These are important terms and notations for this section.

This section aims to introduce the idea of mathematical reasoning and give an example of how it is used.

This section analyzes the previous example in detail to develop a three phase deductive process to develop a mathematical model.

This section aims to explore and explain different types of information.

This section aims to show how mathematical reasoning is different than ‘typical reasoning’, as well as showing how what we are doing is mathematical.

This section contains important points about the analogy of mathematics as a language.

This section aims to name and explain the common sets of numbers.

This is a detailed numeric model example and walkthrough.

This section aims to show the virtues, and techniques, in generalizing numeric models into ‘generalized’ models.

This section explains types and interactions between variables.

This is an example of a detailed generalized model walkthrough

These are important terms and notations for this section.

In this section we discuss a very subtle but profoundly important difference between a relationship between information, and an equation with information.

In this section we discuss what makes a relation into a function.

In this section we demonstrate that a relation requires context to be considered a function.

In this section we cover Domain, Codomain and Range.

In this section we cover how to actual write sets and specifically domains, codomains, and ranges.

This section covers function notation, why and how it is written.

This section covers $f(x)$ notation.

We cover the idea of function composition and it’s effects on domains and ranges.

These are important terms and notations for this section.

This section introduces the origin an application of graphing.

This section describes how we will use graphing in this course; as a tool to visually depict a relation between variables.

This section describes how accuracy and precision are different things, and how that relates to graphs.

This section covers what graphs should be used for, despite being imprecise.

This section describes the vertical line test and why it works.

This section provides the specific parent functions you should know.

These are important terms and notations for this section.

We discuss what Geometric and Analytic views of mathematics are and the different roles they play in learning and practicing mathematics.

We discuss the geometric perspective and what its role is in learning and practicing mathematics.

We discuss the analytic view of mathematics such as when and where it is most useful or appropriate.

This section describes the geometry and useful symmetry of even functions, as well as how to test for them analytically.

This section describes the geometry and useful symmetry of odd functions, as well as how to test for them analytically.

An introduction to the ideas of rigid translations.

This section describes the geometric perspective of Rigid Translations.

This section describes the analytic perspective of what makes a Rigid Translation.

This section describes the geometric interpretation of what makes a transformation

This section describes the analytic interpretation of what makes a transformation and how to use the function notation to perform (or read) a transformation quickly and easily.

This covers doing transformations and translations at the same time. In particular we discuss how to determine what order to do the translations/transformations in.

This section describes types of points of interest (PoI) in general and covers zeros of functions as one such type.

This section describes one of the most useful tools in mathematics - especially in calculus - the sign chart!

This section describes extrema of a function as points of interest (PoI) on a graph.

This section describes one of the most important concepts in calculus - continuity!

This section describes discontinuities of a function as points of interest (PoI) on a graph.

This section describes how to perform the familiar operations from algebra (eg add, subtract, multiply, and divide) on functions instead of numbers or variables.

This section describes the very special and often overlooked virtues of the ‘equals sign’. It also includes when and why you should “set something equal to zero” which is often overused or used incorrectly.

This section describes the very special and often overlooked virtue of the numbers Zero and One.

This section introduces the geometric viewpoint of invertability.

This section discusses the Horizontal Line Test

This section introduces the analytic viewpoint of invertability, as well as one-to-one functions.