## 05.22.2019: One Chapter of Science - Thinking Like a Scientist

Today's soundtrack is Samael: Above, an industrial-sounding modern black metal album. So I've completed my high-school level math courses and taken a few much-needed days off. What's next? Well, in the fall, my plan is to tackle high school science and start on university-level math. To prepare, I'm going to focus on working my way through two books by September: Silvanus P. Thompson's Calculus Made Easy, and Everything You Need to Ace Science in One Big Fat Notebook. Today,

## 05.15.2019: One Lesson of Math - Final Exam of the Final Course!

Today's soundtrack is Sonya Kitchell: This Storm, a beautiful, jazzy, soulful album that I bought because I'd first heard her debut at Starbucks and loved it. I've heard that Kitchell cites Joni Mitchell as an influence, and I can believe it; her songwriting is so timeless and thoughtful. Stylistically, she reminds me a bit of Nora Roberts. As I write this, I'm sitting down to do my final review of the two unit tests before going in to write my final Precalculus 12 exam. I'll

## 05.14.2019: One Lesson of Math - Studying, Part 3

Today's soundtrack is Rebecca St. James: Worship God, a gorgeous, triumphant praise and worship album. This is my last day to study before tomorrow's exam; I'm using this time to review all of the quizzes and tests from both of the module's units. #RebeccaStJames

## 05.13.2019: One Lesson of Math - Studying, Part 2

Today's soundtrack is Andy Hunter°: Exodus, a top-notch electronic album that features the hit single "Go," as heard in "The Italian Job." I bought this album on CD back when I was first learning how to compose music using MIDI in Cakewalk Express Gold 8.0, and it influenced me greatly. This afternoon, I'm reviewing all of the quizzes in the permutation and combinations unit, then reviewing the test that I wrote in the function notation and operations unit. #AndyHunter

## 05.12.2019: One Lesson of Math - Studying, Part 1

Today's soundtrack is Theory of a Deadman: Gasoline, a bangin' modern rock album. I love their sound. Today is the first of four days of study that I have to prepare for my final exam of this course. I'll start by reviewing the quizzes I wrote in the final unit, writing the final unit's test, and then reviewing the test that I wrote in the first of the two units of this module. #TheoryofaDeadman

## 05.12.2019: One Lesson of Math - Function Notation and Operations, 4/4: Compositions of Functions

Today's soundtrack is Xzibit: Restless, bringing some West Coast rap to your ear holes. This is it. The final lesson of the final unit of the final module of the final high school level math course. In it, I'll be learning about composite functions. Composite functions exist when one function is inside of another function. They can be expressed "f of g of x," f(g(x)), or (f∘g)(x) - not to be confused with (f⋅g)(x)! When working with composite functions, we must follow these s

## 05.11.2019: Function Notation and Operations, 3/4: Products and Quotients of Functions

Today's soundtrack is Six Feet Under: Death Rituals, a plodding death metal album featuring Chris Barnes on vocals. He was a founding member of Cannibal Corpse, and thus a huge influence on modern death metal. I bought this album because the album that got me into death metal was Cannibal Corpse's "The Bleeding," and I loved Barnes' raw, gutteral vocal style on it. This morning, I'm learning about multiplying and dividing functions. As we discussed yesterday, we can multiply

## 05.10.2019: Function Notation and Operations, 2/4: Sum and Difference of Functions

Today's soundtrack is Lacuna Coil: Karmacode, a metal album featuring Cristina Scabbia's gorgeous singing. I still remember discovering this band and thinking, "THIS is what Evanescence was going for, but couldn't quite reach!" When we combine two or more functions, we get a new function! Let's say we want to add f(x) =3x-1 to g(x)=x+2. So we are looking for (f + g)(x), the sum of f and g of x. Since 3x + x = 4x, and -1+2=1, f+g(x)=4x+1, but since combining two or more functi

## 05.09.2019: Function Notation and Operations, 1/4: Function Notation

Today's soundtrack is Insomnium: Above the Weeping World, a melodic death metal album. Today, I'm staring the final unit of the final module of this course. Hooray, hooray! This lesson is about function notation (not to be confused with factorial notation). We begin by reviewing relations and functions. Relations are sets of numbers that go together. They can be represented with a table, a graph, or a listing of R={...}. The domain of a relationship is its x-values (its first

## 05.08.2019: Permutations and Combinations, 5/5: Pascal's Triangle and the Binomial Theorem (2/2)

Today's soundtrack is Deep Purple: Machine Head, an album that I bought because I loved playing "Highway Star" on Rock Band. This morning, I'm continuing where I left off yesterday in learning about the binomial powers. Now that we know how to expand a binomial power quickly using the concepts found in nCr, we can establish the Binomial Theorem, with which we can find the value of any term of an expanded binomial. The Binomial Theorem formula is tₖ₊₁ = ₙCₖ aⁿ⁻ᵏ bᵏ Note here

## 05.07.2019: Permutations and Combinations, 5/5: Pascal's Triangle and the Binomial Theorem (1/2)

Today's soundtrack is Figure Four: No Weapon Formed Against Us, a groovy hardcore album that was released in 1999. I'm still trying to wrap my head around the fact that 1999 was 20 years ago! This afternoon, I'm going to be learning about Pascal's Triangle and the Binomial Theorem. Pascal's Triangle is an interesting series of numbers that flows down like a pyramid. The first few rows look like this: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 ...

## 05.06.2019: Permutations and Combinations, 4/5: Combinations

Today's soundtrack is Strauss: Masters of Classical Music, Vol. 4. This afternoon, I'm learning about combinations. Combinations are like permutations, except in a combination, you're looking for a group of things, and their order does not matter. If I am making a pizza, and I have five toppings to choose from, but I want to put only three of them on, how many ways could I arrange the toppings from bottom to top? Would the cheese go on the bottom or the top? Would the olives

## 05.05.2019: Permutations and Combinations, 3/5: Permutations Involving Identical Objects

Today's soundtrack is Hellyeah: Band of Brothers, an awesome southern groove metal album from the American supergroup that features the legendary Vinnie Paul on drums. Today, I'm learning how to calculate the permutations of a series that includes identical objects. If I have five Smarties and I want to see how many ways I can arrange them by colour, I'd of course calculate 5!, which is 120. But what if two of them are blue? I don't want to count the same kind of arrangement

## 05.04.2019: One Lesson of Math - Permutations and Combinations, 2/5: Permutations Involving Differen

Today's soundtrack is The Red Chord: Clients, a technical metalcore album. May the Fourth be with you, and also with you. This morning, I'm learning about permutations, which are ways that we can rearrange the items in a series. This concept was touched on in yesterday's sandwich example. The series B E D has the following permutations: BED, BDE, EBD, EDB, DEB, and DBE. We can break it down like this: We have three choices for our first letter, two choices for our second lett