Deck transformations are important because we want to study the fundamental group of the base space (X) by looking atContinue reading “Deck Transformations”
Category Archives: Lectures
Intractable Integrals (AMATH 112)
Introduction to Julia Programming (MATH 173)
Course Textbook: https://services.publishing.umich.edu/wp-content/themes/mpub-services/library/pdf/PDSdownload102.pdf Prerequisites: Calculus 1-3, Linear Algebra, Mathematical Foundations
Koch Curve, Fractal Geometry, and Measures (MATH 334)
I ended up back here coincidentally, and I think my intuition about this was on the right track. I justContinue reading “Koch Curve, Fractal Geometry, and Measures (MATH 334)”
Introduction to Algebraic Cycles (MATH 568)
Required Reading: Chapter 1 of Hartshorne, Algebraic Geometry Grothendieck, A. (1969), “Standard Conjectures on Algebraic Cycles”, Algebraic Geometry (Internat. Colloq., Tata Inst.Continue reading “Introduction to Algebraic Cycles (MATH 568)”
Polar Coordinates and Coxeter Groups (MATH 127)
Course Textbook: Reflection Groups and Coxeter Groups, James E. Humphreys,Preparing for this Section (Review)Rectangular CoordinatesDefinition of the Trigonometric FunctionsThe Distance FormulaInverseContinue reading “Polar Coordinates and Coxeter Groups (MATH 127)”
Persistent Homology (MATH 528)
Required Reading (Lectures): https://mrzv.org/ Course Website: http://graphics.stanford.edu/courses/cs468-09-fall/ Persistent homology is a method for computing topological features of a space at differentContinue reading “Persistent Homology (MATH 528)”
An Automorphism of de Moivre’s Theorem (Math 347)
Introduction to de Moivre’s Theorem: https://brilliant.org/wiki/de-moivres-theorem/ Practice Problem: Books: PreCalculus text, Dummit and Foote Preliminary Reading: https://www.wikiwand.com/en/Abraham_de_Moivre Abraham de Moivre (FrenchContinue reading “An Automorphism of de Moivre’s Theorem (Math 347)”
Newton’s minimal resistance problem (Phys 540)
Newton’s Minimal Resistance Problem is a problem of finding a solid of revolution which experiences a minimum resistance when it moves through aContinue reading “Newton’s minimal resistance problem (Phys 540)”
Hilbert’s twenty-third problem (Math 540)
Hilbert’s twenty-third problem is the last of Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. In contrast withContinue reading “Hilbert’s twenty-third problem (Math 540)”