THEORY
Acoustics, Hearing Limitations, and Sampling
Time-Domain Signal Processing I
Time-Domain Processes II
Sine Waves
Linear Time-Invariant Systems
Frequency Response
Filters
Frequency-Domain and the Fourier Transform
Spectral Analysis, Vocoders •

Reading
Chapters 1 and 2 of Introduction to Digital Filter
Chapter 4 (Linearity and Time Invariance) and Chapter 5 (Time Domain Filter Representations) of Introduction to Digital Filters
First section of Chapter 9 (Implementation Structures) on the Four Direct Forms
Matrix Filter Representations
Optionally peruse the Music 421 overheads pertaining to acyclic convolution
Supplementary: Audio Signal Processing in Faust

RESOURCES
http://www.dspguide.com/
Designing Audio Effect Plug-Ins in C++: With Digital Audio Signal Processing Theory
https://ccrma.stanford.edu/~jos/filters/
Introduction To Digital Signal Processing: Computer Musically Speaking by Tae Hong Park
http://www.amazon.com/Introduction-Digital-Signal-Processing-Musically/dp/9812790276