I have been a software programmer for over six years and I'm from a non-mathematical background. Though I had some limited exposure to discrete mathematics in my college years it didn't leave any significant impact on me; but now I have been finding many topics on discrete mathematics to be very interesting, especially combinatorics and I'm interested in learning more of it.
However few people I had approached told me that I need to first master calculus in order to take on discrete math, as they say that's how it is taught in universities, is this true? do I need know calculus to appreciate discrete math? (Also, can anyone point me to any books on combinatorics for beginners)
What is termed discrete mathematics is largely independent of calculus. In fact, to appreciate calculus properly, one might need some logic and set theory which is often part of a course in discrete mathematics together with other topics like combinatorics, graph theory and elementary number theory. For a good elementary text in combinatorics, I recommend Principles and Techniques of Combinatorics by Chen Chuan Chong and Koh Khee Meng.