Mathematics 3210

Euclidean and Non-Euclidean Geometry

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Date Topics covered Reading Homework Assignments
Monday January 13
Chapter 1

Wednesday January 15
Euclid's Geometry.
Origins of geometry, the axiomatic method, undefined terms.

Friday January 17
Euclid's first four postulates.

HW1: Due Friday January 24
.pdf, .tex

Monday January 20

Wednesday January 22
The parallel postulate.
Chapter 2
Friday January 24
Introduction to LaTex.
(See the bottom of this webpage)
HW 2: Due Friday January 24
Chapter 1, Exercises: 1, 2, 3, 6, 9, 10, 12
Monday January 27
Misleading diagrams, straight edge and compass constructions.

Wednesday January 29
Introduction to logic.

Friday January 31

Theorems and proofs, proof by contradiction.

HW 3: Due Wednesday February 5
Chapter 1, Exercises: 14, 15.
Chapter 2, Exercises: 1, 2, 3.
.pdf, .tex
Monday February 3

Basic logic, cont.

Wednesday February 5
Incidence geometry.

Friday February 7
HW 4: Due Monday February 10
Chapter 2, Exercises: 4, 7, 8, 10 (a)(b), 11.
Monday February 10
Homework review

Wednesday February 12
Sample Midterm I .pdf
Friday February 14

Monday February 17
Affine planes

Wednesday February 19
Projective planes

Friday February 21
Hilbert's Axioms
Flaws in Euclid.
Chapter 3
HW 5: Due Monday February 24
Chapter 2, Exercise: 14.
Chapter 2, ``Major Exercises'': 1-5.
Monday February 24
Axioms of betweenness.

Wednesday February 26
Axioms of congruence.

Friday February 28
Axioms of continuity.

Monday March 3
Axiom of parallelism.
HW 6: Due Monday March 3
Chapter 3 Exercises on Betweenness: 1-5
Wednesday March 5
Neutral Geometry
Geometry without the parallel axiom.  Alternate interior angle theorem.
Chapter 4

Friday March 7
Exterior angle theorem, measure of angles and segments.

Monday March 10
Sachheri-Legendre theorem.

Wednesday March 12
Equivalence of the parallel postulates.

Friday March 14
Angle sum of a triangle.
HW 7: Due Friday March 14
Chapter 3 Exercises on Congruence: 21-24
Monday March 17
Homework review

Wednesday March 19
Sample Midterm II .pdf
Friday March 21

Week of March 24-March 28
Monday March 31
History of the Parallel Postulate
Proclus, Equidistance, Wallis, Saccheri.
Chapter 5

Wednesday April 2
Clairout's Axiom and Proclus' Theoreom, Legendre, Lambert and Taurinus, F. Bolyai

Friday April 4
Non-Euclidean Geometry
J. Bolyai, Gauss, Lobachevsky
Chapter 6
HW 8: Due Friday April 4
Presentation writing assignment
Monday April 7
Non-Euclidean Hilbert planes, and the defect.

Wednesday April 9
Similar triangles, parallels admitting a common perpendicular.

Friday April 11
Limiting parallel rays, hyperbolic planes.

Monday April 14
Classification of parallels.
HW 9: Due Monday April 14
Chapter 4, Exercises 1, 2, 6, 10, 14
Wednesday April 16
Independence of the Parallel Postulate
Consistency of hyperbolic geometry.

Friday April 18 The Beltrami--Klein model

Monday April 21
The Poincare models.

Wednesday April 23
Models, cont.

Friday April 25
Further topics

HW 10: Due Monday April 28
Chapter 5, Exercises 10, 11, 13
Monday April 28
Further topics

Wednesday April 30
Homework review

Friday May 2

Sample Final .pdf
Monday May 5
FINAL EXAM 8:00-10:00 AM ECCR 151
(Lecture Room)

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I strongly encourage everyone to use LaTex for typing their homework.  If you have a mac, one possible easy way to get started is with texshop.  If you are using linux, there are a number of other possible ways to go, using emacs, ghostview, etc.  If you are using windows, you're on your own, but I'm sure there's something online.  Here is a sample homework file to use: (the .tex file, the .bib file, and the .pdf file).  It is probably easiest to just look at the .tex file, and start to experiment.  There is also the (Not so) short introduction to latex, which will answer most of your questions (although typing your question into your favorite search engine will probably work well, too).  You may also want to try for a cloud version.