Ch 9: Mathematical Logic & Problem Solving

About This Chapter

The Mathematical Logic & Problem Solving chapter uses engaging video lessons to present its topics to you. Different kinds of reasoning in math and logical math connectors are some issues that'll surface during your review of this chapter.

Mathematical Logic & Problem Solving - Chapter Summary

Make sure you're familiar with a range of logical fallacies during your time with this chapter, such as appeal to emotion, hasty generalization and false cause. Look at another lesson that defines what propositions in logic and truth value refer to. You'll also get to check your familiarity with these additional lesson topics:

  • The four steps to Polya's problem-solving process
  • What the contrapositive of a logical statement is
  • The potential drawbacks of mathematical models
  • A number of math principles that help with problem-solving
  • The parts of a conditional statement in math

Conveniently, you may use a number of different devices that are Internet-ready for watching the chapter's video lessons. You'll find that the video lessons have an individual length of only about five minutes. Follow each of these lessons with a practice quiz to verify your understanding of the material.

12 Lessons in Chapter 9: Mathematical Logic & Problem Solving
Test your knowledge with a 30-question chapter practice test
Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

1. 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.

Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

2. 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.

Propositions, Truth Values and Truth Tables

3. 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.

Logical Math Connectors: Conjunctions and Disjunctions

4. 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.

Conditional Statements in Math

5. 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.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

6. 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.

Reasoning in Mathematics: Inductive and Deductive Reasoning

7. Reasoning in Mathematics: Inductive and Deductive Reasoning

Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.

Reasoning in Mathematics: Connective Reasoning

8. Reasoning in Mathematics: Connective Reasoning

Connective reasoning is reasoning that has an operation, or a way to connect two phrases. The five main logic connectives will be reviewed in this lesson.

Polya's Four-Step Problem-Solving Process

9. Polya's Four-Step Problem-Solving Process

Problem solving can be a problem. Any problem is solved easier with an action plan. Polya's 4-Step Problem-Solving Process is discussed in this lesson to help students develop an action plan for addressing problems.

Mathematical Principles for Problem Solving

10. Mathematical Principles for Problem Solving

Solving problems is not just a simple, straightforward process. There are a few principles that can help you as you approach any problem solving scenarios. This lesson covers those principles with examples.

Solving Mathematical Problems Using Estimation

11. Solving Mathematical Problems Using Estimation

Estimating is a method of calculating a result that is close to, but not exactly, the correct answer to a math problem. Why would you ever need to do this? This lesson reviews estimating and answers the question as to why you would do it.

Using Mathematical Models to Solve Problems

12. Using Mathematical Models to Solve Problems

Mathematical modeling simply refers to the creation of mathematical formulas to represent a real world problem in mathematical terms. This lesson reviews the creation and pitfalls of mathematical models.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support