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. These notes and supplements have not been classroom tested (and so may have some typographical errors).
- Chapter 1. Elements of Algebra.
- Chapter 2. Pertinent Properties of Euclidean Space.
- Chapter 3. Finite Fields and Polynomials.
- Chapter 4. Coding Theory.
- Chapter 5. Cryptology.
- Chapter 6. Applications of Groups.
- Chapter 7. Further Applications of Algebra.
Chapter 1. Elements of Algebra.
- Section 1.1. Sets, Functions, and Notation.
- Section 1.2. Alebraic Structures.
- Study Guide 1.
Chapter 2. Pertinent Properties of Euclidean Space.
- Section 2.1. Elementary Properties of ℝ.
- Section 2.2. Elementary Properties of Euclidean Spaces.
- Study Guide 2.
Chapter 3. Lattice Theory.
- Section 3.1. Historical Background.
- Section 3.2. Partial Orders and Lattices.
- Section 3.3. Relations with Other Branches of Mathematics.
- Study Guide 3.
Chapter 4. Lattice Algebra.
- Section 4.1. Lattice Semigroups and Lattice Groups.
- Section 4.2. Minimax Algebra.
- Section 4.3. Minimax Matrix Theory.
- Section 4.4. The Geometry of S(X).
- Study Guide 4.
Chapter 5. Matrix-Based Lattice Associative Memories.
- Section 5.1. Historical Background.
- Section 5.2. Lattice Associative Memories.
- Section 5.3. Discrete Logarithms and Other Ciphers.
- Study Guide 5.
Chapter 6. Extreme Points of Data Sets.
- Section 6.1. Relevant Concepts of Convex Set Theory.
- Section 6.2. Affine Subsets of EXT(B(X)).
- Study Guide 6.
Chapter 7. Image Unmixing and Segmentation.
- Section 7.1. Spectral Endmembers and Linear Unmixing.
- Section 7.2. Aviris Hypershpectral Image Examples.
- Section 7.3. Endmembers and Clustering Validation Indexes.
- Section 7.4. Color Image Segmentation.
- Study Guide 7.
Chapter 8. Lattice-Based Biomimetic Neural Networks.
- Section 8.1. Biomimetic Artificial Neural Networks.
- Section 8.2. Lattice Biomimetic Neural Networks.
- Study Guide 8.
Chapter 9. Learning in Biomimetic Neural Networks.
- Section 9.1. Learning in Single-Layer LBNNS.
- Section 9.2. Mulit-Layer Lattice Biomimetic Neural Networks.
- Study Guide 9.
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