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.

• Introduction.
• Chapter I. The Complex Number System.
• Chapter II. Metric Spaces and the Topology of ℂ.
• Chapter III. Elementary Properties and Examples of Analytic Functions.
• Chapter IV. Complex Integration.
• Chapter V. Singularities.
• Chapter VI. The Maximum Modulus Theorem.
• Mobius Transformations, Transformational Geometry, and Hyperbolic Geometry.
• Additional Notes on Chapters VII-XII

Introduction.

• Supplement. Introduction to Math Philosophy and Meaning. Intro to Math Philosophy notes
• Study Guide 0.

Chapter I. The Complex Number System.

• I.1. The Real Number System. Section I.1 notes
• I.2. The Field of Complex Numbers. Section I.2 notes
• Supplement. Ordering the Complex Numbers. Ordering the Complex Numbers notes
• I.3. The Complex Plane. Section I.3 notes
• Supplement. Proofs of Theorems in Section I.3. Beamer file of Section I.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.3. Print file of Section I.3 proofs
• Supplement. Location of Zeros of Polynomials. Zeros of Polynomials notes
• Supplement. Proofs of Theorems in Location of Zeros of Polynomials. Beamer file of Zeros of Polynomials proofs
• Supplement. Printout of the Proofs of Theorems in Location of Zeros of Polynomials. Print file of Zeros of Polynomials proofs
• I.4. Polar Representation and Roots of Complex Numbers. Section I.4 notes
• I.5. Lines and Half Planes in the Complex Plane. Section I.5 notes
• Supplement. The Ilief-Sendov Conjecture. Ilief-Sendov Conjecture notes
• Supplement. Dr. Bob's Favorite Results on Complex Polynomials. Results on Complex Polynomials notes
• I.6. The Extended Plane and its Spherical Representation. Section I.6 notes
• Study Guide 1.

Chapter II. Metric Spaces and the Topology of ℂ.

• II.1. Definition and Examples of Metric Spaces. Section II.1 notes
• Supplement. Proofs of Theorems in Section II.1. Beamer file of Section II.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.1. Print file of Section II.1 proofs
• II.2. Connectedness. Section II.2 notes
• Supplement. Proofs of Theorems in Section II.2. Beamer file of Section II.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.2. Print file of Section II.2 proofs
• II.3. Sequences and Completeness. Section II.3 notes
• Supplement. Proofs of Theorems in Section II.3. Beamer file of Section II.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.3. Print file of Section II.3 proofs
• II.4. Compactness. Section II.4 notes (This section includes an example of a closed and bounded set which is not compact and a discussion of Cauchy sequences in a topological space.)
• Supplement. Proofs of Theorems in Section II.4. Beamer file of Section II.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.4. Print file of Section II.4 proofs
• Supplement. The Extended Complex Plane. Extended Complex Plane notes
• Supplement. Proofs of Theorems in Supplement, The Extended Complex Plane. Beamer file of Extended Complex Plane proofs
• Supplement. Printout of the Proofs of Theorems in Supplement, The Extended Complex Plane. Print file of Extended Complex Plane proofs
• II.5. Continuity. Section II.5 notes
• Supplement. Proofs of Theorems in Section II.5. Beamer file of Section II.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.5. Print file of Section II.5 proofs
• II.6. Uniform Convergence. Section II.6 notes
• Supplement. Proofs of Theorems in Section II.6. Beamer file of Section II.6 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.6. Print file of Section II.6 proofs
• Study Guide 2.

Chapter III. Elementary Properties and Examples of Analytic Functions.

• Supplement. A Primer on Lipschitz Functions. Lipschitz Functions notes
• III.1. Power Series. Section III.1 notes
• Supplement. Proofs of Theorems in Section III.1. Beamer file of Section III.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.1. Print file of Section III.1 proofs
• III.2. Analytic Functions. Section III.2 notes
• Supplement. Proofs of Theorems in Section III.2. Beamer file of Section III.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section III.2. Print file of Section III.2 proofs
• III.3. Analytic Functions as Mapping, Mobius Transformations. 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
• Supplemental Notes on III.3. Analytic Functions as Mappings: Mobius Transformations-with Supplemental Material from Hitchman's Geometry with an Introduction to Cosmic Topology. Section III.3 Supplemental notes
• Study Guide 3.

Chapter IV. Complex Integration.

• IV.1. Riemann-Stieltjes Integrals. Section IV.1 notes
• 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
• IV.2. Power Series Representation of Analytic Functions. Section IV.2 notes
• 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
• IV.3. Zeros of Analytic Functions. Section IV.3 notes (This section includes a proof of the Fundamental Theorem of Algebra and a version of the Maximum Modulus Theorem.)
• Supplement. Proofs of Theorems in Section IV.3. 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
• IV.4. The Index of a Closed Curve. Section IV.4 notes
• Supplement. Proofs of Theorems in Section IV.4. Beamer file of Section IV.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.4. Print file of Section IV.4 proofs
• IV.5. Cauchy's Theorem and Integral Formula. Section IV.5 notes
• Supplement. Proofs of Theorems in Section IV.5. Beamer file of Section IV.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.5. Print file of Section IV.5 proofs
• IV.6. The Homotopic Version of Cauchy's Theorem and Simple Connectivity. Section IV.6 notes
• Supplement. Proofs of Theorems in Section IV.6. Beamer file of Section IV.6 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.6. Print file of Section IV.6 proofs
• IV.7. Counting Zeros; The Open Mapping Theorem. Section IV.7 notes
• Supplement. Proofs of Theorems in Section IV.7. Beamer file of Section IV.7 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.7. Print file of Section IV.7 proofs
• Supplement. The Stability Theorem for Orders of Zeros of Equations (Theorem IV.7.4). Stability Theorem notes
• IV.8. Goursat's Theorem. Section IV.8 notes
• Supplement. Proofs of Theorems in Section IV.8. Beamer file of Section IV.8 proofs
• Supplement. Printout of the Proofs of Theorems in Section IV.8. Print file of Section IV.8 proofs
• Study Guide 4.

Chapter V. Singularities.

• V.1. Classification of Singularities. Section V.1 notes
• Supplement. Proofs of Theorems in Section V.1. Beamer file of Section V.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section V.1. Print file of Section V.1 proofs
• Supplement. Laurent Series Development (Theorem V.1.11). Laurent Series Development notes
• V.2. Residues. Section V.2 notes
• Supplement. Proofs of Theorems in Section V.2. Beamer file of Section V.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section V.2. Print file of Section V.2 proofs
• V.3. The Argument Principle. Section V.3 notes (This section includes another proof of the Fundamental Theorem of Algebra.)
• Supplement. Proofs of Theorems in Section V.3. Beamer file of Section V.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section V.3. Print file of Section V.3 proofs
• Study Guide 5.

Chapter VI. The Maximum Modulus Theorem.

• VI.1. The Maximum Principle. Section VI.1 notes
• Supplement. Proofs of Theorems in Section VI.1. Beamer file of Section VI.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section VI.1. Print file of Section VI.1 proofs
• Supplement. Applications of the Maximum Modulus Theorem to Polynomials. Max Modulus Theorem Applications notes
• Supplement. Proofs of Theorems in Supplement to VI.1. Beamer file of Max Modulus Theorem Applications proofs
• Supplement. Printout of the Proofs of Theorems in Supplement to VI.1. Print file of Max Modulus Theorem proofs
• VI.2. Schwarz's Lemma. Section VI.2 notes
• Supplement. Proofs of Theorems in Section VI.2. Beamer file of Section VI.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section VI.2. Print file of Section VI.2 proofs
• VI.3. Convex Functions and Hadamard's Three Circles Theorem. Section VI.3 notes
• Supplement. Proofs of Theorems in Section VI.3. Beamer file of Section VI.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section VI.3. Print file of Section VI.3 proofs
• VI.4. Phragmen-Lindelof Theorem. Section VI.4 notes
• Supplement. Proofs of Theorems in Section VI.4. Beamer file of Section VI.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section VI.4. Print file of Section VI.4 proofs
• Study Guide 6.

Supplemental Material on Mobius Transformations, Transformational Geometry, and Hyperbolic Geometry

• Analytic Functions as Mappings: Mobius Transformations. Analytic Functions as Mappings notes (This is based largely on section III.3 of Conway's Functions of One Complex Variable, but includes material from Chapters 3 and 4 of Hitchman.)
• Transformations of ℂ and ℂ_∞ - An Approach to Geometry. Transformations notes (This is based largely on Sections 3.1, 3.2, and 4.1 of Hitchman.)
• Hyperbolic Geometry and the Poincare Disk. Hyperbolic Geometry notes (This is based largely on Chapter 5 of Hitchman.)

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