"Graduate Design Theory Class Notes" Webpage

Graduate Design Theory Class Notes
Design Theory Volume I, Second Edition
Encyclopedia of Mathematics and Its Applications #69
by T. Beth, D. Jungnickel, and H. Lenz
Cambridge University Press (1999) Beth, Jungnickel, and Lenz's Design Theory Volume I book, 2nd edition

Beth, Jungnickel, and Lenz's Design Theory Volume I book, 2nd edition

Graduate Design Theory is not an official ETSU class. A desirable background for approaching this material includes exposure to:

basic combinatorial ideas, such as those covered in Applied Combinatorics and Problem Solving (MATH 3340),
graph theoretic ideas, such as those given in Introduction to Graph Theory (MATH 4347/5347),
knowledge of basic modern algebra, such as that given in Introduction to Modern Algebra (MATH 4127/5127), and
an introduction to design theory, such as that covered in my online notes for Design Theory (also not an official ETSU class).

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).

Preface.
Chapter 1. Examples and Basic Definitions.
Chapter 2. Combinatorial Analysis of Designs.
Chapter 3. Groups and Designs.

Preface. Preface notes

Chapter 1. Examples and Basic Definitions.

Section 1.1. Incidence Structures and Incidence Matrices. Section 1.1 notes

Supplement. Proofs from Section 1.1. Beamer file of Section 1.1 proofs
Supplement. Printouts of Proofs from Section 1.1. Print file of Section 1.1 proofs

Section 1.2. Block Designs and Examples from Affine and Projective Geometry. Section 1.2 notes

Supplement. Proofs from Section 1.2. Beamer file of Section 1.2 proofs
Supplement. Printouts of Proofs from Section 1.2. Print file of Section 1.2 proofs

Section 1.3. t-Designs, Steiner Systems and Configurations.
Section 1.4. Isomorphisms, Duality and Correlations.
Section 1.5. Partitions of the Block Set and Resolvability.
Section 1.6. Divisible Incidence Structures.
Section 1.7. Transversal Designs and Nets.
Section 1.8. Subspaces.
Section 1.9. Hadamard Designs.
Study Guide 1.

Chapter 2. Combinatorial Analysis of Designs.

Section 2.1. Basics.
Section 2.2. Fisher's Inequality for Pairwise Balanced Designs.
Section 2.3. Symmetric Designs.
Section 2.4. The Bruck-Ryser-Chowla Theorem.
Section 2.5. Balanced Incidence Structures and Balanced Duals.
Section 2.6. Generalisations of Fisher's Inequality and Intersection Numbers.
Section 2.7. Extensions of Designs.
Section 2.8. Affine Designs.
Section 2.9. Strongly Regular Graphs.
Section 2.10. The Hall-Connot Theorem.
Section 2.11. Designs and Codes.
Study Guide 2.

Chapter 3. Groups and Designs.

Section 3.1. Introduction.
Section 3.2. Incidence Morphisms.
Section 3.3. Permutation Groups.
Section 3.4. Applications to Incidence Structures.
Section 3.5. Examples from Classical Geometry.
Section 3.6. Constructions of t-Designs from Base Blocks.
Section 3.7. Extensions of Groups.
Section 3.8. Construction of t-Designs from Base Blocks.
Section 3.9. Cyclic t-Designs.
Section 3.10. Cayley Graphs.
Study Guide 3.

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