This book is an interactive introduction to the theory and applications of complex functions from a visual point of view. However, it does not cover all the topics of a standard course. In fact, it is a collection of selected topics and interactive applets that can be used as a supplementary learning resource by anyone interested in learning this fascinating branch of mathematics.
The notes cover introduction to proofs, axioms of fields, complex numbers, some topology, and limits, continuity, derivatives, integrals, sequences and series. For teaching proof writing, many proofs contain in red color parts of proofs that should not be written down but should be thought.
Here, as much for my convenience as anyone else's, is a list of the theorems that have appeared here, with links. Bézout's theorem The intermediate value theorem Vinogradov's three primes theorem Van der Waerden's theorem The square root of 2 is irrational The binomial theorem The Banach-Tarski paradox Eulerian circuits Bachet's duplication formula Lagrange's theorem…
In reality, you are actually coinciding given two points with the points of your ruler. Then you will say, these points are separated by x unit in length.
The textbook An Introduction to the Analysis of Algorithms by Robert Sedgewick and Phillipe Flajolet overviews the primary techniques used in the mathematical analysis of algorithms.
The textbook Analytic Combinatorics by Philippe Flajolet and Robert Sedgewick enables precise quantitative predictions of the properties of large combinatorial structures.