mathematics.A huge number of problems from computer science and combinatorics can be modelled in the language of graphs.