Contents

I realize a blog format isn’t ideal for writing mathematical notes, especially if I need to recall something I wrote about ages ago. So this page just keeps track of the material I’ve written about.

1. Calculus
1.1. Calculus in a Single Variable
1.2. Analysis Interlude
1.3. Vector Calculus
1.4. Special Functions
2. Linear Algebra
3. Puzzles
4. Foundations, including elementary algebra and naive set theory.

Analytical Table of Contents

Calculus

  1. Calculus in a Single Variable
  2. Analysis Interlude
    1. Naive Infinite Series
    2. Sequences, specifically their convergence or divergence
    3. Series Convergence: What Does It Mean? The Definition of Convergence for Series.
    4. Integral Test for Convergence
    5. Comparison Tests
    6. Alternating Series Test
    7. Other Alternating Series Tests
    8. Power Series
    9. Taylor Series
    10. Taylor Polynomials
    11. The Fabulous Useful Applications of Taylor Series:
      1. Taylor Series Uses #1: Complicated Integrals
  3. Vector Calculus
    1. Geometry and Vectors
      1. Introducing Vectors for Geometry
      2. Constructing Orthogonal Vectors, Geometric Implications
      3. Line Constructions
      4. Constructing Planes
      5. Surfaces (…well, “Quadrics”)
    2. Curves, Velocity, “Classical Kinematics”
    3. Differentiation for Multivariable Functions
      1. Continuity for Functions of Several Variables, Partial Derivatives, where we generalize differentiation for multivariable functions
      2. Chain Rule for Partial Derivatives, including revisiting the idea of implicit differentiation
      3. Directional Derivative, Gradient
      4. Finding Extrema of Multivariable Functions
      5. Lagrange Multipliers
    4. Multiple Integrals
      1. Introduction to Double Integration
  4. Special Functions
    1. Trigonometric Functions
    2. Hyperbolic Functions

Linear Algebra

  1. Projective Space
    1. Endomorphisms of the Fano Plane

Puzzles

  1. Puzzle: Network Theory, Petri Nets
  2. March of the Goblins

Foundations

  1. “High School Mathematics”: Naive Foundations

Note to self: when I get to continued fractions, I should redirect the link on my The Natural Logarithm post.

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