Interactive Online System for Mathematical Induction

Mathematical Induction is a foundational proof technique in discrete mathematics, whereas many students struggle to cover the gap from procedural to abstract reasoning. This project is based on the interactive online system for mathematical induction, developed to teach mathematical induction with the help of structural learning, guided examples to build a strong base and real-time feedback of user inputs. Using Java Servlets, the system offers an interactive learning experience that mirrors traditional textbook notation while eliminating the obstacles of complex proof writing syntax. The system features a structured flow of learning which starts with guided examples before diving into hands on exercises. The core innovation of the system is the proof solver, which offers real-time feedback after every user input. If a step is incorrect, the system highlights the mistake and prevents students from proceeding with a defect in the logic. When a user is facing obstacles while solving a question, the system has an option to switch towards the example environment, which has a guided example of the same theorem the user was struggling with. Additionally, the user can ask for hints in case the user does not want to move towards a guided example to scaffold learning without giving away the solution immediately. Unlike many other proof assistants like COQ, the system does not require users to learn any language. Instead, it maintains a natural textbook style interface with readable mathematical symbols to increase the accessibility of the system. Furthermore, the system has exercises and examples beyond numbers, incorporating generalized problem types which require students to specify the properties used in the proof step. With the integration of guided examples and immediate feedback, the system bridges the gap between theory and application. This research aims to make mathematical induction more accessible and engaging for learners with the help of technology.

Name thesis:degree_name

M.Sc. Computer Science

Level thesis:degree_level

Master

Discipline thesis:degree_discipline

Faculty of Mathematics and Science

Department dc:contributor.department

Department of Computer Science

Grantor dc:publisher

Brock University

Year dc:date.issued

2025

Author dc:creator

• Ansar, Fahad

Advisor dc:contributor.advisor

• Dr. Michael Winter

• MATHEMATICS::Algebra, geometry and mathematical analysis::Discrete mathematics
• TECHNOLOGY::Information technology::Computer science::Computer science
• TECHNOLOGY::Information technology::Computer science::Software engineering

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10464/19707

OAI identifier oai:identifier

oai:brocku.scholaris.ca:10464/19707