Math 402 - Spring 2019

Non-Euclidean Geometry

Instructor

Dominic Culver (dculver at illinois dot edu)
230 Illini
Office hours: M 5-6p, W 12-1p, or by appointment.

Time and Place

Sections F13 & F14 at MWF 2:00-2:50pm in 347 ALTGELD HALL

Course info

Historical development of geometry; includes tacit assumptions made by Euclid; the discovery of non-Euclidean geometries; geometry as a mathematical structure; and an axiomatic development of plane geometry.

The syllabus can be found here.

The main text for this class is Hvidsten's Exploring Geometry, which can be obtained here. We will also occasionally use the Hartshorne's Geometry:Euclid and Beyond. This textbook is available through the university's library system here.

Exams

There will be three midterms and a final exam on the material covered in the lectures. Our midterm exams will be held in class. Our final exam will be scheduled by the registrar's office and I will let you know once it is scheduled. If you make travel arrangements before the final exam is scheduled, you should assume that the final will be held on the last day of the final exam period.

Exam 1: February 15
Exam 2: March 15
Exam 3: April 19
Final Exam: TBA

Homework Guidelines

Mathematics (and problem solving in general) is a collaborative discipline. You are strongly encouraged to work in groups and to discuss homework problems with your classmates. However, you must write-up the solution on your own and it must be in your own words. Anything else is plagiarism and will be treated as such.

Your solution needs to be complete and correct (of course!), but to recieve full credit your write-up should also meet the following criteria.

All of the important logical steps in the proof should be present and fully explained.
All assumptions should be clearly identified.
Your write-up should be clear and concise. (I.e., if a sentence or paragraph does not advance the reader's understanding of the solution, it does not belong in the write-up.)
Use full and complete English sentences. Symbols should be used only as a tool to distill a complex mathematical relationship into a readable format.

Schedule

I will put the schedule here as the course progresses. Homework is due at the beginning of class. Late homework will not be accepted under any circumstances, however your lowest homework scores will be dropped. In reverse chronological order: In preparation for the final exam, you should also look at these and these problems. You do not need to turn these problems in.

Date due	Item due
Mon 04/29	Homework due Mon 4/29. Solve these problems and turn them in.
Fri 04/26
Wed 04/24	Reading Hvidsten 7.8
Mon 04/22	Reading. Hvidsten 7.4, Hartshorne 36
Fri 04/20	Exam 3. Will cover chapters 5 and sections 7.1-7.4 of Hvidsten.
Wed 04/17	Reading. Hartshorne Chapter 40, Hvidsten 7.4
Mon 04/15	Reading. Hvidsten Chapter 7.2 and Hartshorne Chapter 34
Fri 04/12	Homework due. Solve these problems and turn them in.
Fri 04/13	Reading. None
Wed 04/10	Reading. Hvidsten Chapter 7.3 and Hartshorne Chapter 34
Mon 04/08	Reading. Hvidsten Chapter 7.3 and Hartshorne Chapter 34
Fri 04/05	Homework due. Solve these problems and turn them in this Friday.
Wed 04/03	Reading. 7.1, 7.2 and Chapter 33 of Hartshorne
Mon 04/01	Reading. Chapter 5.6, 5.7
Fri 03/29	Homework due. Solve these problems and turn them in this Friday.
Wed 03/27	Reading. 5.6, 5.7
Mon 03/25	Reading. Chapter 5.4
Fri 3/15	Exam 2
Wed 3/13	Reading. Chapter 5.2, 5.3
Mon 3/11	Reading. Chapter 5.1, 5.2
Mon 3/11
Fri 3/09	No homework. Exam next Friday
Fri 3/09	Reading. Chapter 5.2 cont
Wed 3/06	Reading. Chapter 5.2
Mon 3/04	Reading. Chapter 5.1
Fri 3/01	Homework due. Solve these problems and turn them in next Friday.
Wed 2/27	Reading. Chapters 3.1, 3.2
Mon 2/25	Reading. Chapter 2.7, 3.1
Fri 2/22	Homework due. Solve these problems and turn them in next Friday.
Fri 2/22	Reading. Chapter 2.7
Wed 2/20	Reading. Chapters 2.6,
Mon 2/18	Reading. Chapter 4.1, 2.5
Fri 02/16	Homework due. Solve these problems and turn them in next Friday.
Fri 02/16	Exam 1
Wed 02/15	Reading. Chapter 2.5
Mon 02/11	Reading. none
Mon 02/05	Reading. Chapters 2.1, 2.2
Fri 02/02	Homework due. Solve these problems and turn them in next friday.
Fri 02/02	Reading Chapters 2.1, 2.2, Appendix D
Wed 01/31	Reading. Chapters 2.1, start 2.2
Mon 01/28	Reading Chapter 2.1, Appendix D. Read the first ten propositions in Euclid's Elements Book 1.
Fri 01/26	Reading. Chapter 1.6
Fri 01/26	Homework (due Feb 1). Solve these problems and turn them in.
Wed 01/24	Reading. Chapter 1.4, 1.5
Mon 01/21	No class.
Fri 01/18	Reading. Chapter 1.4.
Wed 01/16	Reading. Chapters 1.1, 1.2.

Worksheets

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