I couldn't find this question anywhere else so it may not be apt.
I am an undergraduate mathematics major and during my discrete math class I really enjoyed the study of algorithms and recursive functions. I have looked at very few computer languages and not in to much depth (it wasn't within class just on my own) but I would consider myself as someone who has no real understanding of programming.
Now I am aware that there are certain fields in the study of algorithms that do not require much knowledge of computer science directly.Is something like the theory of recursive functions have a similar flavor to algorithms?
Question 1: Is it possible to engage in a study of algorithms from a mathematical perspective without having taken computer sciences classes?
Question 2: Are there any good books you guys can recommend which someone with my background would be able to follow without too much trouble?
Thanks a lot in advance and any answer is appreciated.