#### Xronos Tutorial

This is the Xronos tutorial.

#### What is Xronos?

A Quick Introduction to Xronos

#### How to Access Xronos

A Tutorial on accessing Xronos and how grades work.

#### How to Use Xronos

A Tutorial to Interacting with Xronos

#### How is my work scored?

We explain how your work is scored.

#### Goals of this Section

This is the introduction to the overall course and it contains the syllabus as well as grade information.

#### Goals of this Course

This course has several concurrent but different goals.

#### Expect Differences

What makes this course different from previous courses?

#### Virtues of CBT

Contextual Based Learning (CBT) has many virtues, knowing why we are learning how we are will help your studying and learning process.

#### Methods to Prepare

Suggestions on Studying and Learning

#### General Syllabus

This is the syllabus for the course with everything but grading and the calendar

This is the grading rubric for the course, including the assignments, how many points things are worth, and how many points are needed for each letter grade.

#### Pre-Requisites

This section covers the skills that a MAC1140 student is expected to be fluent in.

#### Goals of this Section

This section is on learning to use mathematics to model real-life situations.

#### Terminology To Know

These are important terms and notations for this section.

#### What is mathematical reasoning?

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

#### Logical Deduction

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

#### Types of Information

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

#### Is this actually math?

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

#### Math as a Language

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

#### Numeric Model Walkthrough

This is a detailed numeric model example and walkthrough.

#### Embrace Laziness!

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

#### Variables and Their Roles

This section explains types and interactions between variables.

#### Generalized Model Walkthrough

This is an example of a detailed generalized model walkthrough

#### Goals of this Section

This section is on functions, their roles, their graphs, and we introduce the Library of Functions

#### Terminology To Know

These are important terms and notations for this section.

#### Relationship vs. Equations

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

#### Relationship vs. Functions

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

#### Functions Require Context

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

#### Domain, Codomain, and Range

In this section we cover Domain, Codomain and Range.

#### Set Notation

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

#### Function Notation

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

#### f(x) Notation

This section covers $f(x)$ notation.

#### Function Composition

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

#### Graphing Introduction

This section introduces graphing and gives an example of how we intuitively use it.

#### Terminology To Know

These are important terms and notations for this section.

#### French History and Dinosaurs!

This section introduces the origin an application of graphing.

#### Graphing To Relate Variables

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

#### Graphs Aren’t Precise

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

#### Using Graphs

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

#### Vertical Line Test

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

#### Library Of Functions

This is an introduction and list of the so-called “library of functions”.

#### Parent Functions

This section provides the specific parent functions you should know.

#### Universal Properties

This section introduces the idea of studying universal properties to avoid memorizing vast amounts of information.

#### Terminology To Know

These are important terms and notations for this section.

#### Geometric Vs Analytic Viewpoints

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

#### Geometric Perspective

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

#### Analytic Viewpoint

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

#### Intro: Rigid Translations

An introduction to the ideas of rigid translations.

#### Rigid Translations: Geometrics

This section describes the geometric perspective of Rigid Translations.

#### Rigid Translations: Analytics

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

#### Transforms: Geometric

This section describes the geometric interpretation of what makes a transformation

#### Transforms: Analytic

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.

#### Transform And Translates

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.

#### Points of Interest on Graphs - Zeros

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

#### Points of Interest on Graphs - Extrema

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

#### Points of Interest on Graphs - Discontinuities

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

#### Algebra with Functions

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

#### Equals Signs are Magic!

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.

#### One and Zero; the Most Useful of Numbers

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

#### Inverse Functions

This section introduces the geometric viewpoint of invertability.

#### Horizontal Line Test

This section discusses the Horizontal Line Test

#### Inverse Function - Analytic View

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

#### Polynomial Functions

This section is an exploration of polynomial functions, their uses and their mechanics.

#### Terminology To Know

These are important terms and notations for this section.

#### What is (and isn’t) a Polynomial?

We know an awful lot about polynomials, but it relies on the very specific structure of a polynomial, and thus it is paramount that one can correctly recognize what is, and isn’t, a polynomial to use these tools.

#### Fundamental Theorem of Algebra

This section covers one of the most important results in the last couple centuries in algebra; the so-called “Fundamental Theorem of Algebra.”

#### An Interjection into Polynomial History!

This section is a quick foray into math history, and the history of polynomials!

#### Exponents and Extrema: An Example

This section contains a demonstration of how odd versus even powers can effect extrema.

#### Exponents and Extrema 2: Local Extrema

This section contains information on how exponents effect local extrema

#### Curvature and Graphing

This section shows and explains graphical examples of function curvature.

#### Factoring: Introduction

Some information on factoring before we delve into the specifics.

#### Factoring: Round One!

First dive into factoring polynomials. This section covers factoring quadratics with leading coefficient of $1$ by factoring the coefficients.

#### Factoring; Grouping Method

Factor higher polynomials by grouping terms

#### Factoring; AC Method

How to factor when the leading coefficient isn’t one.

#### Factoring; Special Forms

Factor polynomials quickly when they are in special forms

#### Completing the Square

This section introduces the technique of completing the square.

#### Polynomial Long Division

In this section we explore how to factor a polynomial out of another polynomial using polynomial long division

#### Polynomial Synthetic Division

Factor one polynomial by another polynomial using polynomial synthetic division

#### Rational Root Theorem

Find factors via rational root theorem

#### Complex Numbers

Intro to complex numbers and conjugates

#### Simplifying Complex Numbers

Simplifying complex numbers

Exploring the usefulness and (mostly) non-usefulness of the quadratic formula

#### Comprehensive Factoring Quiz

A Comprehensive Factoring Practice Quiz.

This section is an exploration of radical functions, their uses and their mechanics.

#### Terminology To Know

These are important terms and notations for this section.

This section introduces radicals and some common uses for them.

This section introduces radicals and some common uses for them.

This section introduces two types of radicands with variables and covers how to simplify them... or not.

This section discusses how to handle type two radicals.

This section discusses how to handle type one radicals.

#### Square Root: the Inverse Function

This section views the square root function as an inverse function of a monomial. This is used to explain the dreaded $\pm$ symbol and when to use (and not use) absolute values.

This section shows techniques to solve an equality that has a radical that can’t be simplified into a non radical form. This has potential drawbacks which is also covered in this section.

#### Exponential Functions: Goals

This section is an exploration of exponential functions, their uses and their mechanics.

#### Terminology To Know

These are important terms and notations for this section.

#### A Review of Exponential Functions

This section reviews the basics of exponential functions and how to compute numeric exponentials.

#### Properties of Exponentials

This section gives the properties of exponential expressions. Most of these should be familiar, although we go into slightly more details as to how and why these properties hold in some cases.

#### Properties of the Exponential Function

This section gives the properties of exponential functions. There is a subtlety between the function and the expression form which will be explored, as well as common errors made with exponential functions.

#### Exponential Growth and Decay

This section discusses the two main modeling uses of exponentials; exponential growth, and exponential decay.

#### Logarithmic Functions

This section is an exploration of logarithmic functions, their uses and their mechanics.

#### Terminology To Know

These are important terms and notations for this section.

#### Introduction and Notation of Logarithms

This section is a quick introduction to logarithms and notation (and ways to avoid the notation).

#### Properties Of Logs

This is one of the most vital sections for logarithms. We cover primary and secondary properties of logs, which are pivotal in future math classes as these properties are often exploited in otherwise difficult mechanical situations.

#### Common Mistakes Of Logs

This is one of the most vital sections for logarithms. We cover primary and secondary properties of logs, which are pivotal in future math classes as these properties are often exploited in otherwise difficult mechanical situations.

#### Change of Base formula

This is one of the most vital sections for logarithms. We cover primary and secondary properties of logs, which are pivotal in future math classes as these properties are often exploited in otherwise difficult mechanical situations.

#### Examples of Logs

This is a demonstration of several examples of using log rules to handle logs mechanically.

#### Piecewise Functions

This section is an exploration of the piece-wise function; specifically how and why they are used and their mechanics.

#### Piecewise Functions: The Geometric View

This section discusses the geometric view of piecewise functions.

#### Piecewise Functions: The Analytic View

This section discusses the analytic view of piecewise functions.

#### Piecewise Functions: Computation

This section discusses how to compute values using a piecewise function

#### Absolute Value Functions

This section is an exploration of the absolute value function; specifically how and why they are used and their mechanics.

#### Absolute Value: Geometric View

This discusses Absolute Value as a geometric idea, in terms of lengths and distances.

#### Absolute Value: Analytic View

This discusses the absolute value analytically, ie how to manipulate absolute values algebraically.

#### Absolute Value: Solving Equalities

This section is on how to solve absolute value equalities.

#### Rational Functions

This section is an exploration of rational functions; specifically those functions that are made by taking a ratio (ie fraction) of polynomials.

#### Terminology To Know

These are important terms and notations for this section.

#### What is a rational function?

We discuss what makes a rational function, and why they are useful.

#### Domain of rational functions

We discuss one of the most important aspects of rational functions; the domain restrictions.

#### Vertical Asymptotes

We discuss the circumstances that generate vertical asymptotes in rational functions.

#### Holes in Domains of Rational Functions

We discuss the circumstances that generate holes in the domain of rational functions rather than vertical asymptotes.

#### Horizontal Asymptotes

We discuss the circumstances that generate horizontal asymptotes and what they mean.