Unit · year 1
MU-105 · Discrete Mathematics
Threads structure · number6 theorems
Counting, graphs, and modular arithmetic — the mathematics of the finite.
Theorems in this unit
T-028
The binomial theorem
An expansion of (x+y)^n in terms of binomial coefficients.
T-029
The inclusion–exclusion principle
The size of a union from the sizes of intersections.
T-030
The handshaking lemma
In any graph the sum of degrees is twice the number of edges.
T-031
Fermat's little theorem
a^p ≡ a (mod p) for prime p.
T-032
The Chinese remainder theorem
Congruences with coprime moduli have a unique joint solution.
T-033
Euler's theorem on circuits
A connected graph has an Eulerian circuit iff every vertex has even degree.