What's the difference between 理系{りけい} , 理科{りか}, and 科学{かがく}?


In my dictionary, `理系{りけい}`, `理科{りか}`, and `科学{かがく}` are defined simply as
"science".

What, if anything, differentiates them?

Especially in terms of the feeling or nuance when used in everyday
conversation.




Excuse me for posting an answer without referring to any sources...  
  
We usually use 理科 to refer to a school subject (which usually includes these 4
fields: physics, biology, earth science and chemistry). We usually use the
word 理科 in upper grades at elementary school, and in senior high we have
[理科第１分野]{りかだいいちぶんや} (=chemistry and physics) and [理科第２分野]{りかだいにぶんや} (=earth
science and biology). In senior high we usually choose 2 to 4 from these 4
fields and don't use the word 理科 anymore. I think we sometimes call these 4
subjects '[理科系科目]{りかけいかもく}...maybe it's like 'the group of scientific
subjects'/'one of the scientific subjects'.  
  
And as Paul-san said, we often say 'She is 理系/あの子は理系だよ。', 'I am
文系[ぶんけい]/私、文系なの。' when we talk about which field of 理系 and 文系 someone
majors/majored in at college, and also 'あそこの大学は文系だ/That university is 文系',
'ここの[学部]{がくぶ}・[学科]{かっか}は理系です/This faculty/department (at college) is 理系' etc.
to talk about what kind of courses a college/faculty/department has.  
  
As for 科学… sorry Dave-san, I still don't know what to write about it here...




Excuse me for posting an answer without referring to any sources...  
  
We usually use 理科 to refer to a school subject (which usually includes these 4
fields: physics, biology, earth science and chemistry). We usually use the
word 理科 in upper grades at elementary school, and in senior high we have
[理科第１分野]{りかだいいちぶんや} (=chemistry and physics) and [理科第２分野]{りかだいにぶんや} (=earth
science and biology). In senior high we usually choose 2 to 4 from these 4
fields and don't use the word 理科 anymore. I think we sometimes call these 4
subjects '[理科系科目]{りかけいかもく}...maybe it's like 'the group of scientific
subjects'/'one of the scientific subjects'.  
  
And as Paul-san said, we often say 'She is 理系/あの子は理系だよ。', 'I am
文系[ぶんけい]/私、文系なの。' when we talk about which field of 理系 and 文系 someone
majors/majored in at college, and also 'あそこの大学は文系だ/That university is 文系',
'ここの[学部]{がくぶ}・[学科]{かっか}は理系です/This faculty/department (at college) is 理系' etc.
to talk about what kind of courses a college/faculty/department has.  
  
As for 科学… sorry Dave-san, I still don't know what to write about it here...

