Sheldon hoped to lure his class into answering Newton as a scientist who contributed to the development of Calculus and had a biscuit named after him so that he could correct them. Although not revealed in the episode, the correct answer is Leibniz, who also contributed to Calculus and has a biscuit that bears his name, "Leibniz-keks".
Sheldon says that the reason why no one signed up for his class is that he has a reputation for being obnoxious. Another reason may be because he gave an extremely boring lecture in The Thespian Catalyst (2011) that was universally panned by students on social media.
The song that Howard is singing whilst disrupting Sheldon's class is 'All I Do Is Win' by DJ Khaled.
Title Reference: The title refers to Sheldon's new junior professor position at Caltech.
Amy and Bernadette go out together without asking Penny, because Bernadette is annoyed that Penny doesn't make more effort preparing for her new job. This is similar to The Anything Can Happen Recurrence (2014), when Bernadette got a bit fed up with Penny's constant complaining about being in a B-horror movie. Although Bernadette claimed in The Shiny Trinket Maneuver (2012) that she wouldn't be a good mother, she is clearly giving Penny the opportunity to get away from bad acting roles, as well as from being "a stunningly poor waitress" (Amy's words), and like any mother, shows frustration when the 'child' isn't taking the opportunity serious.