You mention mathematical operations and, of course, this was the intent of the original op amp - operational amplifier.
There are a number of op amp circuits to be considered but the easy 3 are: Inverter, Summer and Integrator.
Here is a description of a very practical analog computer (in German but the schematics are still helpful) which I built a couple of years ago:
http://www.analogmuseum.org/library/vogel_ar_beschreibung.pdfHere's an English page describing the project:
http://www.analogmuseum.org/english/homebrew/vogel/So, where to start? Get a +- 15V power supply, a +- 10V reference, a few op amps, some 1M and 100K resistors, a couple of 1 ufd percision (say 1%) capacitors and breadboard the various components.
There is a lot to learn with just the Summer. It's kind of neat to see voltages add or subtract. The Inverter changes the sign of a voltage. If the voltage input is +5, the output is -5. The Integrator is the most complex of the 3 because of the need to apply initial conditions.
You will also need some potentiometers of the value shown in the schematic. Ideally, they would be precision wirewound units with 10 turn indicating knobs as shown. For a first start, almost anything will work.
So, build an inverter, add some resistors to change it to a summer and then change the feedback resistor to a capacitor and you have the integrator.