Algorithms with JULIA : Optimization Machine Learning and Differential Equations Using the JULIA Language An Introduction to the Julia Language Functions Variables Constants Scopes and Modules Built in Data Structures User Defined Data Structures and the Type System Control Flow Macros Arrays and Linear Algebra Ordinary Differential Equations Partial Differential Equations Global Optimization Local Optimization Neural Networks Bayesian Estimation. This book provides an introduction to modern topics in scientific computing and machine learning using JULIA to illustrate the efficient implementation of algorithms. In addition to covering fundamental topics such as optimization and solving systems of equations it adds to the usual canon of computational science by including more advanced topics of practical importance. In particular there is a focus on partial differential equations and systems thereof which form the basis of many engineering applications. Several chapters also include material on machine learning (artificial neural networks and Bayesian estimation). JULIA is a relatively new programming language which has been developed with scientific and technical computing in mind. Its syntax is similar to other languages in this area but it has been designed to embrace modern programming concepts. It is open source and it comes with a compiler and an easy to use package system. Aimed at students of applied mathematics computer science engineering and bioinformatics the book assumes only a basic knowledge of linear algebra and programming.