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. 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).

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.)

Single-Variable Calculus, Fall 2016 (Rochester MTH 141) / 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, 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, Spring 2018 (ASU MAT 267):
1. Multivariable Calculus part 1, 18pp: Vectors and 3-Dimensional Geometry.
2. Multivariable Calculus part 2, 24pp: Partial Derivatives.
3. Multivariable Calculus part 3, 24pp: Multiple Integration.
4. Multivariable Calculus part 4, 24pp: Vector Calculus.

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.

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 2017 (Rochester MTH 235):
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.

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.

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.

Number Theory with Applications, Fall 2014 (Rochester MTH 230):
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.