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Discrete Mathematics
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/16/25 - 6/4/25
Discrete Mathematics
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 18260
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Fundamentals of Algebra; Linear Algebra
DESCRIPTION
1. Basic counting techniques: combinatorics
a) Basic counting rules;
b) Permutations and combinations; binomial coefficients and identities;
c) Permutations and combinations with repetition.
2. Recursion
a) Recursively defined sets and functions; dependence tree;
b) Linear difference equations;
c) Time complexity of `divide-and-conquer' algorithms;
3. Binary relations
a) Relations and their basic properties;
b) Order relations;
c) Equivalence relations;
4. Graph theory and applications
a) Graphs: basic definitions and concepts; undirected graphs;
b) Euler and Hamilton paths;
c) Directed graphs;
d) Weighted graphs;
e) Trees.
a) Basic counting rules;
b) Permutations and combinations; binomial coefficients and identities;
c) Permutations and combinations with repetition.
2. Recursion
a) Recursively defined sets and functions; dependence tree;
b) Linear difference equations;
c) Time complexity of `divide-and-conquer' algorithms;
3. Binary relations
a) Relations and their basic properties;
b) Order relations;
c) Equivalence relations;
4. Graph theory and applications
a) Graphs: basic definitions and concepts; undirected graphs;
b) Euler and Hamilton paths;
c) Directed graphs;
d) Weighted graphs;
e) Trees.