Yousif Badri, 29, is on trial at the High Court in Glasgow accused of being involved in conduct "with the intention of committing acts of terrorism".
Advocate depute Richard Goddard has been making his closing speech.
The defence is due to make closing arguments on Wednesday.
The offences are alleged to have been committed April 2006  and June 2013.
Mr Goddard said: "The right thing to do is return guilty verdicts on the two charges."
He told the jury: "It is an offence to collect and make a record of information which is likely to be useful to a person committing or preparing an act of terrorism.
"There is no need for the Crown to demonstrate that Mr Badri had any intention to commit acts of terrorism."
Mr Badri said in evidence he was carrying out research so that he could refute the terrorist viewpoint and show how they twisted verses from the Koran to their own ends.
Defence QC Murdo Macleod will address the jury on Wednesday.
The prosecutor in the trial of a student accused of Aberdeen terrorism offences has told a jury it is the "right thing to do" to return verdicts of guilty.