Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. The "Proofs of Theorems" files have not been classroom tested and may have some typographical errors; these files were created with the help of Jack Hartsell during the spring 2018 semester.

V. Ideals and Factor Rings.

• Section 26. Homomorphisms and Factor Rings. Section V.26 notes
• Supplement. Proofs of Theorems in Section V.26. Proofs of Theorems in Section V.26
• Supplement. Printout of the Proofs of Theorems in Section V.26. Print file of Proofs of Theorems in Section V.26
• Section 27. Prime and Maximal Ideals. Section V.27 notes
• Section 28. Grobner Bases for Ideals.
• Study Guide V.

VI. Extension Fields.

• Section 29. Introduction to Extension Fields. Section V.29 notes
• Section 30. Vector Spaces. Section VI.30 notes
• Section 31. Algebraic Extensions. Section VI.31 notes (This section includes a proof of the Fundamental Theorem of Algebra based on Liouville's Theorem.)
• Supplement. Algebraic Closure of a Field. Algebraic Closure notes
• Supplement. The Fundamental Theorem of Algebra - History. Fundamental Theorem of Algebra - History notes A more visual presentation, including an intuitive argument for the validity of the result, is available in Fundamental Theorem of Algebra - History, PowerPoint version.
• Supplement. Compass and Straight Edge Constructions. There is a PowerPoint presentation (prepared in Microsoft PowerPoint 2010) with embedded audio, a transcript in PDF, and a Windows Media Video: Compass and Straight Edge Constructions in PowerPoint, Compass and Straight Edge Constructions transcript. The video is a Compass and Straight Edge Constructions YouTube video (last accessed 3/1/2024).
• Section 32. Geometric Constructions. Section VI.32
• Supplement. Proofs of Theorems in Section VI.32. Proofs of Theorems in Section VI.32
• Supplement. Printout of the Proofs of Theorems in Section VI.32. Print file of Proofs of Theorems in Section VI.32
• Section 33. Finite Fields. Section VI.33
• Study Guide VI.

VII. Advanced Group Theory.

• Section 34. Isomorphism Theorems. Section VII.34
• Section 35. Series of Groups. Section VII.35
• Section 36. Sylow Theorems. Section VII.36
• Supplement. Proofs of Theorems in Section VII.36. Proofs of Theorems in Section VII.36
• Supplement. Printout of the Proofs of Theorems in Section VII.36. Print file of Proofs of Theorems in Section VII.36
• Section 37. Applications of the Sylow Theorems. Section VII.37
• Supplement. Proofs of Theorems in Section VII.37. Proofs of Theorems in Section VII.37
• Supplement. Printout of the Proofs of Theorems in Section VII.37. Print file of Proofs of Theorems in Section VII.37
• Section 38. Free Abelian Groups. Section VII.38
• Section 39. Free Groups. Section VII.39
• Supplement. Proofs of Theorems in Section VII.39. Proofs of Theorems in Section VII.39
• Supplement. Printout of the Proofs of Theorems in Section VII.39. Print file of Proofs of Theorems in Section VII.39
• Section 40. Group Presentations. Section VII.40
• Study Guide VII.

VIII. Groups in Topology.

• Section 41. Simplicial Complexes and Homology Groups.
• Section 42. Computations of Homology Groups.
• Section 43. More Homology Computations and Applications.
• Section 44. Homological Algebra.
• Study Guide VIII.

IX. Factorization.

• Section 45. Unique Factorization Domains. Section IX.45 (This section includes an algebraic proof of The Fundamental Theorem of Arithmetic.)
• Supplement. Proofs of Theorems in Section IX.45. Proofs of Theorems in Section IX.45
• Supplement. Printout of the Proofs of Theorems in Section IX.45. Print file of Proofs of Theorems in Section IX.45
• Section 46. Euclidean Domains. Section IX.46 (This section includes a proof of The Euclidean Algorithm.)
• Supplement. Proofs of Theorems in Section IX.46. Proofs of Theorems in Section IX.46
• Supplement. Printout of the Proofs of Theorems in Section IX.46. Print file of Proofs of Theorems in Section IX.46
• Section 47. Gaussian Integers and Multiplicative Norms. Section IX.47
• Supplement. Proofs of Theorems in Section IX.47. Proofs of Theorems in Section IX.47
• Supplement. Printout of the Proofs of Theorems in Section IX.47. Print file of Proofs of Theorems in Section IX.47
• Study Guide IX.

X. Automorphisms and Galois Theory.

• Section 48. Automorphisms of Fields. Section X.48
• Section 49. The Isomorphism Extension Theorem. Section X.49
• Supplement. Proofs of Theorems in Section X.49. Proofs of Theorems in Section X.49
• Supplement. Printout of the Proofs of Theorems in Section X.49. Print file of Proofs of Theorems in Section X.49
• Section 50. Splitting Fields. Section X.50
• Supplement. Proofs of Theorems in Section X.50. Proofs of Theorems in Section X.50
• Supplement. Printout of the Proofs of Theorems in Section X.50. Print file of Proofs of Theorems in Section X.50
• Section 51. Separable Extensions. Section X.51
• Review Notes. For Sections X.50 and X.51. Review of Sections X.50 and X.51
• Summary Notes. For Section X.51. Summary of Section X.51
• Section 52. Totally Inseparable Extensions.
• Section 53. Galois Theory. Section X.53
• Summary Notes. For Section X.53. Summary of Section X.53
• Section 54. Illustrations of Galois Theory. Section X.54
• Section 55. Cyclotomic Extensions. Section X.55 (This section includes the conditions for the construction of a regular n-gon.)
• Section 56. Insolvability of the Quintic. Section X.56
• Review Notes. For Section X.56. Review of Section X.56
• Study Guide IX.

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