Table of contents

Mathematics from First Principles

A coherent path from arithmetic and algebra to calculus, linear algebra, proof, probability, and modern mathematical thinking

Read each section in order. Every title can be opened as a TheoryTrace document.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: Numbers, Patterns, and Mathematical Language
• Chapter 2: Arithmetic as Structure
• Chapter 3: Algebraic Expressions and Equations
• Chapter 4: Functions and Graphs
• Chapter 5: Lines, Systems, and Modeling
• Chapter 6: Polynomials, Factoring, and Quadratics
• Chapter 7: Rational, Radical, Exponential, and Logarithmic Functions
• Chapter 8: Geometry and Measurement
• Chapter 9: Trigonometry
• Chapter 10: Mathematical Proof and Logic
• Chapter 11: Sets, Relations, and Discrete Structures
• Chapter 12: Limits and Continuity
• Chapter 13: Derivatives and Rates of Change
• Chapter 14: Applications of Derivatives
• Chapter 15: Integrals and Accumulation
• Chapter 16: Sequences, Series, and Infinite Processes
• Chapter 17: Vectors and Linear Algebra
• Chapter 18: Linear Transformations, Determinants, and Eigenvalues
• Chapter 19: Multivariable Thinking
• Chapter 20: Probability, Statistics, and Uncertainty
• Chapter 21: Differential Equations and Mathematical Models
• Chapter 22: Abstract Algebra and Number Systems
• Chapter 23: Real Analysis and the Foundations of Calculus
• Chapter 24: Geometry, Topology, and Modern Mathematical Perspective
• Conclusion