Partitions and Powers

Const antin Caratheodory, speaking to an M A A meeting, 1936

I n th is chapter, we address the theory of addi t ive par t i t ions and the theory

of representations as sums of squares, b o t h f rom an exper imental perspec-

t ive . Each has a dist inguished history. We w i l l show t h a t computa t iona l

techniques can accelerate b o t h solut ion and understanding of these prob-

lems. W h a t ' s more, these techniques have a number o f interest ing applica-

tions, inc luding , for instance, Madelung's constant i n physical chemistry.