Topic: The Fundamental Group of the Circle and Applications

Worked Winding Numbers for Piecewise Loops

Trigonometric Circle Maps: A Degree-Calculation Workshop

The No-Retraction Theorem for the Disk

The Fundamental Theorem of Algebra by Degree

The Antipodal Difference Map for Borsuk-Ulam

Odd Circle Maps Have Odd Degree

Lift Endpoints and Winding Numbers of Loops

Homotopy Invariance of Winding Number

Homotoping a Polynomial to Its Leading Monomial

Extension over the Disk Forces Zero Degree