Many of his teammates left the Garden this week with sights set on getting some much needed rest. A Stanley Cup run that extended into the early summer will do that to anyone. But rest was the last thing on Dougie Hamilton’s mind as he packed up his belongings and planned to head home this week. The 20-year-old defenseman’s season ended on May 23, following the Bruins’ 4-3 Game 4 overtime loss to the Rangers in the Eastern Conference semifinals. Hamilton was a healthy scratch for the rest of the postseason. He spent 11 games watching in a season of learning that’s made him eager for the start of his sophomore campaign. So when asked if he was taking some time off, Hamilton said he’s had plenty of that already. “I think I’m skating this afternoon. I’ve been working hard in the last month not playing but I think for me, I’m ready to start working out and stuff and I’m looking forward to that,” Hamilton said on Wednesday. “I think it’s going to be a short summer obviously and I’m just going to try to work as hard as I can and improve as much as I can.” Hamilton came to the Bruins as a soft-spoken rookie, and made an instant impact. In 42 games, he had 16 points (five goals, 11 assists) and averaged 17:08 of ice time. Though his future is undoubtedly bright, Hamilton played in only seven playoff games, three in the first round against Toronto and four in the second against New York. He tallied three assists.