The current, corrected, updated syllabus, with active URL links is here.

The thatBridge, your gift from Ken, is here. The code required is all zipped up here, and instructions for programming the bridge is here. Be sure your Python has PyQt5, pyserial, numpy and matplotlib. pip install is your friend.
Much information about THAT is here.
A wiring template for the THAT is here
A bunch of of problems related to solving differential equations is here

Wikipedia has a nice article on the Pascaline and here is an animation of the inner workings.

Of the many papers you'll want to read you should try "Sketch of The Analytical Engine Invented by Charles Babbage" by Ada Augusta, Countess of Lovelace. Babbage never built the Analytical Engine, but what could have been is described by Sydney Padua's video, and "computerphile" has one as well. A detailed look at the Difference Engine, which he did build parts of, is demonstrated here
Babbage's paper about the Analytical Engine is here: here.

If only Charles Babbage had access to K'nex! Only 8 bits, but so was an Intel 8080. ALU , Registers/RAM, and ROM, the Program Coutner and Jumps.

Curta Calculators are Cool! See curta.org for an overview. Simulators are available too, like a 2D and a 3D simulator.

The Turing Tumble is another (theoretically) Turing Complete mechanical computer done with marbles. Simulators are available like this and this.
You can also find "excercises" to do ("programs" to "write") for the Turing Tumble, with solutions, here.

There is a 4 part series on Michaelson's (as in "Michaelson-Morley") Harmonic Analyzer and a '100 year old computer':
Part 1: Intro
Part 2: Synthisis
Part 3: Analysis
Part 4: Operation

Complicated but plain complex plane pictures with fourier series:
See this one from 3blue1brown, from 0:45 to 2:09, and this from SmarterEveryDay, from 5:00 to 6:50.

Water and wind compute too! There are both analog and digital fluidic and pnumatic computers. Steve Mould has a digital water computer on youtube Better, and more applicable to us (but not detailed enough) pneumatics as a front end

Use a virtual slide rule! See The Slide Rule Museum's Virtual Slide Rule Simulators

Antikythra: Was this the first analog calculator? Follow this link for a 30 minute overview , this one for a 6 hour build using tech available at the time, and many other videos about this wonderous machine.

More about planimeters than you want to know (but less than you should know) are here: One with little math and another with lots of math

Biological computing: The most accessable (doesn't require 4 years of graduate work in psychology or biology) is on YouTube: Dr. Steve M Potter at MIT has been at it for years. This is 15 years old, but a good place to start. Some folks are teaching neurons to play games like pong and DOOM. You can put neurons in robots like this. Should one worry about morality? Are these things concious? Maybe.

You can find a previous exam here.

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