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.

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