Evan Dummit's Course Notes Page



Main. Current Teaching. Course Notes. Lectures.

This page contains notes (lying somewhere between lecture notes and a draft of a book) for courses I have taught. If you have encountered copies of my notes elsewhere, please be aware that they may be old versions with uncorrected errors: the newest versions will always appear on my personal webpage.

Obligatory copyright notice:
All material is copyright me, Evan Dummit.
No individual or group has permission to repost, modify, or distribute these files without my express consent.



Single-Variable Calculus:
  1. Calculus part 0, 18pp: Review of Basic Concepts.
  2. Calculus part 1, 12pp: Limits and Continuity (7pp, supplement on Formal Epsilon-Delta Limits).
  3. Calculus part 2, 23pp: Introduction to Differentiation. (2pp, supplement on Trigonometric Limits).
  4. Calculus part 3, 26pp: Applications of Differentiation.
  5. Calculus part 4, 13pp: Introduction to Integration.
  6. Calculus part 5, 9pp: Techniques of Integration.
  7. Calculus part 6, 16pp: Parametric Curves, Polar Coordinates, and Complex Numbers.
  8. Calculus part 7, 20pp: Sequences and Series.
  9. Calculus part 8, 22pp: Power Series and Taylor Series.
  10. Appendix, 10pp: Introduction to Differential Equations (9pp, supplement on Second-Order Differential Equations).


Multivariable Calculus:
  1. Multivariable Calculus part 1, 17pp: Vectors and 3-Dimensional Geometry.
  2. Multivariable Calculus part 2, 23pp: Partial Derivatives.
  3. Multivariable Calculus part 3, 24pp: Multiple Integration.
  4. Multivariable Calculus part 4, 24pp: Vector Calculus.


Differential Equations and Linear Algebra:
  1. Differential Equations and Linear Algebra part 1, 12pp: First-Order Differential Equations. (10pp, supplement on Additional First-Order Topics)
  2. Differential Equations and Linear Algebra part 2, 18pp: Matrices and Systems of Linear Equations.
  3. Differential Equations and Linear Algebra part 3, 29pp: Vector Spaces and Linear Transformations.
  4. Differential Equations and Linear Algebra part 4, 9pp: Eigenvalues and Eigenvectors.
  5. Differential Equations and Linear Algebra part 5, 15pp: Linear Differential Equations.
  6. Differential Equations and Linear Algebra part 6, 7pp: Systems of Linear Differential Equations.
  7. Complex Numbers (appendix), 6pp: Complex Numbers.


Linear Algebra (introductory-level) (in progress):
  1. Linear Algebra part 1, 20pp: Matrices and Systems of Linear Equations.
  2. Linear Algebra part 2, 26pp: Vector Spaces.
  3. Linear Algebra part 3, 16pp: Inner Products.
  4. Linear Algebra part 4, 17pp: Linear Transformations.
  5. Linear Algebra part 5, 22pp: Eigenvalues and Diagonalization.


Linear Algebra (upper-level):
  1. Linear Algebra part 0, 15pp: Preliminaries.
  2. Linear Algebra part 1, 26pp: Vector Spaces.
  3. Linear Algebra part 2, 24pp: Linear Transformations.
  4. Linear Algebra part 3, 22pp: Linear Systems, Inverses, and Determinants.
  5. Linear Algebra part 4, 25pp: Eigenvalues, Diagonalization, and the Jordan Canonical Form.


Mathematical Cryptography:
  1. Cryptography part 1, 25pp: Classical Cryptosystems.
  2. Cryptography part 2, 29pp: Public-Key Cryptography.
  3. Cryptography part 3, 13pp: Discrete Logarithms in Cryptography.
  4. Cryptography part 4, 29pp: Digital Secrecy and Security.
  5. Cryptography part 5, 21pp: Elliptic Curves in Cryptography.
  6. Cryptography part 6, 8pp: Modern Topics in Cryptography.


Chaos, Dynamics, and Fractals:
  1. Chaos, Dynamics, and Fractals part 1, 26pp: Introduction to Dynamics.
  2. Chaos, Dynamics, and Fractals part 2, 20pp: Dynamics of One-Parameter Families.
  3. Chaos, Dynamics, and Fractals part 3, 26pp: Chaotic Dynamics.
  4. Chaos, Dynamics, and Fractals part 4, 21pp: Fractals.
  5. Chaos, Dynamics, and Fractals part 5, 25pp: Introduction to Complex Dynamics.


Number Theory with Applications:
  1. Number Theory part 1, 9pp: The Integers.
  2. Number Theory part 2, 18pp: Modular Arithmetic.
  3. Number Theory part 3, 17pp: Cryptography and Related Topics.
  4. Number Theory part 4, 29pp: Unique Factorization and Applications.
  5. Number Theory part 5, 20pp: Squares and Quadratic Reciprocity.
  6. Number Theory part 6, 21pp: Continued Fractions and Diophantine Equations.
  7. Number Theory part 7, 3pp: The Geometry of Numbers and Minkowski's Theorem.