I am currently an Assistant Professor at California State University San Bernardino. This channel features worked examples from the courses I teach there, as well as examples I encounter in my research.

Section 3.4, Principal Ideal Domains, Irreducibles are Prime in a PID
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Section 3.4, Principal Ideal Domains, Irreducibles are Prime in a PID
Section 3.4, Principal Ideal Domains, Prime Implies Maximal in a PID
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Section 3.4, Principal Ideal Domains, Prime Implies Maximal in a PID
Section 3.4, Principal Ideal Domains, All Maximal Ideals are Prime Ideals
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Section 3.4, Principal Ideal Domains, All Maximal Ideals are Prime Ideals
Section 3.4, Principal Ideal Domains, Quotienting by Maximal Ideals
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Section 3.4, Principal Ideal Domains, Quotienting by Maximal Ideals
Section 3.4, Principal Ideal Domains, Ideal Generated by Maximal Ideal and Element is Everything
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Section 3.4, Principal Ideal Domains, Ideal Generated by Maximal Ideal and Element is Everything
Section 3.4, Principal Ideal Domains, A Non-Maximal Prime Ideal
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Section 3.4, Principal Ideal Domains, A Non-Maximal Prime Ideal
Section 3.4, Principal Ideal Domains, Maximal Ideals and Examples
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Section 3.4, Principal Ideal Domains, Maximal Ideals and Examples
Section 3.4, Principal Ideal Domains, Quotienting by Prime Ideals
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Section 3.4, Principal Ideal Domains, Quotienting by Prime Ideals
Section 3.4, Principal Ideal Domains, Prime Ideal Examples and Non-Examples
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Section 3.4, Principal Ideal Domains, Prime Ideal Examples and Non-Examples
Section 3.4, Principal Ideal Domains, Prime Ideals and Prime Elements
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Section 3.4, Principal Ideal Domains, Prime Ideals and Prime Elements
Section 3.4, Principal Ideal Domains, PIDs have GCDs
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Section 3.4, Principal Ideal Domains, PIDs have GCDs
Section 3.4, Principal Ideal Domains, F[x] is a PID for F a Field
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Section 3.4, Principal Ideal Domains, F[x] is a PID for F a Field
Section 3.4, Principal Ideal Domains, Definition and Z is a PID
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Section 3.4, Principal Ideal Domains, Definition and Z is a PID
Section 3.4, Principal Ideal Domains, Guiding Questions
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Section 3.4, Principal Ideal Domains, Guiding Questions
Section 5.5, Example 5, Using the Maximum Modulus Theorem
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Section 5.5, Example 5, Using the Maximum Modulus Theorem
Section 5.5, Maximum Modulus Theorem
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Section 5.5, Maximum Modulus Theorem
Section 5.5, Morera's Theorem
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Section 5.5, Morera's Theorem
Section 5.5, Fundamental Theorem of Algebra
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Section 5.5, Fundamental Theorem of Algebra
Section 5.5, Liouville's Theorem and Proof
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Section 5.5, Liouville's Theorem and Proof
Section 5.5, Cauchy's Inequality and Infinite Differentiability
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Section 5.5, Cauchy's Inequality and Infinite Differentiability
Section 5.5, Example 4, Using Cauchy's Integral Formula for Derivatives
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Section 5.5, Example 4, Using Cauchy's Integral Formula for Derivatives
Section 5.5, Example 3, Using Cauchy's Integral Formula for Derivatives
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Section 5.5, Example 3, Using Cauchy's Integral Formula for Derivatives
Section 5.5, Cauchy's Integral Formula for Derivatives, Proof Sketch
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Section 5.5, Cauchy's Integral Formula for Derivatives, Proof Sketch
Section 5.5, Example 2, Using Cauchy's Integral Formula
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Section 5.5, Example 2, Using Cauchy's Integral Formula
Section 5.5, Example 1, Using Cauchy's Integral Formula
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Section 5.5, Example 1, Using Cauchy's Integral Formula
Section 5.5, Cauchy Integral Formula, Proof Sketch
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Section 5.5, Cauchy Integral Formula, Proof Sketch
Section 3.3, Quotient Rings, Cosets and Integral Example
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Section 3.3, Quotient Rings, Cosets and Integral Example
Section 5.4, Example 5, Using an Antiderivative of z^{-1/2} in Contour Integrals
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Section 5.4, Example 5, Using an Antiderivative of z^{-1/2} in Contour Integrals
Section 5.4, Example 4, Using the Logarithmic Function in Contour Integrals
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Section 5.4, Example 4, Using the Logarithmic Function in Contour Integrals
Section 5.4, Analytic and Simply Connected Domain Implies Antiderivative
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Section 5.4, Analytic and Simply Connected Domain Implies Antiderivative