📘 A mathematical and ethical investigation into decryption complexity, password entropy, and the proactive defense of vulnerable populations through the lens of Calculus II.
This project represents both an academic paper and supporting code designed to simulate and model attacker behavior using infinite series, recurrence relations, and entropy decay.
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Diverging_the_Partial_Sums(JRivas).pdf
📗 Final research paper submitted for MATH 2414 – Calculus II
Instructor: Dr. Mehran Hassanpour
Term: Spring 2025, Texas Tech University -
recursive.cpp
🔁 Sample brute-force recursion model simulating password traversal -
detection_script.cpp
🛡️ Conceptual loop-based detection algorithm for series convergence-based intrusion analysis
This repository is intended for:
- Students seeking applied mathematical models in cybersecurity
- Educators exploring real-world applications of Calculus II
- Researchers modeling brute-force, entropy decay, and network resilience
- Advocates and analysts working to protect vulnerable users in digital spaces
- Infinite geometric series and divergence
- Maclaurin series for entropy modeling
- Recurrence relations and brute-force loop simulation
- Piecewise defense modeling
- Parametric phase space analysis
- Ethics in digital design for marginalized communities
📜 License
- The PDF paper is licensed under CC0 1.0 Universal (JRivas12). Attribution is appreciated.
- The C++ code files, will be licensed under the Apache License 2.0 in a future update. They are currently shared for academic review.
See the included LICENSE.txt and Appendix for more details.
✉️ Contact & Social Links
Feel free to reach out or connect professionally:
- 📧 jrivas12@stu.southtexascollege.edu
- 📧 riv42599@ttu.edu
- 🎥 YouTube: joerivas1404
- 🎬 TikTok: @fiascoDev
- 💼 LinkedIn: Joe Lee Rivas
“The limits we once feared became the very boundary conditions that made our function solvable.”
– Diverging the Partial Sums of Two Men of Calculus