# Chapter 1: Boolean functions and the Fourier expansion

In this chapter we describe the basics of analysis of boolean functions. We emphasize viewing the Fourier expansion of a boolean function as its representation as a real multilinear polynomial. The viewpoint based on harmonic analysis over ${\mathbb F}_2^n$ is mostly deferred to Chapter 3. We illustrate the use of basic Fourier formulas through the analysis of the Blum–Luby–Rubinfeld linearity test.

### 4 comments to Chapter 1: Boolean functions and the Fourier expansion

• As this page seems to use mathjax, it is worth pointing out that the rendering is improved if certain fonts ( http://www.mathjax.org/help/fonts/ ) are installed. These fonts also allow better rendering when printing.

• Thanks Michael. I should also point out that (at least on my machine) pages take an unusually long time to render in IE. Chrome seems to be the fastest option. I wish I didn’t have to suggest “Use a different browser” if people find it slow, but unfortunately I’m committed to MathJax at this point.

• MathJax script is included using hardcoded http scheme, so formulas won’t get rendered if a page is loaded using https (modern browsers block insecure scripts).

You’d better get rid of scheme name altogether by using src=’//www.contrib.andrew.cmu.edu/…blabla…’.

• Thanks — it’s too hard for me to change anything now, though. In any case, the whole website should be finished up by the end of the month