The University of the District of Columbia has agreed to pay $45,000 to a white accounting professor as settlement of reverse discrimination and freedom of speech suits he brought against the school.

In settlement documents filed in court this week, the university did not admit any wrongdoing in its treatment of Harry R. Mathis, who has been a professor at the school since 1972. But UDC said that in the future it "will not discriminate on the basis of race against Mathis," nor will it "engage in any acts of reprisal" against him for filing the suits.

The 52-year-old Mathis had claimed in one of his suits that after he filed charges of financial impropriety in 1977 against a UDC superior, he was denied pay raises, demoted for two years and refused summer teaching assignments.

Mathis said he agreed to the settlement "reluctantly," but described the agreement as "all in all, a pretty good settlement."

Under the terms of the agreement, UDC said it would grant Mathis' request for a sabbatical leave for the academic year 1983-84 and also would write letters of recommendation for him if any are requested by prospective employers.

In the meantime, Mathis was given the right in the next month to review his personnel records and voice his objections to any material that he considers "to be derogatory and untrue or kept in violation of university policy." UDC then will have another 15 days to respond to his objections and both sides agreed to let U.S. District Judge Thomas A. Flannery decide what, if anything, should be removed from Mathis' personnel files.