The engagement of Jessica Tuchman to Colin Mathews, son of Mr. and Mrs. Thomas Mathews of Washington, D.C., is announced by the future bride's parents, Dr. and Mrs. Lester R. Tuchman of New York City and Cos Cob, Ct. A wedding is planned for February 25.

Miss Tuchman is section chief for Global Affairs in the National Security Council in Washington. Her fiance is an attorney in the General Counsel's office of the Department of Energy. He ia an alumnus of Philips Andover Academy, Stanford University, and the Unviersity of Pennsylania Law School. His father is vice-president of Craver, Mathews, Smith & Co., management consultants. His mother, Mrs. Bonnie Mathews, is an editor with the Civil Rights Commission.

The prospective bride is a graduate of the Brearley School, Radcliffe College, and the California Insitute of Technology where she received a Ph. D. in molecular biology after studying also at the Massachusetts Institute of Technology. Awarded a Congressional Science Fellowship by the the American Association for the Advancement of Science in 1973, she served as legislative assistance to U.S. Rep. Morris Udall and subsequently as issues director of his campaign for the presidency, of which Mr. Mathews was assistant campaign manager. As an equestrian while in high school, she was Junior National Reserve Champion in 1962 and a finalist in the Olympic Trials of 1963.

Her father is consultant physician to the Mount Sinai Hospital and emeritus professor of clinical medicine at its medical school. He was formerly editor of the Mt. Sinai Journal of Medicine and chief of medicine at the City Hospital, Elmhurst. Her mother is the historian, Barbara Tuchman, twice winner of the Pulitzer Prize. On the maternal side, Jessica Tuchman is a granddaughter of the late Maurice Wertheim, investment banker, and the late Alma Morgenthau, and a great-granddaughter of the late Henry Morgenthau Sr., former ambassor to Turkey.