Mathematical Induction (Presentation) by R Horan & M Lavelle
Mathematical Induction (Presentation) - Table of Contents
- 1. Introduction to the Principle of Mathematical Induction
- 2. The Base Step: Verifying Initial Statements
- 3. Formulating the Inductive Hypothesis Step
- 4. Proving Summation Formulas for Natural Numbers
- 5. Induction Proofs for Divisibility Properties
- 6. Proving Algebraic Inequalities with Induction
- 7. Common Pitfalls and Logical Errors in Proofs
- 8. Worked Examples, Practice Exercises, and Solutions
What You Will Learn in Mathematical Induction (Presentation)
Mathematical Induction by R. Horan and M. Lavelle is a concise, highly structured introductory guide designed to help students master the foundational principles of mathematical proof. Published under the Plymouth University HELM (Helping Engineers Learn Mathematics) project, this text breaks down complex proof logic into manageable steps. It covers core topics such as the Base Step (Initial Verification), the Inductive Hypothesis, Algebraic Proof of the Inductive Step, and practical applications including Summation Formulas and Series, Divisibility Properties, and Algebraic Inequalities.
This guide serves as an invaluable self-study module for undergraduate engineering, computer science, and mathematics students who are transitioning from basic computation to formal proof techniques. Horan and Lavelle utilize clear annotated examples, self-assessment exercises, and step-by-step solutions to ensure students build confidence in structuring rigorous proofs.
Due to its clear pedagogical framework and practical clarity, it is widely recognized as an outstanding supplementary learning resource for discrete mathematics, linear algebra, and introductory analysis. Rather than focusing on abstract theory, it equips learners with key problem-solving skills for university-level examinations and computer science algorithm analysis.
Book Details & Specifications
Title:
Mathematical Induction (Presentation) by R Horan & M Lavelle
Publisher:
Not specified
Year:
2005
Pages:
34
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
University Educational Resource
Amazon:
Amazon
About the Author: Martin Lavelle
The author Martin Lavelle
and R Horan are distinguished academics and mathematics educators at the University of Plymouth. As key contributors to open educational initiatives, they have produced extensive modular teaching materials designed to support university students across engineering, science, and technology disciplines.
Through Mathematical Induction, Horan and Lavelle streamline proof methodology into an intuitive, student-friendly format. Their clear explanation of logical transitions and structured exercise sets make this text a masterpiece guide for mastering mathematical proof techniques.
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