Stay to Study with Luck

“Sorry, Ruby, but I think I’m going to stick around here a little longer with Professor Luck,” you say. “Maybe some other day?”

“Aw, okay,” Ruby pouts, and then she gives you a good humoured smile. “I’m counting on that!”

Professor Luck chuckles as Ruby leaves.

“There aren’t many guys your age who would turn down a study session with her,” she remarks.

“Well, there aren’t many guys my age so spoiled for choice,” you reply, giving her an easy smile.

She laughs, shaking her head, and then picks up her chalk.

“So, was there anything else there that I could clarify?”

I’d like your clothes to clarify, you think, but you say aloud: “Nah, I was just sticking around because I enjoy your company.”

“Is that right?” Professor Luck laughs as she sits back down at her desk.

“All I mean is that, should I run into any difficulties while trying to solve this problem, you’ll be right there for me.”

“Best get to work then,” she says, pulling out a sheaf of paper and twirling a black ballpoint point. Glancing at her, you catch the small smile on her face, and that’s got to be worth something.

“How are you holding up?” she asks, a few minutes later.

“I’m a bit stuck,” you say, staring at your page full of half-crossed out ideas. “Do you mind giving me a hand?”

“That’s what I’m here for,” she smiles. She comes over to look at what you’ve got on your page.

The smile on her face quickly turns into a puzzled frown as she brushes a stray strand of brown hair out of her eyes.

“Sorry, I’m having a bit of trouble following this,” she says, eyes darting across the page.

“I am too,” you say, feeling embarrassed. “There’s not really a logic to it. It’s mostly just bad attempts to solve the problem, but… I’m not really sure what it even means to construct a new integral.”

“I can see how that might be confusing,” Professor Luck says. She pauses. “You’ve never heard of a Lebesgue integral before, right?”

You shake your head, no.

“Hm…”

She thinks for a moment, and then heads up to the blackboard, drawing a squiggly curve over a x- and y-axis. She draws a bunch of tall vertical rectangles beneath the curve.

“This should be familiar, right? The Riemann integral?”

“Yeah, that makes sense to me,” you say. “But I’m not sure how we’re supposed to relate that to this measure you’ve given us…”

“Well, what if we tried using, not a bunch of vertical rectangles, but horizontal ones?” she says, drawing another squiggy curve and filling it up with long horizontal ones this time.

You stare at the board for a second, and then a lightbulb goes off in your head.

“Oh! I think I get it! We can get the size of the rectangle with the measure, so…”

You hurriedly scribble down some lines on a fresh sheet of paper, not wanting to lose the moment of inspiration before it leaves you. A few minutes later, you look up to see Professor Luck’s adorable smile, clearly some pride in her eyes.

“Almost!” she says. “Just a small correction here when you take the sum…”

“Oh right,” you say, seeing what she means.

“And there we go! That’s question two done, and I can’t imagine question three will be much harder, now that you understand what’s going on,” she says.

“Wow,” you say, looking over your work. “I can’t believe it just clicked like that.”

“It’s addicting, isn’t it,” Professor Luck smiles. “That moment when everything comes together.”

“Don’t tempt me, or I might just become a math major,” you laugh.

Luck +15