# Teaching Materials

Each chapter of the textbook comes with the following teaching materials:

- Lesson plan for a 50–60 minute class in a first-semester course in abstract algebra. These plans refer to the “Whiteboard,” which are the in-class slides described below.
- In-class slides created using OpenBoard, a free interactive whiteboard available on Windows, Mac, and Linux. The UBZ document is the OpenBoard file that can be used in the classroom. The PDF document shows how the slides would look after the lesson. Watch this short video to learn how to use the in-class slides.
- In-class worksheet (and solutions) that is at the heart of each lesson. Through these worksheets, students conduct experiments, look for patterns, make conjectures, and uncover underlying structures and connections—all
*before*the formal definitions, formulas, and theorems are introduced. Such an environment allows students to learn and make sense of mathematics through their own*doing*of mathematics. - Lesson video that can be used to review the concepts learned in class or by students engaged in a self-study.

#### Chapter 1: Introduction to Proofs

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 2: Sets and Subsets

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 3: Divisors

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 4: Modular Arithmetic

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 5: Symmetries

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 6: Permutations

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 7: Matrices

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 8: Introduction to Groups

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 9: Groups of Small Size

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 10: Matrix Groups

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 11: Subgroups

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 12: Order of an Element

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 13: Cyclic Groups, Part I

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 14: Cyclic Groups, Part II

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 15: Functions

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 16: Isomorphisms

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 17: Homomorphisms, Part I

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 18: Homomorphisms, Part II

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 19: Introduction to Cosets

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 20: Lagrange’s Theorem

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 21: Multiplying / Adding Cosets

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 22: Quotient Group Examples

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 23: Quotient Group Proofs

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 24: Normal Subgroups

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 25: First Isomorphism Theorem

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 26: Introduction to Rings

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 27: Integral Domains and Fields

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 28: Polynomial Rings, Part I

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 29: Polynomial Rings, Part II

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 30: Factoring Polynomials

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 31: Ring Homomorphisms

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 32: Introduction to Quotient Rings

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 33: Quotient Ring ℤ_{7}[*x*]/⟨*x*^{2} – 1⟩

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 34: Quotient Ring ℝ[*x*]/⟨*x*^{2} + 1⟩

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 35: *F*[*x*]/⟨*g*(*x*)⟩ Is/Isn’t a Field, Part I

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 36: Maximal Ideals

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video

#### Chapter 37: *F*[*x*]/⟨*g*(*x*)⟩ Is/Isn’t a Field, Part II

- Lesson plan
- In-class slides: UBZ and PDF
- In-class worksheet and solutions
- Lesson video