Teaching Materials

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

Chapter 2: Sets and Subsets

Chapter 3: Divisors

Chapter 4: Modular Arithmetic

Chapter 5: Symmetries

Chapter 6: Permutations

Chapter 7: Matrices

Chapter 8: Introduction to Groups

Chapter 9: Groups of Small Size

Chapter 10: Matrix Groups

Chapter 11: Subgroups

Chapter 12: Order of an Element

Chapter 13: Cyclic Groups, Part I

Chapter 14: Cyclic Groups, Part II

Chapter 15: Functions

Chapter 16: Isomorphisms

Chapter 17: Homomorphisms, Part I

Chapter 18: Homomorphisms, Part II

Chapter 19: Introduction to Cosets

Chapter 20: Lagrange’s Theorem

Chapter 21: Multiplying / Adding Cosets

Chapter 22: Quotient Group Examples

Chapter 23: Quotient Group Proofs

Chapter 24: Normal Subgroups

Chapter 25: First Isomorphism Theorem

Chapter 26: Introduction to Rings

Chapter 27: Integral Domains and Fields

Chapter 28: Polynomial Rings, Part I

Chapter 29: Polynomial Rings, Part II

Chapter 30: Factoring Polynomials

Chapter 31: Ring Homomorphisms

Chapter 32: Introduction to Quotient Rings

Chapter 33: Quotient Ring ℤ7[x]/⟨x2 – 1⟩

Chapter 34: Quotient Ring ℝ[x]/⟨x2 + 1⟩

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

Chapter 36: Maximal Ideals

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

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