[Verse 1] In the land of graphs and trees we start our journey here Vertices connected by edges crystal clear Trees have no cycles, spanning all the nodes While planarity checks if crossing can be closed Coloring vertices with minimum hues Matching pairs perfectly, no vertex confused [Chorus] Discrete math dancing, counting all the ways Graphs and combinations fill our learning days From zero-knowledge proofs to Ramsey's mighty call Combinatorics conquers, we can learn it all Count it up, match it down Optimize what can be found [Verse 2] Generating functions hold the counting power Pólya's method counts through symmetry's tower Partitions break numbers into smaller parts While extremal problems push the theory's arts Turán's theorem limits edges we can place Szemerédi's lemma shows structure's hidden face [Chorus] Discrete math dancing, counting all the ways Graphs and combinations fill our learning days From zero-knowledge proofs to Ramsey's mighty call Combinatorics conquers, we can learn it all Count it up, match it down Optimize what can be found [Bridge] Linear programming finds the optimal way Integer constraints make problems harder to weigh Matroids abstract the independence game While error codes protect data just the same Hamming distance measures how far codes can be Reed-Solomon saves what networks send to me [Verse 3] RSA encryption keeps our secrets safe Elliptic curves provide a crypto base Lattices hide problems hard for foes to break Zero-knowledge proves without mistakes we make Sumsets grow in additive domains Green-Tao shows primes in arithmetic chains [Chorus] Discrete math dancing, counting all the ways Graphs and combinations fill our learning days From zero-knowledge proofs to Ramsey's mighty call Combinatorics conquers, we can learn it all Count it up, match it down Optimize what can be found [Outro] From Freiman's theorem to network flows Discrete mathematics endlessly grows Path six complete, our journey's at an end Count, graph, and cipher, mathematics we defend
← Path 5: Probability & Statistics | Path 7: Number Theory →