Galois’ Dream: Group Theory and Differential Equations by Kuga
‘Galois’ Dream: Group Theory and Differential Equations
Michio Kuga
정규특이점을 가지는 이계선형미분방정식, 즉 이계 Fuchsian 미분방정식의 해가 언제 리우빌 확장의 원소가 되는지 모노드로미군을 통해 할 수 있는 이야기를 펼쳐보인다.
excepts from the preface
(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 for student exercises.
(v) Above all, I cannot forget the old dogma that the most interesting aspect of analysis is its algebraic structure.