NEW YORK — When Serena Williams plays in the US Open semifinals Friday, her coach, Patrick Mouratoglou, probably will pull out a pen and jot some notes in his ever-present black notebook.
He does that at most of her matches, finding things to focus on so Williams can keep improving. Yes, that’s right: Williams already owns 16 Grand Slam titles, is ranked No. 1, is three weeks from her 32d birthday — and yet she still wants to get better.
‘‘She’s open to discussion, changing things,’’ Mouratoglou said. ‘‘She’s very open to working hard and doing things that she needs to do.’’
To that end, Mouratoglou and Williams will sit together and watch video of her matches, going over the positives and negatives he picked out while courtside.
‘‘She’s working like if she was 19 years old and she wanted to win her first Grand Slam. She has the same appetite, and she’s open mentally the same way to get better every day. So that makes a huge difference,’’ Mouratoglou said.
Williams is two wins away from her second consecutive US Open championship and fifth in all. Having dropped a total of 13 games through five matches — including a 6-0, 6-0 victory in the quarterfinals — she next faces No. 5 Li Na of China, the 2011 French Open winner. No. 2 Victoria Azarenka of Belarus, the two-time Australian Open champion and last year’s runner-up in New York, meets 83d-ranked Flavia Pennetta in Friday’s other semifinal.
Williams began working with Mouratoglou shortly after a first-round loss at the 2012 French Open, the only time she’s exited a major tournament after her opening match.
‘‘Seeing that match, and seeing her practice a few days after, I just saw that she was lacking balance. The body weight was going everywhere, except where it should go,’’ Mouratoglou said. ‘‘So it was tough for her to be hitting well, the way she would like to, to have her usual power.’’
Since being beaten at Roland Garros, Williams has won 96 of 101 matches and earned 13 titles. In 2013 alone, she is 65-4 and has matched her career high with eight titles.
In addition to her eye on the singles prize, Serena and sister Venus Williams rolled through the top-seeded defending champions, Roberta Vinci and Sara Errani, to take their spot in the doubles semifinals.
Bryan brothers ousted
Trying to become only the second men’s doubles team to win all four Grand Slam tournaments in a single year, Bob and Mike Bryan saw their bid end with a 3-6, 6-3, 6-4 loss to Leander Paes and Radek Stepanek in the semifinals.
‘‘As competitors, we hate to lose and we knew what was riding on this match and the opportunity of what we could have accomplished,’’ Bob Bryan said. ‘‘And then in one sense, it’s a little bit of a relief where you get to kind of exhale for the first time in a few months.’’
For nearly 12 months, a span that included 28 straight wins in Grand Slam matches, seemingly every bounce and every bit of luck went the Bryans’ way. It put them two wins away from joining the 1951 Aussie team of Ken McGregor and Frank Sedgman as only the second to capture the calendar Slam in men’s doubles.
But the 35-year-old identical twins ran into a pair of fast-handed veterans who have never backed down.
This match was no different.
‘‘You leave that door a little ajar, I will find my foot through it,’’ said Paes, 40, who has 13 major titles of his own, seven in men’s doubles and six more in mixed. ‘‘Once I get my foot through it, I got my body through it. Once I get my body through it, I get him through it.’’