The Golden ratio / Fibonacci sequence are studied under which branch of math?
Can you recommend some good textbooks on the subject?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
I put my card in for Number Theory, only because there are, at minimum, cursory notes on this topic in every basic number theory book on my shelf. I have no number theory book to recommend at the moment (I like them all). There is however a really nice easy read on my shelf called The Divine Proportion by H.E. Huntley. It is a Dover publication so it should be pretty affordable. This would be my first recommendation for anyone with an interest in this particular topic (and no other lit.), and I consider it an especially good recommendation by virtue of the price, ease of read, and quality. It is not a textbook in the academia sense, but it should give you a good grasp of where to go and what the world finds interesting about the golden ratio and the Fibonacci sequence. While there are no textbook exercises, there is plenty of opportunity to break out the pencil and paper.
Usually recurrence relations fall under the wide umbrella of discrete math. A nice book on the topic is Concrete Mathematics by Graham, Knuth, and Patashnik.
These topics, have their own chapter in K. K. Tung Topics in Mathematical Modeling. In fact, you can legally download that chapter for free because they offer the pdf of it as a sample on the book's website: http://press.princeton.edu/chapters/s8446.pdf .