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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.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: Numbers, Patterns, and Mathematical Language5
- Chapter 2: Arithmetic as Structure6
- Chapter 3: Algebraic Expressions and Equations7
- Chapter 4: Functions and Graphs8
- Chapter 5: Lines, Systems, and Modeling9
- Chapter 6: Polynomials, Factoring, and Quadratics10
- Chapter 7: Rational, Radical, Exponential, and Logarithmic Functions11
- Chapter 8: Geometry and Measurement12
- Chapter 9: Trigonometry13
- Chapter 10: Mathematical Proof and Logic14
- Chapter 11: Sets, Relations, and Discrete Structures15
- Chapter 12: Limits and Continuity16
- Chapter 13: Derivatives and Rates of Change17
- Chapter 14: Applications of Derivatives18
- Chapter 15: Integrals and Accumulation19
- Chapter 16: Sequences, Series, and Infinite Processes20
- Chapter 17: Vectors and Linear Algebra21
- Chapter 18: Linear Transformations, Determinants, and Eigenvalues22
- Chapter 19: Multivariable Thinking23
- Chapter 20: Probability, Statistics, and Uncertainty24
- Chapter 21: Differential Equations and Mathematical Models25
- Chapter 22: Abstract Algebra and Number Systems26
- Chapter 23: Real Analysis and the Foundations of Calculus27
- Chapter 24: Geometry, Topology, and Modern Mathematical Perspective28
- Conclusion29