Math 6080 Summer 2018

The course syllabus is available here.

Worksheets

  • Platonic Solids July 17
  • Groups, Symmetry Groups July 18
  • More group theory, cosets July 19
  • Stereographic projection July 20
  • Modular arithmetic: Bezout's lemma, Chinese remainder theorem, Fermat's little theorem July 25
  • Pascal's triangle and roots of unity July 26
  • Conic sections, intersections July 27
  • Intersection multiplicity, projective space July 30, July 31
  • Transylvanian lottery, Fano plane August 1
  • Continued fractions, Farey diagram August 2

    • Lesson Plans

  • Thinking in higher and lower dimensions, Shae and Dave: Lesson Plan outline, Worksheet
  • Projective Space over finite fields and the game Spot It, Merilee and John: Presentation, Worksheet
  • Modular arithmetic, the Euclidean algorithm and Billiards problems, Emre: Problems on Euclidean algorithm, gcd, moodular arithmetic, Problems on modular arithmetic and billiards
  • Isometries and Rigid Transformations, Charlotte and Becca: Worksheet on Euclidean Transformations, Worksheet on Symmetries of a Square, Worksheet on building a hypercube
  • Modular arithmetic and time, ISBN and UPC codes, Jennifer and Brooke: Worksheet, Slide presentation
  • Sine, cosine and Lissajous curves, Merry: Worksheet
  • Modular arithmetic and shift cyphers with Python, Jessica and Heather: Screenshot of code