## Spelman's Got (Math) Talent, Spring 2016

In the spring 2016 semester, students in both my Math 324 (Cal III) and Math 463 (Real Vars) classes were given the option of doing something "artistic" for extra credit. The following statement was included in all of my syllabi:at the discretion of the instructor, for coming up with and sharing

an innovative original artistic creation about class material

in the form of a poem, rap, song, video or dance."

This is what they came up with!

## Cal III

**Journey of Discovery: Mystique of the Double Integral (Abiana Adamson)**
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Late this afternoon I wondered

Late this afternoon I pondered

Late this afternoon I discovered

The double integral

With domains of 2 dimensions

With the chance of 2 integrations

With the prospect of volume calculations

The double integral

I can tell Carol the center of mass

I can tell Daryl the volume between surfaces

I can tell Cheryl the average value

The double integral

Early next morning I wondered

Early next morning I pondered

Early next morning I remembered

The double integral

**The Creation of Partial Derivatives (Kristina Brown)**
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There once was a family of variables who lived deep in the textbook of Calculus 3

The parents liked to be called F, and the children were x, y, and sometimes z

The children never liked to do anything together, even though they had so much in common

Because of this everything was done separately, giving respect to each child

One day at the school of FUNCTIONS

X and Y both decided to play in coloring Math and Arts

They were supposed to work together, but of course this didn’t happen

In coloring math and Arts the children picked a picture to color

And at the end of Coloring Math and Arts the children have to take derivatives

Derivatives is when all the children show how the picture has changed after coloring it

X and Y did not want to present together

So two derivatives had to be done so each child could feel special

X went first and Y did not want to participate at all

So when it was Y’s turn X didn’t want to play

Finally when both children did there derivatives a strange image was made

Together they were able to make the slope of the curves on the picture

The children were so happy about their accomplishments

And since then they have been making partial derivative history

**3D Surfaces (Amanda Collins)**
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3D surfaces are solid, not flat.

Look at a cone; it is like a pointy hat.

Even a cylinder looks like a can.

Of course, a sphere is like a ball man.

However, if it loses air it looks more like an ellipsoid.

Even an hourglass is shaped like a one sheet hyperboloid.

Nevertheless, a paraboloid is more like a bowl.

With a 2- sheet hyperboloid, you get two for one bowl goal.

3D surfaces can be so much fun.

**Two Is Better than One (Hannah Floyd, with Audio)**
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“Two is Better Than One” (Double Integration)

Let’s go back to the day when we first learned

It came into our lives and I thought

Double integration is helpful

‘Cause even though you’re harder than single

You help me with real world applications

And now I know a lot more

Maybe it’s true, that much more can be done with you

It’s clear two is better than one

There’s so much to compute

Like volume, area, and centers of mass

And you’ve already got me doing much more

And I’ve been thinking two is better than one

You’re defined as limits of sums

And evaluated using the

Fundamental Theorem of Calculus

But don’t forget to do that more than once

That’s what makes the double more special

than single integration

Everyone knows youuu

have a different domain

Because there’s two variables

It’s a plane region whose boundary may be curved

Now lets get much more into the details

Because we all know two is better than one

Double integration

There’s 3 steps

Subdivision, summation, and passage to the limit

It’s true that double integration

Can be used in more than one way

Over a rectangle, or over more general regions

Letting us define Volume of a region

And yes it’s true there’s even more than two

Remember two is better than one

There is also triple integration

And I’ve already covered just so much

Aren’t you thinking two is better than one?

**Haikus on vectors (Sydney Harris)**
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**Haiku Poems on Vectors**

__ __

Two dimensional,

Sometimes three dimensional,

Vectors are unique.

Two points in the plane,

An initial point P and

Terminal point Q.

Length or magnitude,

The distance from P to Q,

Is easy to find.

Distance formula,

Square-root of a^{2}+b^{2},

Length of the vector.

Compute the dot product,

Multiply corresponding

Components and add.

Calculus three has

Vector geometry and

Many more concepts.

**What Do You Do? (Morgan Lipkins)**
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Based on "How Will I Know" by Whitney Houston

__https://www.youtube.com/watch?v=LzgaJpp5edM__

There’s some things I know, all in Chapter Four-Teen

In the end you’ll see, how it will all come to be

Here comes the first one, just for several variables

It’s **partial derivatives**, and it measures rate of change

[Chorus #1]

What do you do? (With **Partial Derivatives**)

What do you do?

What do you do? (Given a nice Function)

What do you do?

You have to single out each variable

Then take their distinct derivative

Fx for “x” and fy for “y”

Well, it depends on what dimension I’m in

Treat the other variable as a constant

And if there are some given points (Keep Colm)

All you have to do is plug them in

Now you’re done what else could there be?

Oh, of course, higher order, partial derivatives

Said there’s no mistaking, it’s the second-order deriatives

[Chorus #2]

Ooh There’s more: What do you do? (for a Mixed Partial)

What do you do?

What do you do? (Relation to another)

What do you do?

Look at the first partial derivatives,

Take the rate of change of one nice variable

In accordance of the other variable

Find mixed partials in respect of both variables

And just remember mixed partials must match

If you try it and it fails you (replay)

Solving it out is all very easy

If you listen to me, credits to Mulcahy

Now you know too, all that this includes (3x)

What do you do?

What do you do?

What do you do?

[Chorus #3]

What do you do? (With Partial Derivatives)

What do you do?

What do you do? (Given a nice Function)

What do you do?

You have to single out each variable

Then take their distinct derivative

Fx for “x” and fy for “y”

Well, it depends on what dimension I’m in

Treat the other variable as a constant

And if there are some given points (Keep Colm)

Now all you do is continue through

This short process, and now you it too!

**Haiku on integrals (Faith Lyons)**
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Volume of Solids.

Make them iterated then,

Fubini's Theorem.

**The Class of Oh My! (Sheveika Robinson, with Audio)**
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What is the cross product?

Can you sketch part of the plane?

Is the equation of a 2-sheet hyperboloid x^{2}-y^{2}-z^{2}=1?

Ummm,

Note to self, Calculus 3 is not a game!

Gradients and Derivatives and Integrals OH MY,

Gradients and Derivatives and Integrals OH MY,

Gradients and Derivatives and Integrals OH MYYYYYYY!

Is it a min?

Is it a max?

Can you find the derivative?

What is the directional derivative?

What is the partial derivative?

Ummm,

Reality Check, Calculus 3 is still not a game!

XY-Planes to XYZ-Planes,

XY Coordinates to Cylindrical Coordinates to Spherical Coordinates,

Integration of one variable to Integration in two variables,

Single Integrals to Double Integrals to Triple integrals.

Calculus 1 and Calculus 2 and Calculus 3, OH MY,

Calculus 1 and Calculus 2 and Calculus 3, OH MY,

Calculus 1 and Calculus 2 and Calculus 3, OH MYYYYYYY!

None of it is a game!

**The Best of Both Worlds (Maenishia Simmons, with Audio)**
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The Best of Both Worlds: Rendition of Hannah Montana lyrics

Oh yea, come on

You got the vector in the plane

Any length, two dimensions, two points

Yea when you’re a vector, it can get confusing

It’s really simple but no one ever discovers

In some ways vectors represent direction

But it is just a line

You get the best of both worlds

Three dimensions

Then you have three coordinates now

You get the best of both worlds

Switch it up, same concept

Then you know it is the best of both dimensions

Best of both dimensions

Vectors are in physics

See your applications

Living two dimensions is a little weird

But it’s cool because it is the same

You start with an initial point

But end with a terminal one

You get the best of both worlds

The length is magnitude

And is from P to Q

You get the best of worlds

Switch it up, same concept

## Real Variables

**I Got a Feelin' (Veron Frith)**
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**I Got a Feelin’ Remix (Black-Eyed Peas)**

**Some Words of Wisdom**

** **

Some words of wisdom, I’ll share a good few theorems,

I’ll share a few good theorems

I’ll share a few good the-e-orems

Some definitions, remember definitions

Remember definitions

These really important definitions

Todays the day! Lets turn it up!

I got my Reals notes, lets learn it up!

Just attempt it, its not so hard

Contradiction! Round of applause!

I know that we’ll have a ball

Let’s start with the order properties of R

It says, that there of three of them

P is closed under addition and multiplication!

Law of Trichotemy! (shout)

Let’s move on, lets talk closed balls

With center x, and radius r

Represented, just like this Br(x)={y Î R | ||y-x||£ r}

Remember tis equation for other things

Lets do it, let’s do it, lets do it, lets do it

And do it, and do do it, (do it again)

Lets do it, let’s do it, lets do it, lets do it

Lets do it, let’s do it, lets do it, lets do it

Some words of wisdom, I’ll share a good few theorems,

I’ll share a few good theorems

I’ll share a few good the-e-orems

Some definitions, remember definitions

Remember definitions

These really important definitions

Another topic, lets talk about points

Interior, exterior, boundary points

All together, they make the set

But x can only be, one of them

Here it comes, Heine-Borel

It makes this easy, we’ll use it well

A set is compact if its bounded and closed

So what’s this set [0,1] (compact)! Round of applause

Now guess what we’re at the end

Another topic, sup and inf

They describe bounds greatest and least

They’re from a property called Complete!

Lets do it, let’s do it, lets do it, lets do it

And do it, and do do it, (do it again)

Lets do it, let’s do it, lets do it, lets do it

Lets do it, let’s do it, lets do it, lets do it

**Cartoon (Micah Henson, Video)**
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**A Conversation (Tyler Howe)**
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A Conversation between the Number Groups

Starring: The Rational and Irrational Numbers

**Rational:**
Oh Real Numbers, how do I love thee? Let me count the ways…

**Irrational: **
Dear brother, you cannot, do not lead my love astray.

Because someone like you cannot comprehend the power that she holds.

A number group so uncountable, so unbounded, and so bold.

**Rational: **
But can you not see how different she is?

How unafraid?

She is my hero.

The way she carries herself so gracefully while including the number zero.

**Irrational: **
Are you sure you really love her if that is the only quality you see?

If so, you can gladly love the Integers and leave the Real Numbers to me.

**Integer: **
So am I just disposable to two number groups like you?

Because I am exclusive and never include you two?

I have a certain way of doing things so don’t sneer about me.

Zero, positive, and negative numbers are my friends.

Something you all will never be!

**Rational: **
I thought I came here all alone to court my lady love.

**Irrational: **
*Your *
lady love?

**Rational: **
*My *
lady love!

**Real: **
Must we always have this argument?

I’m simply sick of this.

You two are both a part of me!

This quarrel must be dismissed!

I refuse to choose between you two.

This decision is making us all tense.

Just know, I love you both the same.

In the heart of me, so dense.

**Rational and Irrational: **
*blank stares*

**Real: **
*triumphant exit*

**Integer: **
*wondering why she was mentioned in the first place*

**The "Reals I" Struggle (Hadiyah Jones, with Audio)**
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When you hear the word math, what comes to mind?

Most people say numbers, both composite and prime.

My hardest math course thus far has been Reals,

While taking this class, I struggled a great deal.

A’s and B’s in Reals took effort to earn,

But I came out smarter and this is what I learned.

The first thing you should know is how to write a proof,

Using all the rules and theorems to show something is true.

If a set has an upper bound, it has one below,

And it has an inf and supremum fa’sho!

If the complement of a set is open then it’s closed,

if a point is interior in the set it’s enclosed!

Exterior points are in the complement of a set,

And since they aren’t included they always are upset!

Cluster points are cool when talking about sets,

Every open ball contains a point that isn’t x!

Compact sets are, closed, bounded, and covered,

And we proved that in class, word to yo’ mother!

Sequences and limits were my least favorite topics,

The stressful subjects almost turned me into an alcoholic

If a limit of a sequence is zero it converges,

But if it’s limit is infinite then you know it diverges!

When proving convergence, there’s a few things you must know,

Like seek an epsilon that is greater than zero!

Even though this the end, there’s much more I could say,

But if I talked about it all we’d be here all day!

My relationship with Reals is made up of love and hate,

I am thankful for the knowledge plus my teacher was great.

Will I see these theorems again? Only time will tell.

But for now goodbye "Reals I" I bid you farewell!

** **

**Wannabe (Naccari Murphy & Taylor Sain)**
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Based on www.youtube.com/watch?v=gJLIiF15wjQ

by the Spice Girls

**“Wanna Learn about Reals”**

**CHORUS:**

Yo, I'll tell you what I know, what I really really know,

So tell me what you know , what you really really know (x2)

I gonna, I gonna, I gonna, I gonna, I gonna really really really teach you some reals.

**Verse 1:**

Reals is the study of functions and continuity.

Whole numbers, Integers, and rationals alike

Real numbers are these sets combined

Plus the irrationals like e and π.

**CHORUS**

**Verse 2:**

If you wanna learn about reals, a couple things you should understand

Make the reals a field, you can order it,

If you have bounded sets, you need sups and infs,

It sounds too easy, but that's the way it is.

**Bridge:**

What you think about that? now you know some reals,

Can you handle this math? Prove it for real

Does root 2 exist? Lets give it a try.

If the sequence diverges, then I’ll say goodbye.

**CHORUS**

**Real (Nyla Walker)**
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Real…

Real analysis is equal to

Proofs measured by time spent,

And the names attached to them

Equal to the open balls of endless opportunities

Analysis of mainstream minds

In search of the challenge of real life

Solutions uncovered by any means necessary

Real time multiplied by answers

Only meant to detract from the

Real analysis of

Life.