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Week 04 October - Recursion and Induction

Class Description

This week we dive deep into the elegant connection between mathematical induction and recursive programming. You'll discover how these two powerful concepts mirror each other: induction provides the mathematical foundation for understanding why recursion works, while recursion gives us a computational tool to implement inductive reasoning.

Focus Strategy: Master induction and recursion first, and while loops will become intuitive! While loops are simply the next iteration of the for loops you already know - they're just another way to repeat actions. But recursion and induction represent a fundamentally different (and often more powerful) way of thinking about problems by breaking them into smaller, self-similar pieces.

Key Learning Objectives: - Understand how mathematical induction proves statements for infinite sets - See how recursive functions implement the same logical structure as inductive proofs - Recognize when problems naturally decompose into recursive subproblems - Master the essential components: base cases and recursive/inductive steps - Apply while loops as an extension of iteration concepts you already know

This integrated approach will show you that mathematics and programming aren't separate subjects - they're two sides of the same logical coin!

Study Strategy for This Lesson

Step 1: Watch the Videos First - Start with the CS 5002 induction videos to build the mathematical foundation - Then watch the CS 5001 recursion videos to see how the math translates to code - Finally, watch the while loop videos - you'll find them much easier after understanding recursion!

Step 2: Use the Tutoring Prompts After watching the videos, use the structured tutoring prompts at the end of this page to deepen your understanding: - Proof by Induction Prompt: Master the mathematical reasoning - Recursion Prompt: Connect the math to programming - While Loops Prompt: Apply your iteration knowledge

Step 3: Make the Connections As you study, actively look for the parallels: - Base case in induction ↔ Base case in recursion - Inductive step ↔ Recursive call - "Assume P(k) is true" ↔ "Trust that the recursive call works"

This strategy ensures you build understanding from the ground up, making each concept reinforce the others!

Before Class

Flipped Classroom Reminder

Remember: Watch the videos before class so we can spend our time together on active learning and problem-solving!

Videos to Watch Before Class

Please watch the following videos before our class meeting:

CS 5001 - October 7 Class: While Loops and Recursion

Recursion
While Loops

CS 5002 - October 7 Class

New Material

After watching the induction videos above, read through the Tower of Hanoi: Problem, Solution, and Proof explanation to see a concrete example of how mathematical induction and recursive algorithms work together. This will help you understand the deep connection between the mathematical reasoning you just learned and the recursive programming concepts you'll encounter next.

Previous Material

Class Materials

📋 Handouts

To be added

💻 Code Examples

Interactive Python examples to explore during and after class:

To be added

🎯 Tutoring Resources

Need help with this week's topics? Use our structured tutoring prompts:

Programming Topics (CS 5001):

  • While Loops Tutoring Session Prompt - A comprehensive prompt you can copy and paste to start a focused tutoring session about while loops in Python, covering common patterns, debugging, and when to use them.

  • Recursion Tutoring Session Prompt - A comprehensive prompt you can copy and paste to start a focused tutoring session about recursion in Python, connecting mathematical induction to recursive programming.

Mathematical Foundation (CS 5002):

  • Proof by Induction Tutoring Session Prompt - A comprehensive prompt you can copy and paste to start a focused tutoring session about mathematical induction, showing how it connects to recursive thinking and provides the theoretical foundation for recursive algorithms.

💡 Tip: Click on any example above to view the code directly in your browser, then copy and run it in your Python environment!