Think like an engineer

You've taken your intuitions about language, described them as algorithms operating on data structures, and now you need to make them work: time for some engineering...

Signal Processing

Unsurprising, we use a lot of the mathematical foundation on the Brush up your mathematics page to build our tools for speech signal processing. Besides linear algebra and calculus, a lot of this depends on understanding the relationship between complex numbers and trigonometric functions. It’s not necessary to know all the maths behind the Fourier transform, for example, but it will give you a deeper understanding (and give you more evidence that maths is awesome!).

Go through Circuit analysis, only “AC circuit analysis” from “Trigonometry review” to “Euler’s cosine wave”
Digital Signal processing primer
3blue1brown video “But what is the Fourier Transform? A visual introduction”
Smarter Every Day “Fourier series visualization”

Machine learning

Now it’s time to start applying all of this to some actual tasks, and that’s usually going to mean using machine learning. If you’re willing to pay a little money, and dig a little deeper into this area, then there are various Machine Learning courses out there, such as the Machine Learning Specialization from the University of Washington.

Natural Language Processing

Finally, you might even try to put all of this together to do some Natural Language Processing, and the NLTK toolkit with its associated book is what we use for teaching in Edinburgh.