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Estimated Schedule for Math 360 Spring 2004 last update: Sunday, 2 May 2004 at 03:44 PM EDT |
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| 1/26 | Administrivia and Introduction. Axiomatic Systems (axiomatic systems; snow day; finite geometries). | Chapter 1 | Unless otherwise stated, homeworks are due the Wednesday
of the following week. Sections and problem numbers refer to the
third edition of the text, corresponding problem in the second edition
will be in square brackets following.
1.1: 1, 5, 10;
1.2: 5, 6, 7, 8, 9;
1.3: 5, 7, 8, 16[15], 27[23],
30[see here];
Solutions. |
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| 2/2 | Axiomatic Systems continued: (more finite geometries, incidence geometries). Axioms for Geometry (Euclid, Hilbert, Birkhoff). | Chapter 2 |
1.4: 3, 4, 7;
2.2: 2, 13;
2.4: 5, 6, 14;
2.5: 1;
2.6: 3, 4;
Due date extended until friday, 2/13. No late homeworks. Solutions. |
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| 2/9 | The
SMSG
axioms for (Euclidean) geometry. Neutral Geometry ( preliminaries, congruence conditions) |
Chapter 3, sect 1-3 |
3.2: 1(parts i,iv,vi,viii,x) [1(parts a,d,f,h,j)], 8, 12, 13;
3.3: 1, 7; (Note that part of this assignment moved to next week) Solutions. |
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| 2/16 | Neutral Geometry continued: (finish congruences, parallels in neutral geometry, the Saccheri-Legendre Thm) | Finish Chapter 3 | 3.4: 2, 3, 11;
3.5: 1, 2;
3.6: 2, 3, 7;
Solutions. |
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| 2/23 | finish Neutral Geometry (Saccheri-Legendre continued, rectangles).
Euclidean Geometry some implications of the parallel postulate. |
Sections 4.1, 4.2 | 3.6: 12, 24;
4.2: 1, 12[11], 14[13], 23[22];
Solutions. |
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| 3/1 | Euclidean Geometry: Median Concurrence Thm, Area, Similarity, Pythagorean Theorem. | 4.3, 4.4 | 4.3: 4, 13, 17, 22;
4.4: 7, 13, 15, 22;
Solutions. |
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| 3/8 | Euclidean Geometry: Circles and arcs, Triangles and various special points related to them (the centroid, circumcenter, orthocenter, incenter, and excenters). | 4.5, 4.6 | 4.5: 26, 38, 39;
4.6: 11, 14;
Solutions. |
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| 3/15 | nearly finish Euclidean Geometry: The Euler line and the Nine-Point Circle; Theorems of Ceva and Menelaus; Review; midterm exam. | (nearly) finish chapter 4 | midterm on 3/19 on Chapters 1-4 For your reading pleasure, here is the midterm. |
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| 3/22 | Euclidean Constructions; start Hyperbolic Geometry: the angle of parallelism, parallels and hyperparallels in hyperbolic geometry. | Chapter 6 | optional extra credit:
correct your exam (due 4/2/04). Euclidean constructions: midpoint of a segment, and tangent to a circle, and a regular octagon. (due 4/2/04) 6.3: 7, 20. (due 3/31). Solutions. |
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| 3/29 | Hyperbolic Geometry: A triangle which cannot be circumscribed, models for Hyperbolic geometry, the defect of a hyperbolic triangle or polygon. | Chapter 6 | Nahh... it is time to relax for a while. | ||
| 4/5 |
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| 4/12 | No class on monday, 4/12 Hyperbolic geometry: area and defect; length. | Chapter 6 | oops. | ||
| 4/19 | Elliptic geometry double elliptic (spherical) and single
elliptic. Begin knot theory. |
finish chapter 6. | 6.4: 5, 7, 16;
6.5: 11, 13;
6.6: 12;
6.8: 4.
(due wednesday, 4/28) Solutions. Hyperbolic constructions: equilateral triangle, inscribed regular quadrilateral, and a circumscribed regular quadrilateral. |
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| 4/26 | Knot Theory: examples, crossing number, linking number, unknotting number, Reidemeister moves, introduce Lake&Island polynomial. | These notes and this applet. | In the knot theory notes: p.7: 4, 5, 8, 9; p.15: 1 (use the applet), 2, 3, 6, 7. | ||
| 5/3 | Knot Theory | ||||
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