After two weeks of intensive study, the five members of the team entering the VMC are assembled in the room, waiting for the competition's start time. There are also other students in the calculus BC course, who, wanting to use the extra credit policy, will unofficially take the test. Here' my chance to grab the attention of the girls in the other calculus BC section! Zack claimed that mathletes were the most coveted girls but a non-mathlete taking the course and is brave enough to face the mathletes on their field is still worth my interest, albeit not necessarily more coveted than an otherwise ordinary girl, Vontae thinks while wondering who's in a couple or not among those who unofficially enter the VMC's first round. All of them seemed to be in calculus BC, but Ted was there for his mathlete GF.

"Even though you know the town counts on us all, since this competition follows the format and content of a regular test, please treat it as such" Geneviève strongly advised.

"Ted! What are you doing here?" Krista asks, surprised to see the fullback attempting to take an exam that he had received no training for.

"I love you, Krista, but you're so obsessed by this competition that you let me down" Ted then declares to Krista.

"Of course not, Ted, I simply believe this competition is not for you. You still have some way to go mathematically before you can enter it. I don't want to see you suffer anxiety crises just for me. Randy is more mathematically mature" Krista then tells her boyfriend.

"Even though I know none of you need it, good luck. As for me, since I can't get extra credit from the VMC in pre-calculus, I'm gone" Ted then leaves.

"One last thing: to ensure the tournament's security, I ask you not to be too close to each other in the room. Gen, Krista, Marcia, you will respectively be on the front left corner, front and center, and in the front right corner. Cory and Vontae will then be on the back left and back right corners of the room" Trent instructs his mathletes.

What this means: the good old pyramidal cheating will make it so that the others dreaming of extra credit in calculus will go on the rear diagonals of their stars. Some even went to consider their position in the room as a good-luck charm. That was too easy, way too easy... Krista thinks, while it was THE contest for which she transferred! But she knows, however, that it's just the first round, with the first half of the contest that's supposed to last at most 105 minutes and containing 45 multiple-choice questions of single-variable calculus. If the people on the rear diagonals counted on pyramidal cheating to get extra credit, their speed, which is lightning-fast to their eyes... may have played some tricks to them. They answered so rapidly that the people relying on pyramidal cheating spent almost an hour left to their own devices. Cory and Vontae are a little slower on series and integral questions but for derivatives, no problem.

"Is it regret I am seeing on your face?" Gen asks Krista. "During the first half of the season, you were super happy to share in your mathletic and mathematical evolution with me and you had no regret about these contests and this transfer"

"Regret is probably not the right word, but this contest does not meet my expectations. It was potentially good for me last year, but after everything you made me do during the holidays, you did well to warn the town about the glorification of some aspects of mathletic contests at the dinner" Krista answers her.

"You're nice, but the warning I issued was actually relevant only for those who wanted to enter mathletic contests. You know very well it's not for everyone. There are people for whom the contests themselves can cause health problems. You also know that mathletics is much more than simply about intellect"

"And yet you know that intellect is the first thing that comes to people's minds when we ask them to draw a stereotypical image of a mathlete. Granted, an aspect that's a little narrow, but already better than no intellect at all. To what extent it can be transferrable, I don't know"

But at least both keep in mind that neither mathletics contests aren't for everyone, nor calculus, even single-variable, is for everyone either. It's not everyone that even needs it. Nevertheless, all five seem more comfortable in free-response questions. If no one is worried for their mathletes, the same didn't hold of people who wanted to take advantage of the VMC for extra credit, banging their heads against the wall to calculate derivatives and especially integrals for most.

Krista is surprised when Ted sees her again at the end of the competition, that all five of them finished before the end of the 90 minutes allotted for free-response questions, with a pair of football cleats appropriate for a strong safety.

"You have the right shoe size, Ted, and I know you play football as a fullback, but what makes you think that these football shoes are my kind of shoes?" Krista asks Ted.

"It's just a gift on my part. I love you, you're very nice, and you're a change from my teammates' girlfriends, except for Randy"

"It's bizarre that you're talking about your teammates' girlfriends, especially when Zack talked about how we were super coveted. How am I different from your teammates' girlfriends?" Krista asks.

"There are all kinds of them. Curtis dates Flo, who is usually pretty eloquent, the long snapper dating a girl that's relatively lazy, compared to Flo or you, and hand on tight, Zack who doesn't date a girl from this school but with one of your opponents"

"Zack did what?" Krista asks, a little surprised of the person that Zack dates.

"Zack is not really a mathlete; he's a strong safety, he thinks Tara will make him stop envying me or Randy. I met her on three occasions, twice at football games and the third time at the dinner. In his mind, he doesn't need to make the intellectual difference between her vs you three. After all, he can barely calculate a limit. Also, you always appeared easily accessible"

"But I prepared myself like crazy before the new year's countdown for tonight's tournament. You want to see what I did during all this time with Gen?" Krista asks Ted, while Ted knows it will contain math that's too advanced for him.

"I feel like it's about advanced mathematics. But you feel inclined to show it to me, so I accept"

"Very well, Krista then takes out a sheet of quad paper with a wad of Christoffel symbol calculations on a sphere of radius r, calculated shortly before New Year's countdown"

First calculate the metric, i.e., the first fundamental form. First derivative of the manifold's parametrization, and we have S(r,φ,θ)=(r sin φ cos θ, r sin φ sin θ, r cos φ). Consequently, we have

Sr(r,φ,θ)=(sin φ cos θ, sin φ sin θ, cos φ)

Sφ(r,φ,θ)=(r cos φ cos θ, r cos φ sin θ, -r sin φ)

Sθ(r,φ,θ)=(-r sin φ sin θ, r sin φ cos θ, 0)

We take the scalar product between each of the tangent vectors to obtain the metric coefficients. And the metric is therefore a diagonal matrix grr=1, gφφ= r^2 et gθθ=r^2 sin^2φ, having for inverse grr=1, gφφ= r^-2 et gθθ=r^-2 sin^-2φ. After that, we calculate:

There are 17 other Christoffel symbol calculations (of the second kind!) that follows on the pile of quad paper sheets that follow (by symmetry of the metric they were able to reduce 27 calculations to 18) and only 5 of them are nonzero [https://img.wattpad.com/1774ceef4e8e122303cfc05b28fe5e9ecf0291fe/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f776174747061642d6d656469612d736572766963652f53746f7279496d6167652f3331693444742d4465686c6f53773d3d2d313239323238343232382e313732646139343166396338623437623231393639393035303536362e706e67?s=fit&w=1280&h=1280]

There are 17 other Christoffel symbol calculations (of the second kind!) that follows on the pile of quad paper sheets that follow (by symmetry of the metric they were able to reduce 27 calculations to 18) and only 5 of them are nonzero.

"Wow! It's visually pretty but I must admit that the indices of the eighteen calculations at the end completely confuse me"

"Ted? I'm surprised on your part to see you say that equations can be visually pretty"

"Gen and you are machines"

Ensure your favorite authors get the support they deserve. Read this novel on the original website.

"Normally we do these kinds of things in third or fourth year of undergrad at the earliest. For the VMC we wanted to learn new notions that made use of what tonight's VMC covered. Gen's mom said we were going way too fast, but at the same time, we could both do this without complication. Yet these appeared like contradictory statements to me"

Ted gives him another kiss after having the same wads of calculations that Geneviève's mom must have seen after the New Year's Eve countdown.

Meanwhile, the members of the neighboring parish's VMC team, which actually comprised two Concepts and three Majors, are together for a pizza after this contest.

"I told you that I am dating a Venomous Agendas football player!" Tara claims with vehemence to the other two Majors on the neighboring parish's VMC team.

"We might hate on the Venomous Agendas because they win title after title, my dad had the chance to talk to their math captain and she seemed to understand the issues surrounding extracurriculars well" another Majors mathlete comments.

"And how is your boyfriend?" asks the other boy at the VMC for the Majors.

"He seems to accept me as I am, which is not obvious. He can barely calculate a limit, but..."

"In your position I would not date him!" Annette howls in Tara's direction.

"Annette? How dare you say this kind of absurdities?" Trevor asks, surprised by his girlfriend's statement. "You have an explanation?"

"It would limit what we can do on a date"

"For the national final, if we qualify, we must put our differences aside" Trevor warns Annette.

"While our opponents are the defending national co-champions, their three girls are inspiration sources for me" Tara told the others.

"How do you want to compete against a team with a girl capable of solving PDEs in open air? She appeared able to solve them without complication" Annette questions her teammates.

"Annette, you seem to be a bundle of nerves. We were both there when she did that, and our ex-teammate forced her hand about this" Trevor tries to calm Annette down.

"Krista was, yes, stronger than the both of us, but in the end, not many Concepts fans had any real interest in mathletics. Most people at school didn't hold it against her" Annette then tells her boyfriend.

"It hurts doubly, Trevor. I would love to believe that just qualifying for the national final would already be a lot for us, and even more so without Krista" a Majors mathlete tells them.

"We won't know until the end of the month whether we qualify or not" Tara points out. "By the way, I don't hold his mathematical inferiority against Zack, especially if I can make him stop envying his teammates"

At the end of the competition, Marcia feels, however, that something's not right. Why do the town seem to treat the first round of the VMC as they would have the AMC12, while the SRA last year was the big tournament that made us explode in popularity? Did Gen throw a cold shower without knowing it? Or is the town treating this as a formality, like a fan of these European soccer super-teams regarding the regular season? Or they just wait on the result? Marcia thinks, while the parish media strangely kept quiet about the first round.

"It's really not obvious, Marcia... I wonder how you can do this so easily" Randy comments.

"Now you know what to expect from the AP calculus BC Exam, four months before. I think about it a little, I wonder what made this competition lose its luster among the parish's public" Marcia tells her boyfriend.

"The population probably took for granted the qualification to the grand final, and you might not know it, but eight teams in this state entered the VMC" Trent points out.

Of which three are already out right out of the gate in the coach's mind: Lafayette, Brother Martin and Alexandria. There are five teams remaining capable to qualify for the grand final: Bâton-Rouge, Benjamin-Franklin, Caddo, the neighboring parish and themselves, obviously. Said neighboring parish defied all predictions in the Math Madness; they weren't expected to start the playoffs in the top division. That said, the Majors' fans haven't been as fast to get behind their own on the national mathletic stage.

"Remember the Math Madness regular season, reminds a girl that entered the VMC unofficially for extra credit. Did the population follow our regular season with the same fanaticism as in the playoffs?" Imélie asks when she hears her teacher comment on the loss of the VMC's luster among the population.

"No?" Vontae answers, a little annoyed.

"Also remember the AMC..."

"But, the AMC was held in the middle of the playoffs, it's not a good example. In fact, you're not in my calculus section; what's your name?"

"Imélie"

"I am Vontae"

"I feel the rest of the year will be painful" Imélie sighs.

Does the loss of the VMC's luster among the public mean that our popularity as a team is declining, or it's just that the public only cares about advanced tournaments? Geneviève ponders while she kept quiet in this discussion. But why, one day, the parish newspaper seems to anoint us as the only hope of the state for the EGMO and, by extension, the IMO, Krista and I, and the next day, no prediction regarding the VMC? Bi-zarre.

"But why would the parish newspaper have omitted to issue predictions on the VMC? They issued, indirectly, sure, predictions on à the AIME such that Krista and I are the only two girls of the state in position to qualify for the EGMO, as well as an outside chance for the IMO" Geneviève speaks, and Marcia leaves the scene as soon as she hears the word EGMO. Now, the two girls are alone with their coach.

"Please excuse my brutality but the EGMO represents your only hope for the IMO; this year the MAA announced that, starting this year, all EGMO contestants will be automatically invited to the MOP, the camp where the national team members for the IMO are chosen. The only reason for which the parish newspaper just talked about an outside chance for the IMO is they wanted to be nice to you and present it as nonzero. If you want an idea of what to expect of life at the MOP and at the IMO, you should do well to watch the movie X+Y. The biggest difference between the IMO and the EGMO about competing is that the EGMO is purely feminine while the IMO is male dominated" Trent lectures his two stars.

"X+Y?" Gen asks, not knowing what X+Y is about as a movie.

"Jesus! It's good to dream but we already know that if only one of us qualifies for the USAMO it's already a great victory for the parish. For the female mathletes of the state. For years there has been no Louisiana girl qualified for the USAMO" Krista points out.

"It would be the moment of mathletic glory that will mark Venomous Agendas history like the national co-championship of the SRA last year. Consider the following: on an average year, there are at most thirty to forty girls that qualify for the USAMO, and sometimes twenty or fewer, and the majority comes from other schools capable of winning at the VMC also. I narrowly missed this last year. That said the best four of them will enter the EGMO. Anything regarding the post-AIME competitions would simply be a cherry on top. We pursue mathletic glory like madwomen, I dragged Krista, Marcia and the town in this quest..."

"Geneviève, I think you feel remorse about your mathletic life. You have nothing to regret. You did nothing that could make you feel guilty of anything. Never in my life as a math teacher would I have imagined that an elite mathlete that's a source of inspiration for so many in the parish could regret having performed at such a high level. Maybe you won't believe me but, while, in Odessa, some kindergarteners dream of playing football for Permian as if it was a lifetime aspiration, some kindergarteners in our town dream of wearing the purple and the green of the Venomous Agendas in mathletic competition! But there's one thing you have that Éliane didn't. Yes, Éliane had brains, too, but she had no charisma among the population. Gen, you have more charisma than all other female mathletes that can win it all at the VMC, or that could qualify for the EGMO or the IMO!"

"You talked on a few occasions about how you are responsible of the intellectual excesses committed by the two of us at first, and later those of the entire town. And yet you continue to make me commit what you call intellectual excesses. I don't understand your lack of coherence. Me, however, I know that you push me harder intellectually than practically everyone I have known. You know deep down how hard I'm willing to push you" Krista had a remark to make.

"I acknowledge that we push each other very hard. But when I have panic attacks, I have the impression of being someone else that I'm not. You had that experience, too, Krista; when you feel like you're losing control over your intellect, or that your brain doesn't otherwise function at a level that appears acceptable to you, you feel hurt internally, do you not?"

"Yes, but it's not like an impostor's syndrome. I know very well what I'm capable of, but I have the impression that my intellect is a big piece of who I am as a person, maybe too big a chunk, but still... I don't necessarily need to maintain an optimal level of mental functionality at all times"

"At your age, I was a mathlete, too. But unlike you, I've never been very popular in class, I never accomplished a whole lot as a mathlete. I told myself that maybe, by coaching you, I can accomplish what I couldn't do as a mathlete, if only vicariously. But I must warn you, mathematics competitions won't necessarily give you a good overview of the discipline. That goes for everyone on the team, at the AIME"

"From everything I've seen about the USAMO, if I'm not mistaken, it's a proof contest that rewards someone that can be ingenious and quickly. Same goes with the EGMO and the IMO. It might be realistic for the two of us to qualify, to the USAMO I mean, but glorifying speed and curricular skills was the warning I issued at the dinner. Not very succinct as a warning" Gen then reiterates her warning.

"Learning speed to be exact. I am aware, like you, that these contests that the parish newspaper alludes to and described us on multiple occasions as the only hope of Louisiana on it are extremely difficult. Let's not delude ourselves, if we qualify for the USAMO, even getting a nonzero score is already very good. Here's the plan: after the AIME we start using the WOOT system and we'll train for this competition" Krista displays her viewpoint.

"Don't neglect the other subjects just for this contest. I understand your desire to bring back mathematical glory here, but another fundamental aspect of mathematics is that sometimes you need to ask good questions and sometimes solving one can take years. Nevertheless, I think you have a better chance of continuing to like the subject if you don't overdose on it. Practicing is one thing, but you must do so intelligently. Don't forget, at the USAMO, it will take two days of four and a half hours each, you will have three problems per day and each problem is graded on seven. If it still interests you, I hope that you're not afraid to get a result which, on a regular test, would be a complete failure; it can be a traumatic experience" Trent advises them before stopping this conversation that lasted too long to him.

Historically, girls haven't always performed well on the USAMO, and attempting to reproduce their feminine top-15 on the USAMO would essentially amount to do better than the median. Said median is typically between 8 and 15 points.