ETSU does not offer a formal graduate level linear algebra class, but does offer a Theory of Matrices (MATH 5090) class; online notes for Theory of Matrices are available. The notes presented here are based on the Thomas W. Hungerford's "suggested course outline" for a (one quarter/30 class meeting) graduate level linear algebra class. Additional notes based on Hungerford's Algebra (some of which overlap with the notes below) are online on groups, rings and modules, and fields. Sophomore Linear Algebra (MATH 2010) notes are available online based on J. Fraleigh and R. Beauregard's Linear Algebra, 3rd Edition (Addison-Wesley Publishing Company, 1995).

Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of results which are particularly lengthy (shorter proofs are contained in the notes themselves). The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. Some of these notes and supplements have not been classroom tested (and so may have some typographical errors).

III. Rings.

• Section III.3. Factorization in Commutative Rings. Section III.3 notes
• Supplement. Proofs of Theorems in Section III.3. Beamer file of Section III.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.3. Print file of Section III.3 proofs
• Section III.4. Rings of Quotients and Localization. Section III.4 notes (This section includes the price paid for trying to "divide by 0" in a ring of quotients; see Note III.4.B.)
• Supplement. Proofs of Theorems in Section III.4. Beamer file of Section III.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.4. Beamer file of Section III.4 proofs
• Section III.5. Rings of Polynomials and Formal Power Series. Section III.5 notes
• Supplement. Proofs of Theorems in Section III.5. Beamer file of Section III.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.5. Print file of Section III.5 proofs
• Section III.6. Factorization in Polynomial Rings. Section III.6 notes
• Supplement. Proofs of Theorems in Section III.6. Beamer file of Section III.6 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.6. Print file of Section III.6 proofs
• Study Guide III

IV. Modules. Modules notes

• Section IV.1. Modules, Homomorphisms, and Exact Sequences. Section IV.1 notes (Includes a statement of the Snake Lemma; see Note IV.1.J.)
• Supplement. Proofs of Theorems in Section IV.1. Beamer file of Section IV.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.1. Print file of Section IV.1 proofs
• Supplement. A Proof of the Snake Lemma. Proofs of the Snake Lemma notes
• Section IV.2. Free Modules and Vector Spaces. Section IV.2 notes (This section includes a proof that there is no field strictly between ℝ and ℂ; see Note IV.2.K.)
• Supplement. Proofs of Theorems in Section IV.2. Beamer file of Section IV.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.2. Print file of Section IV.2 proofs
• Section IV.3. Projective and Injective Modules. Section IV.3 notes
• Supplement. Proofs of Theorems in Section IV.3 (partial). Beamer file of Section IV.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.3. Print file of Section IV.3 proofs
• Section IV.6. Modules over a Principal Ideal Domain (partial). Section IV.6 notes
• Section IV.7. Algebras. Section IV.7 notes
• Supplement. Proofs of Theorems in Section IV.7 (partial). Beamer file of Section IV.7 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.7 (partial). Print file of Section IV.7 proofs
• Study Guide IV.

VII. Linear Algebra.

• Section VII.1. Matrices and Maps (partial). Section VII.1 notes
• Section VII.2. Rank and Equivalence.
• Appendix VII.2. Abelian Groups Defined by Generators and Relations.
• Section VII.3. Determinants.
• Section VII.4. Decomposition of a Single Linear Transformation and Similarity.
• Section VII.5. The Characteristic Polynomial, Eigenvectors, and Eigenvalues.
• Study Guide VII.

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