Symbolic Logic: Conditional/Indirect Proofs and Proving Theorems

Hey guys! So, this time, we're going look at other methods we can use to construct proofs when just deriving from the premises isn't enough. Conditional Proof (CP) The setup: Basically, you use this method when the conclusion or a part of the conclusion you want is a conditional. This makes it so you assume…

Symbolic Logic: 10 Replacement Rules

This is part two of our little intro to Symbolic Logic. We're going to expand our repertoire of rules we can employ in our proofs. These rules are all about putting logic statements into an alternative form. A lot of these rules will be familiar as they're used in mathematics. One of the differences between…

Symbolic Logic: 8 Basic Inference Rules

Hi y'all! So, if you're computer science majors/philosophy major/etc., you probably have to take this class in college. I love this stuff because it's very procedural and the proofs they give for you to solve are like puzzles and puzzles are super fun. Today, we're gonna look at the 8 basic rules and then we'll…

How To Read/Trace Recursive Methods

So, recursion, one of the hardest units in APCS. The concept is pretty easy but the execution is a bit trickier. Today, I'm going to pass on a trick that my teacher taught me on how to trace your way through a recursion problem. I'm going to assume that y'all already know what recursion is…

Commonly Missed Concepts of AP Macroeconomics

Alright, let's review for AP Drawing Graphs and go over some of the most commonly missed (and least taught) concepts on the AP exam. First off, C + I + G + NX = Y, which means consumption (by households aka the public) plus investment (by companies) plus gov't spending plus net exports (which is…

AP Bio Cell Energetics Diagrams

Side Note: I don't know if my little notes on the margins are entirely correct but the diagrams should be. If in doubt, always refer to your textbook or ask the teacher. This is one of the harder units along with genetics. Good luck!

APCS Chapter 6: 2D Arrays and ArrayLists

Alright, it's time to tackle 2D arrays and arrayLists. 2D arrays are basically arrays of arrays. First off, 2D arrays: 2D Arrays To start off with, the declaration and instantiation. Since 2D arrays are objects, we will use the new operator. There are several ways to do this: The "normal" way:data type [] [] name = new data type…

APCS Ch 6: Sorting and Searching Methods

Sorting methods as it pertains to arrays isn't the simplest thing to wrap your head around but the concept and the way they should work should be pretty intuitive. You would need to know about two main sorting methods in APCS; the selection sort and the insertion sort. Like the different types of loops, both of these…

APCS Ch 6: Arrays Basics

Arrays are basically lists of things. This list can contain both objects and primitive data. The basic array can be declared and instantiated as such: (data type)[ ] (arrayname) = new (data type) [(number of elements)]; Since arrays are considered as objects, the declaration and instantiation follow the pattern of other objects. So, if I…

AP Com Sci Chapter 2 Lab Review

This lab review goes over three labs within Chapter 2: the base conversion lab, the circle lab and the string manipulation lab. Even if you aren't an AP Comp Sci student, if you are learning Java and want some practice, these lab reviews are a good resource. Chapter 2 covers the concept of objects and primitive data.

AP Lang Essay Prep: How Your Essay Should Look

Welcome y’all. So, as you all should know, there are three essays that you need to write for AP Lang. Synthesis Argumentative Rhetorical Analysis   Synthesis If you’ve taken an AP history class, then you are in for an easy ride. Synthesis is exactly like the DBQ except a whole lot easier because you’re only…

APUSH Discussion Groups: Was MLK essential to the success of the Civil Rights Movement? (No)

For this debate, I was in charge of the misconceptions about MLK's role and motives in the Civil Rights Movement while my partner was in charge of what he actually did (or didn't do) so I only have half the argument. Synthesis and Thesis: Abraham Lincoln is named the Great Emancipator in honor of his…

APUSH Discussion Groups: Did Yellow Journalism cause the Spanish-American War? (Yes)

A bullet outline for the debate of how fake news stories kicked off one of the most pointless wars in the history of mankind.

APUSH Discussion Groups: Was Lincoln the best president? (No)

While I disagree with my given stance, this was the position given to me to argue, so I had to take it. I like arguing the on the losing side anyway; it's much more exciting and fresh. In any case, since each side of the debate is made up of a team of two people,…

APUSH Discussion Groups: Was Andrew Jackson’s Indian Removal Policy Motivated by Humanitarian Impulses? (Yes)

Alright, so this discussion group was one where I had to argue the more difficult position; the position that Andy Jackson deported the Native Americans from their own lands "for their own good". Basically, the gist of my argument is the fact that the Native Americans would have entered into conflict with the white settlers…