Mathematics and Plausible Reasoning

They were not textbooks for any course. But I liked these: 1. Mathematics and Plausible Reasoning by George Pólya 2. Probability Theory: The Logic of Science by E.T. Jaynes

Some favorites below. Books 0-3 are accessible. The remaining books are more difficult but I'd highly recommend them to math students. 0. Jan Gullberg, Mathematics, From the Birth of Numbers. A highly accessible popular survey on different branches of higher mathematics. I read this over the Summer between high school and starting my undergraduate degree. It's what made me want to study math. Previously I'd wanted to be a guitar player, but had to find a new ambition after an injury left me unable to play. 1. The high school mathematics series by Israel Gelfand. Algebra, Trigonometry, The Method of Coordinates, and Functions and Graphs. I didn't have much mathematics background in high school, but working through these really solidified my grasp on the basics. 2. George Polya. How to Solve it. A short book giving excellent high level advice on mathematical problem solving.…

Instead of How To Solve It, which is organized dictionary–style with short sections on particular named problem solving topics, and is somewhat hard to interpret for novices without guidance, let me recommend Polya’s other two books (each 2 volumes), Mathematical Discovery and Mathematics and Plausible Reasoning.