It’s the dream of many. To retire to the shed, knock out a DIY synth and watch the world change in its wake. Generously, Sean Luke of George Mason University has authored a set of lecture notes that explains what goes into the build of a soft synth.
Aside from the technical aspects the note range from a brief history of synthesis, components, with good helping of maths. 
If you’re keen on developing your own soft synth, here’s a good place to start. A college professor has generously shared his notes on building computer based synthesizers.
Sean Luke teaches an undergrad computer science course, so while it might not be a whole step-by-step guide to a complete build, it will be very illuminating, especially for those who have a background in programming.
For the rest of us mere mortals, there is a primer on the history of synthesis, additive and subtractive synthesis, modulation tools like LFOs, sequencers and so forth.
Being a computer science course, it addresses the all important digitisation of signal, an essential for building a computer based synth. Mathematically, it’s not for the faint of heart.
And in the spirit of egalitarianism, it is a free download. Visit the Computational Music Synthesis website for all the details.
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