What electronics should I study to create something like a fridge temperature monitor? I would like to be able to design an Arduino circuit for a fridge monitor that would have a temperature sensor, a small speaker to emit a sound when the temperature changes past a threshold and an LCD screen showing the current temperature.

I have found a few examples online, but I would like to know why components like capacitors and transistors are used in their circuits so I'd be able to design similar circuits myself.

I found this list of electronics topics:


Basic Theory
Basic Passive Components
Passive Circuits
Discrete Active Components
Active Circuits
Integrated Circuits
Digital Logic
Analog
Signals
Outputs
Inputs
Digital Electronics


Some of these things, like digital logic seem unnecessary in such a project, but obviously some others are useful, but I don't know which. I'd like to know what it would be useful to study so I can understand the reasons for the circuit design of something like a fridge monitor.
A fridge temperature monitor (or any system that talks to world using some data) will include a sensor (temperature sensor like LM35), a controller (to do calculations, arduino ofcourse) and an output (display, like LCD). The topics you should be aware of, are digital electronics, basic passive components (working of resistor, capacitor etc). And a little arduino programming and lots of logic.