List of Chapters

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