Martha, as a medical student, was a huge fan of taking meticulous notes. She believed in classifying, sorting, categorizing, and in observing her subject to help her understand and, ultimately, conquer it. Whenever she had a problem she couldn't immediately grasp, she would study it in painstaking detail until she knew it better than she knew herself.
Her initial impression of the Doctor was that here - here was the subject of a lifetime. She had been with him now for several days, both in the Royal Hope Hospital, and later in 16th century England. They'd spent one night in Shakespeare's London, awkwardly sharing a tiny bed, before she ever got the chance to settle down into a proper bunk in the TARDIS, and honestly she hadn't thought she would ever really sleep on the ship since all she'd been promised was one trip.
When they came back from the Globe, though, the Doctor suggested that she get some rest, and she took him up on it. He led her to a room that contained some minimalist furnishings, bid her a distant good night, and disappeared quickly into the heart of the ship.
Martha took a moment to stretch – and to somewhat girlishly throw her arms out and spin around in the center of the room because heavens, she was in SPACE, thank you very much and how often does a girl get to have a bedroom on a spaceship?
It was on making a more careful tour of the room that she discovered a lovely writing desk with several blank notebooks, all creamy, high quality paper with both blank sheets and graph paper, and a jar full of lovely pens. She pulled out the chair and set to work.
Day one observations, she wrote. Subject appears to be humanoid in form, from what can be observed, except for what appears to be a binary circulatory system. Suspect CPR for total cardiac arrest would require stimulation of both hearts simultaneously, although not observed in the field. Body temperature appears to be somewhat lower than humans. Pupils appear equal and reactive in the expected manner to which one is familiar…
She continued writing long into the night, quitting only when her eyes became too tired to focus, at which point she carefully tucked away the notebook in the pocket of her coat and curled up on top of the sheets for a quick nap.
This was going to be the study of a lifetime, she thought to herself as she drifted off into a dreamless sleep.