What you need for this book
You will need a computer with at least 2 GB of memory and a recent version of Windows, Mac OS X, or Ubuntu in order to use Titanium SDK properly. You will also require the Oracle Java Development Kit as well as an install of Node.js to use the Titanium Command Line Interface (CLI) tools.
If you are developing an iOS application, you will also need to install the Xcode Integrated Development Environment (IDE). For Android development, you will need the Android SDK provided by Google for free (Titanium Studio provides wizards that can automate the installation).
To develop iOS (iPhone, iPad) applications, you absolutely need a Mac. This limitation is enforced by Apple requiring the use of its own tools. This is not related to Titanium.