About This Chapter
Who's it for?
Anyone who needs help learning or mastering college preparatory math material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding how mathematical elements intersect or join together.
- Need an efficient way to learn about mathematical sets.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Sets 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 Sets chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- What is a mathematical set, subset or infinite set?
- What do I do to calculate the Cartesian product?
- What is a Venn diagram, and how do I use one?
- How do I convert between categorical proposition and standard form?
- How do I read a 2-way table?
1. Mathematical Sets: Elements, Intersections & Unions
Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.
2. Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty)
In this video, we will add to our knowledge of sets. We will talk about cardinality, infinite, finite, equal and the empty set. I think you will find these very straightforward, so let's begin.
3. How to Find the Cartesian Product
The Cartesian product allows us to take two sets of mathematical objects and create one new one. With one simple idea, the Cartesian product becomes quick and easy.
4. Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union
The Venn diagram was introduced by John Venn. Yes, the Venn diagram is named after a real person! His idea was to show sets in terms of pictures. The Venn diagram is now used in many fields, including mathematics. Let's take a look at John Venn's idea.
5. Categorical Propositions: Subject, Predicate, Equivalent & Infinite Sets
Watch this video lesson to learn how categorical propositions are written. You will also see what the subject and predicate are as well as learn about equivalent and infinite sets.
6. How to Change Categorical Propositions to Standard Form
Watch this video lesson to learn what categorical propositions are and how you can turn your statements into one of the four standard forms. Also, learn the names of these four standard forms and what they look like.
7. What is a Two-Way Table?
Do you believe in Martians? Do you watch football on television? A Two-Way Table or Contingency Table is a great way to show the results of all kinds of survey questions. In this video we will learn how to read a two-way table.
8. Closed Set: Definition & Example
After reading this lesson, you'll see how both the theoretical definition of a closed set and its real world application. You'll learn about the defining characteristic of closed sets and you'll see some examples.
9. Closed Set vs. Open Set
In math, there's two different types of sets. These sets are there to help you with numerical boundaries and limits. They help you determine whether a number you are looking at is part of a set or not. Learn how in this lesson.
10. History of the Collatz Conjecture
The Collatz conjecture is a fascinating conjecture in mathematics. In this lesson, we will explore the Collatz conjecture, taking time to look at the conjecture itself, its history, and various examples of working with the conjecture.
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Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Problem Solving & Reasoning Skills
- Percents in Math Basics
- Decimals & Fractions Overview
- Understanding Fractions & Mixed Numbers
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Complex and Imaginary Numbers: Help and Review
- Properties of Exponents: Help and Review
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Properties of Functions: Help and Review
- Logarithms and Exponential Equations: Help and Review
- Data & Estimation
- Logic in Math: Help and Review
- Basic Probability and Statistics: Help and Review
- Geometric Laws & Proofs
- Geometry in College Preparatory Math: Help and Review
- Grade Level Math Vocabulary: Help and Review