Galois’ Dream: Group Theory and Differential Equations by Kuga
‘Galois’ Dream: Group Theory and Differential Equations
Michio Kuga
정규특이점을 가지는 이계선형미분방정식의 해가 언제 리우빌 확장의 원소가 되는지는 공부한다
preface
Namely,
(i) It can serve as an introduction to algebraic systems (groups), topology and analysis (function theory)
(ii) Only elementary knowledge of these three subjects is needed, but all three are necessary. This theory is the most primitive example that the intersection of many different disciplines is the most interesting mahtematics. It can help convince students that mathematics is a unity; it also gives a wider perspective of mathematics
(iii)It gives a geometric understanding of Galois theory
(iv) There are many challenging problems which are not too difficult
... in partial differential equations as preliminary to a group-theoretic study o
good research problems left in the theory of Fuchsian differential equations