University of Massachusetts, Amherst
Math 461

Geometry I
Fall 2013

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Course News:
Monitor this space weekly for important course news, such as:

The First Quiz will be administered on Friday September 20, in class. Please arrive on time!

The October 24th midterm will take place 7-9 pm in LGRT 141.

Meeting times: MWF 10:10-11:00, in LGRT 204.

Instructor: Professor Farshid Hajir
Office: Lederle 1623C
Phone: 545-6025
Email: hajir atsymbol

Office Hours: Office hours are Tue 10-11, W 8:30-9:30, and W 11-12. You are always welcome to set up an appointment by sending me an e-mail or calling me on the phone.

Prerequisites: Linear Algebra (MATH 235), and Math 300 or COMPSCI 250. For students who have not taken Math 300 or COMPSCI 250, the instructor may permit students with sufficient experience in reading and writing mathematical arguments to enroll.

Course Description: This is a course on Affine and Projective Geometry, with an emphasis on the Axiomatic Approach introduced by Euclid and further developed by Hilbert. We will touch on several other approaches as well: constructions with straight-edge and compass, analytic geometry via linear algebra, and Klein's approach using symmetries and transformations, projective and spherical geometry, etc. This will open the doors to many non-Euclidean flavors of geometry to be further explored in MATH 462. We will examine how these approaches relate to teaching mathematics in grades K-12 by examining the geometry strands in the Common Core State Standards for Mathematics.

Required Text: Axiomatic Geometry, by John M. Lee, American Mathematical Society, Edition: 1, Year Published: 2013, Price: 75.00 USD, ISBN 9780821884782.

Optional Additional Resources:
1. Exploring Advanced Euclidean Geometry with GeoGebra by Gerard A. Venema, Mathematical Association of America, 2013, ISBN 978-0-88385-784-7 and Electronic Edition ISBN 978-1-61444-111-3. 47.50 USD.
2. Euclid's Elements translated by Heath.

Moodle Bulletin Board: A virtual M461 discussion may be set up via the Campus Moodle resource if there is student demand for it. Stay tuned for details. Please use this service responsibly. (Assuming I actually set it up, I will monitor it semi-regularly, but if you want to direct a question specifically at me, the best way to reach me is during office hours or by e-mail.

Homework: Homework will be posted on The Homework Page and collected every Monday at the beginning of lecture. Late homework will not be accepted and the lowest homework grade will be dropped. Be sure to read and follow the homework rules.

Attendance: Attendance is required during lectures. I consider attendance AND participation important ingredients for your success in the course. Frequent absences will be reflected in your grade.

Quizzes: There will be two in-class quizzes. Each of these will count as 10% of your grade. There will be no make-up quizzes for unexcused absences, see policy below about make-up quizzes and exams..

Exams: There will be one midterm and one final exam. The midterm will take place on Thursday evening October 24th, 7-9 pm, room TBA.. The final exam date and time are TBA - please do not make travel arrangements for end of term prior to learning about the final exam time.

Make-up Exam Policy: If you have a legitimate (e.g. multiple exams at the same exact time, medical problems, emergency absences, religious observances) scheduling conflict with any of the exams, it is your responsibility to notify me of the conflict as soon as you become aware of it. The final decision regarding allowing a make-up exam is mine, subject to University regulations, of course. Please note that previously arranged travel plans are not a valid reason to be given a make-up exam.

Computers: Geometry is an inherently computational subject (yes!) and we will undoubtedly have some use for machine calculations over the course of the semester, though this will not be a required aspect of th course necessarily. When the time comes, you will probably be able to get away with one exceptionally good program freely available: GeoGebra. You can find out more from the website GeoGebra Home Page.

Extra Credit: Some extra credit problems will occasionally be included in the homework assignments, or given during class.  The number of points for each problem will vary, as will the difficulty of the problem. The student with the most points at the end of the semester wins a fabulous prize. You may hand in Extra Credit solutions at any time throughout the term, until the last class meeting.

   homework and participation - 30%
   2 quizzes - 10% each
   1 midterm - 20%
   Final Exam - 30%

Grading Scale


≥ 93%


≥ 90% and < 93%


≥ 86% and < 90%


≥ 82% and < 86%


≥ 78% and < 82%


≥74% and < 78%


≥ 70% and < 74%


≥65% and < 70%


≥ 60% and < 65%


< 60%

Course topics: We will cover about two-thirds of the book, concentrating on chapters 1-15.