bCourses Site

DSP students should speak to the instructor as soon as possible, even if you don't have a letter yet.

Guidelines on what to do if you think you may have a conflict between this class and your extracurricular activities. In particular, you must speak to the instructor before the end of the second week of classes.

Academic honesty in mathematics courses: A statement on cheating and plagiarism, courtesy of Michael Hutchings.

How to get an A in this class, courtesy of Kathryn Mann.

January 22:intro, Euclid's postulates Reading: Stillwell 1.1 Handout: Euclid's Elements for the adventurous, here's a Greek versionJanuary 24:Euclid's constructions; Thales' theorem Reading: Stillwell 1.1–1.3 / Hartshorne 1–2 Random: story about Thales by Plutarch (starts at VI, goes onto page 419) Activity:Euclid: the gameActivity: Play with GeogebraJanuary 29:arithmetic with Euclidean constructions Reading: Stillwell 1.3–1.4 Review for Thursday: fields (16.1—2) Worksheet 1: click here * Homework 1: click hereJanuary 31:square roots; parallel postulate Reading: Stillwell 1.5–2.2 Reading: Critique of superposition, Hartshorne pp 31–34February 5:area; Thales' theorem Reading: Stillwell 2.3–6 / Hartshorne 22 * Homework 2: click hereFebruary 7:equidecomposability Some resources: Hartshorne 22, Wikipedia, interactive demonstrations For fun: Hinged dissectionsFebruary 12:constructibility Reading: field extensions Reading: Constructible n-gons and field extensions (fromConjecture and Proofby M. Laczkovich) Reading: Hartshorne 28–29 Video: Construction of 17-gon (other videos: 1 and 2)February 14:more constructibility; impossible constructions Reading: see February 12 * Homework 3: click hereFebruary 19:constructibility of regular polygons; Gauss–Wantzel theorem Reading: Regular polygons (fromGalois Theoryby Ian Stewart)February 21:Hilbert's axioms: incidence and betweenness Reading: Hartshorne 6–7 Notes on the real projective plane: click here * Homework 4: click hereFebruary 26:betweenness: plane/line separation; rays, angles, triangles Worksheet 2: click here Reading: Hartshorne 7February 28:intro to project; more betweenness: crossbar theorem, "in between point" Reading: Hartshorne 7March 5: Midterm (in class) Material: everything up to and including betweenness (Feb 26 class), all homework questions plane/line separation, angles, but no triangles, no crossbar theorem, no "in between point" You will be given a list of Hilbert's axioms You do not need to cite Euclid's axioms by number (you can assume unique lines); any construction will be "from the axioms" unless stated I will not ask you to reprove anything we did in class, but you might need to give definitionsMarch 7:congruence axioms Reading: Hartshorne 8–9 * Homework 5: click hereMarch 12:finishing Hilbert's axioms; starting projective geometry Reading: Hartshorne 10, Stillwell 5.1–5.3 Reading: How to Win the Lottery with Projective Geometry (fromHow Not To Be Wrong, by Jordan Ellenberg)March 14:projective geometry Reading: Stillwell 5.1–5.5 * Homework 6: click hereMarch 19:fractional linear transformations; invariants Reading: Stillwell 5.5–5.9March 21:cross-ratio; other projective planes Reading: Stillwell 5.7–5.9April 2:projective Pappus, Desargues; planar ternary rings Reading: Stillwell 6 Worksheet 3: click here * Homework 7: click hereApril 4:geometry via transformation groups Reading: Stillwell 7.1–7.3April 9:Möbius transformations; hyperbolic lines; angles Reading: Stillwell 8.1–8.5 * Homework 8: click hereApril 10:angles; disc model; hyperbolic distance Reading: Stillwell 8.6–8.7April 16:area on sphere and hyperbolic plane Reading: Stillwell 8.5April 18:practice presentationsApril 23, 35, 30, May 2:presentationsMay 16:Final exam (in class, 8:10am–11am) Details on bCourses announcement

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