Modular programming is the art and science of breaking a program into pieces that can be individually developed. This lecture introduces functions (Java methods), a fundamental mechanism that enables modular programming. Motivating examples include functions for the classic Gaussian distribution and an application that creates digital music.

A recursive function is one that calls itself. This lecture introduces the concept by treating in detail the ruler function and (related) classic examples, including the Towers of Hanoi puzzle, the H-tree, and simple models of the real world based on recursion. We show a common pitfall in the use of recursion, and a simple way to avoid it, which introduces a different (related) programming paradigm known as dynamic programming.

When you develop a program, you need to be aware of its resource requirements. In this lecture, we describe a scientific approach to understanding performance, where we develop mathematical models describing the running time our programs and then run empirical tests to validate them. Eventually we come to a simple and effective approach that you can use to predict the running time of your own programs that involve significant amounts of computation.

In Java, you can create your own data types and use them in your programs. In this and the next lecture, we show how this ability allows us to view our programs as abstract representations of real-world concepts. First we show the mechanics of writing client programs that use data types. Our examples involve abstractions such as color, images, and genes. This style of programming is known as object-oriented programming because our programs manipulate objects, which hold data type values.

Creating your own data types is the central activity in modern Java programming. This lecture covers the mechanics (instance variables, constructors, instance methods, and test clients) and then develops several examples, culminating in a program that uses a quintessential mathematical abstraction (complex numbers) to create visual representations of the famous Mandelbrot set.

We conclude the course with an overview of important issues surrounding programming languages. To convince you that your knowledge of Java will enable you to learn other programming languages, we show implementations of a typical program in C, C++, Python, and Matlab. We describe important differences among these languages and address fundamental issues, such as garbage collection, type checking, object oriented programming, and functional programming with some brief historical context.