Pre-Calculus Branch

Pre-Calculus, with all of the details

This set of notes contain lectures to enrichen the study of precalculus with clear and concise definitions that are often omitted in a standard Pre-Calculus Course in College. These set of notes are to accompany a course of Pre-Calculus to further the knowledge for the students

Pre-Requisites

• All that is required to understand these notes are basic Addition, Subtraction, Multiplication, and Division.(PEMDAS is nice to know) THAT’S IT. These notes are to be as lament as possible! Please tell me if there are any aspects of this set of notes that are unclear, I’ll be more than happy to expand in this area. :) Below I will list an explicit list of items that you really should master(its more of a time thing) that will help you under stand Pre-Calculus Materials

1. Addition and Subtraction
   • Adding Integers, Fractions, and decimals
2. Multiplication and Division
   • Times Tables (at least 10x10, but 12x12 is usually standard)
   • Multiplication of Integers, Fractions, and Decimals
   • Understand multiplicative Inverses (makes division 10x easier)
3. Orders of Operations (PEMDAS in the U.S. Math Curriculum)
4. Rules of Exponents and Logarithms
   • Exponents include roots as well $\sqrt{2}$ as an example of $2^{\frac{1}{2}}$ where the exponent is not an integer

Fun Websites

• This timeline helps us aid in all of mathematicians that aided in the development of all of our modern tools! Timeline of Mathematics | Mathigon

Week 1

• Week 1 will be heavy on definitions. The definitions are fundamental to learning higher levels of mathematics as we are able to explain abstract mathematical concepts into our own language! I will digress that some definitions are not as important, but are often used later in mathematics, or your professor may say them unconsciously!

Mathematicians of the Week!

Euclid (Father of Geometry)

• Greece, 300 B.C.
• Euclid | Biography, Contributions, Geometry, & Facts | Britannica

Rene Descartes (Father of Analytic Geometry)

• France, 1596-1650 A.D.
• We named the x-y plane the Cartesian Plane after him!
• Descartes’ Mathematics (Stanford Encyclopedia of Philosophy)

Weekly Content

Day 1)

Number Systems, Sets, Unions, And Ordering

Cartesian Plane and Euclidean Spaces

Intro to Functions

Day 2)

Intro To Polynomials

Linear Equations (Lines)

Day 3)

Intro To Limits

Week 2) Parabolas

Day 4)

Quadratic Equations(Parabolas)

Week 3) Cubics

TO-DO:

Cartesian Plane and Euclidean Spaces

• Explain Rise/Run

Fascinating Sources :

1. The Etymology of Sine, Cosine, Tangent
   • https://math.stackexchange.com/questions/33175/etymology-of-arccos-arcsin-arctan
2. What does “arc” mean in terms of trig functions
   • https://math.stackexchange.com/questions/2917663/what-does-arc-in-arcsin-arccos-arctan-stands-for?noredirect=1&lq=1
3. What’s the actual difference between $\sin ,\arcsin ,{\sin }^{-1},\csc$
   • https://math.stackexchange.com/questions/3025518/difference-between-arcsin-and-inverse-sine
4. THE DOTTIE NUMBER! (cos(cos(cos…cos(x))))
   • https://www.reddit.com/r/math/comments/rgfl3h/why_does_the_infinite_cosine_coscoscosx_aproach/

Bibliography

1. (Number Systems Image) https://science.howstuffworks.com/math-concepts/real-numbers.htm