About This Chapter
Who's it for?
Anyone who needs help understanding high school geometry 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 the role of mathematical logic in geometry.
- Need an efficient way to learn about logic in mathematics.
- 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 Logic in Mathematics 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 Logic in Mathematics 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 roles do critical thinking and logic play in mathematics?
- What are the four types of logical fallacies, and how can they be avoided?
- How do appeals to emotion, ignorance or popularity lead to logical fallacies?
- What is a proposition, and how can it influence a truth value?
- How do conjunctions and disjunctions in math differ?
- What is the definition of a conditional statement?
- How do direct proofs work?
- What steps are involved in using a geometric proof?
1. Critical Thinking and Logic in Mathematics
Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.
2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice
Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.
3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity
Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.
4. Propositions, Truth Values and Truth Tables
Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.
5. Logical Math Connectors: Conjunctions and Disjunctions
Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.
6. Conditional Statements in Math
Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.
7. Logic Laws: Converse, Inverse, Contrapositive & Counterexample
Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.
8. Direct Proofs: Definition and Applications
In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.
9. Geometric Proofs: Definition and Format
Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.
10. Basis Point: Definition, Value & Conversion
In this lesson, you will learn the definition and value of a basis point. You will also learn how to convert a basis point to a percentage and vice versa. Following this lesson will be a brief quiz to test your new knowledge.
11. Tautology in Math: Definition & Examples
Discover what a tautology is, and learn how to determine if a statement is a tautology by constructing a truth table. Test your skills with a short quiz.
12. Antisymmetric Relation: Definition, Proof & Examples
This lesson will talk about a certain type of relation called an antisymmetric relation. We will look at the properties of these relations, examples, and how to prove that a relation is antisymmetric.
13. Difference Between Asymmetric & Antisymmetric Relation
We will explore relations that are antisymmetric and asymmetric in both a real-world context and a mathematical context. We will examine properties of each of these types of relations, and determine how best to tell them apart by their differences.
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Other chapters within the High School Geometry: Help and Review course
- Foundations of Geometry: Help and Review
- Introduction to Geometric Figures: Help and Review
- Properties of Triangles: Help and Review
- Triangles, Theorems and Proofs: Help and Review
- Parallel Lines and Polygons: Help and Review
- Similar Polygons: Help and Review
- Quadrilaterals: Help and Review
- Circular Arcs and Circles: Help and Review
- Conic Sections: Help and Review
- Geometric Solids: Help and Review
- Analytical Geometry: Help and Review
- Introduction to Trigonometry: Help and Review