About This Chapter
Mathematical Proofs & Reasoning - Chapter Summary
This collection of fun math lessons covers basic mathematical proof and reasoning concepts. You can expect to evaluate a variety of mathematical proofs and explore the applications of mathematical induction and deductive reasoning. Upon completion of the chapter you should be able to:
- Recognize examples of mathematical proofs
- Define the concept of deductive reasoning
- Explain the uses of mathematical induction
- Understand the steps that are involved in proof by induction
These lessons present proof and reasoning topics in an engaging and easy-to-understand manner. Take the accompanying self-assessment quizzes to make sure you fully understand the material. Our instructors are available to answer any questions you may have, and you can use any Internet-connected device to access the chapter.
1. Mathematical Proof: Definition & Examples
Have you ever made a statement that someone challenged you to prove to be true? You have to explain things in a logical and indisputable way in order to do that. In this lesson, you'll learn different ways that statements can be proven in mathematics.
2. Deductive Reasoning: Examples & Definition
Deductive reasoning involves drawing conclusions from specific statements called premises. Learn more about deductive reasoning and test your knowledge with a quiz.
3. Mathematical Induction: Uses & Proofs
Watch this video lesson to learn about mathematical induction and how you can use it to prove mathematical statements. See how it is similar to falling dominoes.
4. Proof by Induction: Steps & Examples
Mathematical induction is a method of proof that is often used in mathematics and logic. We will learn what mathematical induction is and what steps are involved in mathematical induction.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards