Functions and Graphs

There are literally hundreds of threads with this topic on the Web. Most of them contain the same standard references which IMO are not always the best for people without much mathematical maturity and wishing to learn from first principles. That said, here are my recommendations for them (pdfs of almost all are available online and they can also be purchased cheaply as used books); * 1) Functions and Graphs and 2) The Method of Coordinates by I.M.Gelfand et. al. - These give you the basics on functions and how to visualize them which is crucial for understanding. * Introductory Logic and Sets for Computer Scientists by Nimal Nissanke - Nice succinct introduction to various required topics for Comp. Sci. * Compared To What?: Introduction to the Analysis of Algorithms by Gregory Rawlins - This is a classic book which takes you by hand and walks you through Algorithm Analysis and the reqd. mathematics. You will find this more approachable than most other text books and well worth a study. * How to Think about Algorithms by Jeff Edmonds - Practical techniques without too much mathematical formalism.…

Some of the books that you mention seem a bit too hard for a teen, so you have to be careful not to demotivate them by expecting too much of them; instead i suggest a simpler approach before tackling the big ones; * Functions and Graphs by Gelfand et al. - A small but great book to develop intuition. * Who is Fourier? A Mathematical Adventure - A great "manga type" book to build important concepts from first principles * Concepts of Modern Mathematics by Ian Stewart - A nice overview in simple language. * Mathematics: Its Content, Methods and Meaning by Kolmogorov et al. - A broad but concise presentation of a lot of mathematics. * Methods of Mathematics Applied to Calculus, Probability, and Statistics by Richard Hamming - A very good applied maths book. All of Hamming's books are recommended. There are of course plenty more but the above should be good for understanding.