Math 461

Geometry I

Fall 2013

** 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 math.umass.edu

**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.

**Grading:**

homework and participation - 30%

2 quizzes - 10% each

1 midterm - 20%

Final Exam - 30%

A |
≥ 93% |

A- |
≥ 90% and < 93% |

B+ |
≥ 86% and < 90% |

B |
≥ 82% and < 86% |

B- |
≥ 78% and < 82% |

C+ |
≥74% and < 78% |

C |
≥ 70% and < 74% |

C- |
≥65% and < 70% |

D |
≥ 60% and < 65% |

F |
< 60% |