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Your clutch needs to be adjusted. But defining the problem depends on if the RPMs jump when you push the clutch in while in gear, or just from a stand still. If its while your in gear, then your throttle cable is too tight, and you're not letting off the gas early enough. Sounds like when the clutch pedal is out, the clutch may be still rubbing on the pressure plate or whatever and that it isnt released fully, so when you push the pedal in, it finally releases, thus releasing the tension on the driveline, and causing the engine to spin freely again. Tell us if it happends when in gear or in neutral, or both.
That would lead me to go with the first theory. That either your throttle cable is too tight, and your foot is what is causing the jump in RPMS, or that your computer is at the forefront of the problem. Does the RPM jump and stay at a certain number or does it just jump up and then slowly come back down?