Equations of Survival: How Humanity Solved Its Way to Modern Mathematics
Edition: 1
Copyright: 2026
Pages: 374
Edition: 1
Copyright: 2026
Pages: 640
Choose Your Format
Print Package
$100.00 USD
Ebook
$80.00 USD
Before the algorithm, there was the abacus. Before the spreadsheet, there was the counting stone. Before the equation, there was a human being facing an impossible problem, and refusing to stop until they solved it.
Mathematics was not invented in ivory towers. It was forged in the fires of necessity, by merchants who needed to count, farmers who needed to measure, engineers who needed to build, and scientists who needed to understand a universe that refused to stand still. Equations of Survival: How Humanity Solved Its Way to Modern Mathematics is the sweeping, exhilarating story of how our greatest intellectual tool was shaped, century by century, crisis by crisis, by the relentless demands of human survival and ambition.
From the first primitive marks scratched into bone to the quantum algorithms rewriting the boundaries of computation, the book traces the full arc of the mathematical history, not as a sequence of abstract discoveries, but as a deeply human narrative of ingenuity, and the extraordinary power of a mind determined to find order in chaos.
About the Authors
Video Library
Introduction
Chapter 1: Introduction to Mathematical Problem Solving
Introduction to Mathematical Problem Solving
Historical Context of Problem Solving
Introduction to Systematic Approaches
Types of Mathematical Problems
Objectives of This Journey
Wrapping Up
Chapter 2: The Origins of Counting Systems
Exploring Primitive Counting Techniques
Early Counting Methods and the Transition to Numerals
Advancements in Numeral Systems
The Influence of Counting on Trade and Societal Development
Cultural Variations and the Need for Standardization
Lessons Learned
Main Points Recap
Chapter 3: Ancient Geometry: Solving Space Problems
The Birth of Geometry: Origins and Foundations
Significant Contributions From Ancient Civilizations
Practical Applications of Geometry in Daily Life
Foundational Early Theorems of Geometry
Transition From Practical to Theoretical Geometry
Final Thoughts
Chapter 4: The Rise of Algebra: Formalizing Problems
Understanding Algebraic Thinking
From Arithmetic to Algebraic Expressions
Influential Mathematicians in Algebra
Real-Life Applications of Algebra
The Transformative Impact of Algebra on Mathematics
Bringing It All Together
Chapter 5: The Scientific Revolution and Mathematics
The Intersection of Science and Mathematics
Developing Mathematical Frameworks and Statistical Techniques for Empirical Data
Advancements During the Renaissance
Key Mathematical Innovations
The Influence of Mathematicians on Science
Final Thoughts
Chapter 6: Calculus: Solving Change and Motion Problems
The Origins of Calculus
Key Figures in Development
Fundamental Concepts of Calculus
Applications of Calculus in Physics
The Legacy of Calculus
Final Thoughts
Chapter 7: Statistics: Understanding Data and Uncertainty
Introduction to Statistics and Its Importance
Historical Development of Statistical Methods
Contributions of Key Figures in Statistics
Practical Applications of Statistics
The Evolution of Statistical Thinking
Final Thoughts
Chapter 8: The Age of Reason: Logic and Mathematics
The Emergence of Mathematical Logic
Influential Philosophers: Euclid and Aristotle
Influential Mathematicians: Descartes and Cantor
Principles of Mathematical Reasoning
Application of Logic in Solving Problems
Final Thoughts
Chapter 9: Modeling the World: The Role of Mathematics in Engineering
Defining Mathematical Modeling in Engineering
Historical Applications of Mathematics in Engineering
The Necessity of Mathematical Accuracy in Engineering
Case Studies of Practical Mathematical Solutions
Emerging Trends in Engineering Mathematics
Final Insights
Chapter 10: Mathematics in Economics: Addressing Scarcity
Defining Mathematical Economics and Its Significance
Applications of Mathematics in Economics
Historical Foundations of Economic Mathematics
Classical Economic Theories and Industrial Advances
Economic Decision-Making and Modern Applications of Mathematics
Final Insights
Chapter 11: Mathematics and Computer Science: Algorithms and Logic
Understanding Algorithms: Definition and Importance
Historical Evolution of Algorithms
Influential Figures in Computer Science
Practical Applications of Algorithms in Diverse Fields
Emerging Trends in Algorithm Development
Final Thoughts
Chapter 12: Mathematics and the Arts: Harmonizing Numbers and Creativity
The Intersection of Mathematics and Art
Historical Examples of Mathematical Art
Mathematical Patterns in Nature
Using Mathematics in Artistic Creation
The Role of Mathematics in Music
Final Thoughts
Chapter 13: Mathematics and Social Sciences: Analyzing Society
Mathematics’ Role in Social Sciences
Quantitative Research Methodologies
Case Studies Demonstrating Statistical Applications
Challenges in Mathematical Modeling
Future Directions for Mathematics in Social Sciences
Final Thoughts
Chapter 14: Mathematical Ethics: The Responsibility of Data Use
Defining Mathematical Ethics
Ethical Issues in Data Handling
Historical Cases of Ethical Dilemmas in Mathematics
The Role of Ethics in Mathematical Decision-Making
Future of Ethics in Mathematical Applications
Final Insights
Chapter 15: Mathematics and Medicine: Solving Health Problems
The Role of Statistics in Medicine
Historical Development of Medical Mathematics
Key Mathematical Models in Epidemiology
Applications of Math in Clinical Trials
Future Trends in Medical Mathematics
Final Thoughts
Chapter 16: Mathematics and Environmental Science: Modeling Ecological Systems
The Importance of Mathematics in Environmental Studies
Case Studies in Environmental Modeling
Mathematical Approaches to Resource Management
Ethical Considerations in Environmental Mathematics
Future Challenges and Opportunities in Environmental Mathematics
Final Thoughts
Chapter 17: Mathematics and Transportation: Solving Logistics Problems
Defining Transportation Mathematics: Foundations and Applications
Historical Overview of Logistics Challenges: Key Developments
Key Mathematical Models in Transportation: Frameworks for Solutions
Applications of Mathematics in Traffic Management: Enhancements in Practice
The Future of Mathematics in Transportation Solutions: Innovations Ahead
Wrapping Up
Chapter 18: Mathematics and Climate Change: A Calculated Approach
Defining Climate Mathematics and Its Frameworks
Statistical Analysis Techniques for Climate Data
Mathematical Models for Accurate Climate Predictions
The Role of Mathematics in Influencing Policy Decisions
Future Directions and Innovations in Climate Mathematics
Bringing It All Together
Chapter 19: Globalization and Mathematics: Solving Worldwide Challenges
Mathematics in Globalization
Cross-Cultural Collaborations in Mathematics
Challenges in Global Mathematics Education
Mathematics in International Development
The Future of Mathematics in a Global Context
Final Thoughts
Chapter 20: The Future of Mathematics: Emerging Concepts and Technologies
Innovations in Mathematical Research: Complexity Theory and Topological Data Analysis
Innovations in Mathematical Research: Modeling in Pandemic Response and AI Developments
The Role of Technology in Mathematical Advancement: Software Tools and Online Resources
Emerging Fields in Mathematics: Data Science and Cryptography
The Importance of Math Education in the Future: Foundations and Inclusivity
Final Thoughts
Chapter 21: Mathematics in Society: Historical Perspectives and Modern Impacts
The Historical Role of Mathematics in Society
Modern Applications of Mathematics in Society
The Impact of Mathematics on Social Justice
The Relationship Between Mathematics and Public Policy
Future Trends in Mathematics for Societal Development
Final Thoughts
Chapter 22: Reflections on Mathematics: A Journey Through Time and Space
Recap of Key Themes in Mathematical History
Personal Reflections on Mathematics’ Impact
The Continual Evolution of Mathematics
Interconnections Between Mathematics and Other Fields
The Importance of Embracing Mathematics in Life
Wrapping Up
Chapter 23: The Enduring Power of Mathematics
Summary of the Mathematical Journey
The Ongoing Relevance of Mathematics
Mathematics as a Universal Language
Encouragement for Lifelong Learning in Mathematics
What We’ve Learned
Further Readings
Index
Dr. Alfred Basta is a distinguished Professor of Cybersecurity, Computer Science, Information Technology, and Mathematics with a PhD in Cryptography and a Master’s in Computer Science. With nearly 3 decades of academic leadership and industry expertise spanning since 1997, Dr. Basta has established himself as a towering figure in both cybersecurity education and research.
Dr. Basta’s expertise is underscored by an exceptional portfolio of 60+ professional certifications representing the highest levels across multiple security and technology domains. His credentials span security leadership (ISO 27001:2022 Lead Auditor, CCISO, CISM, CGEIT, CISA, CRISC), penetration testing and ethical hacking (OSCP, CRTO, CPENT, Licensed Penetration Testing Master, CEH, CHFI), governance and compliance (Certified CMMC Professional, Lead Certified CMMC Assessor), cloud architecture (AWS Certified Solutions Architect Professional, Google Cloud Certified Professional Cloud Architect and Data Engineer), Microsoft cloud security (Azure Security Engineer, Security Operations Analyst, Microsoft 365 Security Administrator), incident response and forensics (CHFI, ECIH), health care security (CHPSE), and infrastructure (CompTIA comprehensive security suite including CASP+, CySA+, PenTest+, Security+, Linux+, and Cloud+). Beyond traditional teaching, Dr. Basta has been a visionary architect of distance education, collaborating with faculty and administrators to design, implement, and assess transformative online learning programs. Dr. Basta represents a rare synthesis of scholarly rigor, practical expertise, and spiritual depth.
Rebecca M. Basta is a distinguished bioinformatics and cybersecurity education specialist with deep expertise at the critical intersection of health care technology, data science, and cybersecurity. Holding a Master of Science in Bioinformatics and a Bachelor of Science in Biochemistry with a Minor in Biotechnology, Basta combines advanced academic credentials with hands-on laboratory and educational expertise.
With an impressive portfolio of 30+ professional certifications spanning health care data analytics, AI governance, cybersecurity, risk management, and emerging security technologies, Basta demonstrates exceptional breadth across intersecting disciplines. Her credentials include Certified Health Data Analyst (CHDA), Certified Information Privacy Professional/United States (CIPP/US), Artificial Intelligence Governance Professional (AIGP), ISO 27001 and ISO 42001 Certified Lead Auditor, Certified Analytics Professional Expert (CAP), Certified Lean Six Sigma Master Black Belt, Certified Red Team Operations Management (CRTOM), and Certified Artificial Intelligence Security & Risk (CAISR). This diverse certification landscape reflects her commitment to understanding security from multiple angles: defensive, offensive, and governance perspectives. Basta’s research and publication record is exceptionally prolific, focusing on the convergence of health care security and advanced data analytics.
Stavros E. Basta is an accomplished cybersecurity professional and published researcher
specializing in industrial control systems (ICS) security and critical infrastructure protection. Holding a Master of Science in Cybersecurity and a Bachelor of Science in Cybersecurity, Basta brings advanced academic credentials alongside extensive industry experience.
With an impressive portfolio of 25+ professional certifications spanning security leadership, penetration testing, risk management, and cloud security, including GIAC Global Industrial Cyber Security Professional (GICSP), Certified Information Security Manager (CISM), Licensed Penetration Testing Master (LPTM), GIAC Security Leadership (GSLC), and Certified Penetration Testing Professional (CPENT), Basta demonstrates deep expertise across the cybersecurity landscape. Basta’s research investigates the critical gap between traditional cybersecurity frameworks and the unique vulnerabilities of industrial control systems and critical infrastructure.