"Introduction to Modern Geometry - Axiomatic Method Class Notes" Webpage

Introduction to Modern Geometry - Axiomatic Method Class Notes
Foundations of Geometry,
by C. R. Wylie, Jr.
McGraw-Hill (1964), reprinted by Dover Publications (2009) Wylie's Foundations of Geometry book

Wylie's Foundations of Geometry book, Dover Publications reprint

These notes would constitute part of the material of "Introduction to Modern Geometry" (MATH 4157/5157). The catalog description of this course (as of fall 2021) is: "An introduction to Euclidean and non-Euclidean geometries, emphasizing the distinction between the axiomatic characterizations, and the transformational characterizations of these geometries. Some history of the development of the discipline will also be included." The other parts of Introduction to Modern Geometry for which I have online notes include some history of geometry and transformational geometry.

I am drawn to C. R. Wylie's book because I took the class Foundations of Plane Geometry (MH 447) in summer 1982 at Auburn University at Montgomery taught by Dr. Jimmy Nanny (December 19, 1943 - October 28, 2016). Dr. Nanny was my unofficial undergraduate mentor.

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 the results from the class notes. 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. The Axiomatic Method.
Chapter 2. Euclidean Geometry.
Chapter 3. The Geometry of Four Dimensions.
Chapter 4. Plane Hyperbolic Geometry.
Chapter 5. A Euclidean Model of the Hyperbolic Plane.

Preface. Preface notes

Chapter 1. The Axiomatic Method.

Section 1.1. Introduction. Section 1.1 notes
Section 1.2. Inductive and Deductive Reasoning. Section 1.2 notes
Section 1.3. Axiomatic Systems. Section 1.3 notes
Section 1.4. Consistency. Section 1.4 notes
Section 1.5. Independence. Section 1.5 notes
Section 1.6. Completeness and Categoricalness. Section 1.6 notes
Section 1.7. Finite Geometries. Section 1.7 notes

Supplement. Proofs of Theorems in Section 1.7. Beamer file of Section 1.7 proofs
Supplement. Printout of the Proofs of Theorems in Section 1.7. Print file of Section 1.7 proofs

Chapter 2. Euclidean Geometry.

Section 2.1. Introduction. Section 2.1 notes
Section 2.2. A Brief Critique of Euclid. Section 2.2 notes
Section 2.3. The Postulate of Connection. Section 2.3 notes

Supplement. Proofs of Theorems in Section 2.3. Beamer file of Section 2.3 proofs
Supplement. Printout of the Proofs of Theorems in Section 2.3. Print file of Section 2.3 proofs

Section 2.4. The Measurement of Distance. Section 2.4 notes

Supplement. Proofs of Theorems in Section 2.4. Beamer file of Section 2.4 proofs
Supplement. Printout of the Proofs of Theorems in Section 2.4. Print file of Section 2.4 proofs

Section 2.5. Order Relations. Section 2.5 notes

Supplement. Proofs of Theorems in Section 2.5. Beamer file of Section 2.5 proofs
Supplement. Printout of the Proofs of Theorems in Section 2.5. Print file of Section 2.5 proofs

Section 2.6. Angles and Angle Measurement. Section 2.6 notes

Supplement. Proofs of Theorems in Section 2.6. Beamer file of Section 2.6 proofs
Supplement. Printout of the Proofs of Theorems in Section 2.6. Print file of Section 2.6 proofs

Section 2.7. Further Properties of Angles. Section 2.7 notes

Supplement. Proofs of Theorems in Section 2.7. Beamer file of Section 2.7 proofs
Supplement. Printout of the Proofs of Theorems in Section 2.7. Print file of Section 2.7 proofs

Section 2.8. Triangles and Polygons. Section 2.8 notes
Section 2.9. The Congruence Postulate. Section 2.9 notes

Supplement. Proofs of Theorems in Section 2.9. Beamer file of Section 2.9 proofs
Supplement. Printout of the Proofs of Theorems in Section 2.9. Print file of Section 2.9 proofs