The defense got a boost at the end of the day's practice session from Hall of Famer Ronnie Lott.
Four of the new assistant football coaches are under 30 years old.
Odum joins the Spartans staff after coaching Oregon State's defensive backs the last two seasons while Brennan was coaching the team's receivers.
"I'm extremely excited to have Coach Odum join the Spartans. Working with him at Oregon State the last two years, I've seen his incredible ability to relate to his players. His players loved him and they played their hearts out for him," says the San Jose State head coach.
"He is an expert secondary (defensive backs) coach and he brings a lot of knowledge about the kind of defensive football we want to play and the kind of effort and energy we want to bring to the coaching staff."
Odum's coaching experience includes being part of nine teams that played in a Football Bowl Subdivision (FBS) bowl game, two squads that went to the Football Championship Subdivision (FCS) playoffs and four conference champions. He began his coaching career at his alma mater, the University of Utah, as a graduate assistant in 1996. Odum coached at Montana (1998-99), Utah State (2000-02), Houston (2003-04), Utah (2005-07) and SMU (2008-14) before moving to Oregon State.
His players earned 28 all-conference awards and eight of them were selected in a National Football League draft.
"This (being a defensive coordinator) is a career goal of mine going way back. Coach Brennan's given me the opportunity to achieve this goal. I'm real excited to be a part of San Jose (State) and get us moving in the right direction," says Odum about his first opportunity to be a defensive coordinator.
"We're going to see what our personnel can do, who we have on the scene, and evaluate everyone we have in the program. We'll be real multiple with a lot pressures, mixing and matching. It will depend on whom we are playing and their style of offense as well.
"Our front has to be real solid in the run game. We have to shore that up before any of that other stuff happens.
"I'm looking forward to the challenge. It's going to be a lot of fun for our guys."
The 1993 University of Utah graduate majored in political science. A two-sport athlete, he played for the 1989 through 1992 Ute football teams as a defensive back and was a centerfielder on the 1992 and 1993 baseball teams.
He and his wife, Ania, have two sons, Dominic and Jeremiah, and a daughter, Ryann.