Evan Dummit's Course Notes Page


Main. 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. The headers indicate the most recent time I taught a course that used the associated notes (and thus, tends to be the last time the notes were updated).

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. (I am happy to allow non-profit or educational uses, but please ask: mostly it's just nice to hear if someone is using my materials!)



Single-Variable Calculus, Fall 2019 (Northeastern Math 1341) / Spring 2015 (Rochester MTH 143):
  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, 27pp: Introduction to Differentiation. (2pp, supplement on Trigonometric Limits).
  4. Calculus part 3, 27pp: Applications of Differentiation.
  5. Calculus part 4, 27pp: 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, Spring 2021 (Northeastern Math 2321):
  1. Multivariable Calculus part 1, 20pp: Vectors and 3-Dimensional Geometry.
  2. Multivariable Calculus part 2, 26pp: Partial Derivatives.
  3. Multivariable Calculus part 3, 24pp: Multiple Integration.
  4. Multivariable Calculus part 4, 34pp: Vector Calculus.


Probability and Statistics, Summer 2022 (Northeastern Math 3081):
  1. Probability and Statistics part 1, 26pp: Counting and Probability.
  2. Probability and Statistics part 2, 36pp: Random Variables.
  3. Probability and Statistics part 3, 18pp: Parameter and Interval Estimation.
  4. Probability and Statistics part 4, 21pp: Hypothesis Testing.
  5. Probability and Statistics part 5, 31pp: Topics in Hypothesis Testing.


Differential Equations and Linear Algebra, Spring 2016 (Rochester MTH 165):
  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.


Introduction to Proof, Fall 2022 (Northeastern Math 1365/1465):
  1. Introduction to Proof part 1, 28pp: Proofs, Logic, and Sets.
  2. Introduction to Proof part 2, 19pp: The Integers and Modular Arithmetic.
  3. Introduction to Proof part 3, 23pp: Relations, Orderings, and Functions.
  4. Introduction to Proof part 4, 13pp: Cardinality and Countability.
  5. Introduction to Proof part 5, 16pp: Elements of Algebra.
  6. Introduction to Proof part 6, 23pp: Counting Principles.


Linear Algebra (introductory-level), Fall 2017 (ASU MAT 342):
  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), Spring 2022 (Northeastern Math 4571):
  1. Linear Algebra part 0, 21pp: Preliminaries.
  2. Linear Algebra part 1, 20pp: Vector Spaces.
  3. Linear Algebra part 2, 22pp: Linear Transformations.
  4. Linear Algebra part 3, 23pp: Inner Product Spaces.
  5. Linear Algebra part 4, 34pp: Eigenvalues, Diagonalization, and the Jordan Canonical Form.
  6. Linear Algebra part 5, 25pp: Bilinear and Quadratic Forms.


Number Theory, Spring 2022 + Fall 2022 (Northeastern Math 3527 + Math 4527):
  1. Number Theory part 1, 17pp: The Integers.
  2. Number Theory part 2, 20pp: Modular Arithmetic.
  3. Number Theory part 3, 29pp: Cryptography and Related Topics.
  4. Number Theory part 4, 32pp: Unique Factorization and Applications.
  5. Number Theory part 5, 27pp: Squares and Quadratic Reciprocity.
  6. Number Theory part 6, 35pp: Rational Approximation and Diophantine Equations.
  7. Number Theory part 7, 30pp: Elliptic Curves.
  8. Number Theory part 8, 42pp: Quadratic Integer Rings.
  9. Number Theory part 9, 27pp: The Geometry of Numbers.
  10. Number Theory part 10, 17pp: Analytic Number Theory.


Complex Analysis, Fall 2022 (Northeastern Math 4555):
  1. Complex Analysis part 1, 19pp: Complex Numbers and Complex Derivatives.
  2. Complex Analysis part 2, 24pp: Complex Power Series.
  3. Complex Analysis part 3, 23pp: Complex Integration.
  4. Complex Analysis part 4, 29pp: Applications of Cauchy's Integral Formula.
  5. Complex Analysis part 5, 21pp: Local Behavior of Holomorphic Functions.


Mathematical Cryptography, Spring 2016 (Rochester MTH 233):
  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, Fall 2015 (Rochester MTH 215):
  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.


Ring Theory, Spring 2018 (ASU MAT 441):
  1. Ring Theory part 1, 15pp: The Integers.
  2. Ring Theory part 2, 24pp: Rings.
  3. Ring Theory part 3, 23pp: Homomorphisms, Ideals, and Quotients.
  4. Ring Theory part 4, 26pp: Arithmetic and Factorization in Integral Domains.


Fields and Galois Theory, Fall 2020 (Northeastern Math 5111):
  1. Fields and Galois Theory part 1, 38pp: Integers, Polynomials, and Rings.
  2. Fields and Galois Theory part 2, 40pp: Fields and Field Extensions.
  3. Fields and Galois Theory part 3, 49pp: Groups.
  4. Fields and Galois Theory part 4, 48pp: Galois Theory.