# Ch 1: Number Theory & Foundations

### About This Chapter

## Who's It For?

Anyone who needs help learning or mastering number theory and foundations material will benefit from the lessons in this chapter. There is no faster or easier way to learn about number theories and foundations. Among those who would benefit are:

- Students who have fallen behind in understanding number properties
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about number theory and foundations
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How It Works:

- Find videos in this chapter that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Number Theory & Foundations chapter exam.

## Why It Works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the Number Theory & Foundations chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any number theory and foundations question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

## Students Will Review:

This chapter helps students review the concepts in a number theory and foundations unit of a standard number properties course. Topics covered include:

- Types of numbers
- The mathematical order of operations
- Arithmetic calculations with whole and signed numbers
- Prime factorization
- Finding the greatest common factor & the least common multiple

### 1. What are the Different Types of Numbers?

Learn all of the different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. This video lesson teaches you how to classify any numbers you come across.

### 2. What Is The Order of Operations in Math? - Definition & Examples

The order of operations is the steps used to simplify any mathematical expression. In this video, learn how to solve problems using these steps and easy tricks to remember them.

### 3. Arithmetic with Whole Numbers

There are four basic mathematical operations: addition, subtraction, multiplication, and division. These four operations are used in a wide range of everyday skills and are the fundamental blocks of arithmetic.

### 4. Arithmetic Calculations with Signed Numbers

Signed numbers are often referred to as integers. Integers include both positive and negative numbers. In this lesson, you will learn how to add, subtract, multiply, and divide integers.

### 5. How to Find the Prime Factorization of a Number

The prime factorization of a number involves breaking that number down to its smallest parts. This lesson will show you two different ways to discover the prime factorization of any number.

### 6. How to Find the Least Common Multiple

The least common multiple of two numbers is the smallest number that can be divided evenly by your two original numbers. See some examples of what I'm talking about here!

### 7. How to Find the Greatest Common Factor

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

### 8. Chen Prime Number Theorem

Chen's prime number theorem has been invaluable in the study of prime numbers and number theory. This lesson will introduce the theorem, solidify our understanding of it, and briefly discuss the areas in which it has been most significant.

### 9. Chen Jingrun: Biography & Facts

Chen Jingrun (1933-1996) was a Chinese mathematician who dedicated his life to proving the still unproven Goldbach's conjecture. In this lesson, learn about the many challenges he overcame and his contributions to mathematics.

### 10. What is a Dihedral Prime Number?

This lesson will define dihedral prime numbers. We will explore the properties of these types of numbers, and look at some examples of how to determine if a prime number is a dihedral prime.

### 11. Bezout's Identity: Proof & Examples

A linear combination of two integers can be shown to be equal to the greatest common divisor of these two integers. This is the essence of the Bazout identity. In this lesson, we prove the identity and use examples to show how to express the linear combination.

### 12. How to Prove Cassini's Identity

In this lesson, individual Fibonacci numbers are related by the Cassini identity. We clarify what this identity means and show how to prove it using the method of induction.

### 13. Catalan Numbers: Formula, Applications & Example

Catalan numbers are an important and prevalent sequence in mathematics. In this lesson, you'll find the formula for identifying Catalan numbers and learn how to apply them through some examples.

### 14. Catalan Numbers: History & Definition

This lesson will define the Catalan numbers. We will then review the history of these numbers, including some of the mathematicians and applications that led to the discovery and development of these numbers.

### 15. Chromatic Number: Definition & Examples

In this lesson, we will briefly review some definitions pertaining to graphs, and then go on to define the chromatic number of a graph and work with an application and example of the chromatic number of a graph.

### 16. Complex Numbers Conjugates

This lesson will review what a complex number is, and then we will explore complex number conjugates. We will look at how to find the complex conjugate of a complex number, and we will look at a really neat property that complex conjugates satisfy.

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### Other Chapters

Other chapters within the Number Properties: Help & Review course