In manual mode on my Nikon D3200 I cannot change just the f/stop setting. It only changes in relation to the other settings. How can I reproduce settings that I have found in books on photography if I cannot adjust the f/stop separately? Is this something I'm doing wrong or is it a fault with the camera?
You're almost certainly doing something wrong. If you're truly in manual mode - i.e. the mode dial is set to the "M" position - then the aperture won't (normally) change in response to other settings. You change the shutter speed by turning the command dial normally, and you change the aperture by holding down the exposure compensation button (the "+/-" button just backwards and right of the shutter button) and turning the command dial. If that doesn't happen, try finding an experienced SLR user and asking them to try. If they can't get it to work, then's the time to start thinking there may be an issue with the camera.
The only situation I can immediately think of where changing other settings would change the aperture is zooming in on a variable aperture lens - for example, if you have a standard 18-55mm f/3.5-5.6 kit lens set at 18mm, f/3.5 and then zoom in to 55mm, the aperture will change to f/5.6 as it's limited by the lens.
You will need to be in "M" mode on the main control dial.. Then you can set the aperture (f/stop), shutter speed, and ISO completely independently of each other. Important to note though that any under or over exposure is therefore your issue for you to sort out. The camera is NOT making any decisions about exposure when in "M" mode.
I just discovered for myself that I am unable to manually change the aperture in manual mode if taking photos using the LCD screen as the viewfinder. When I switched it back to the standard viewfinder, and hit the information button on the bottom left, I was able to control everything as normal again.