Geometry for Computer Applications
Math/AMSC 431 Fall 2016
This course explores the use of geometry (including projective geometry)
for applications in graphics, vision and robotics.
Official Course Number:
AMSC/MATH 431 (Section 0101) (3 credits)
2:00 -- 3:15, 0104 Kirwan Hall
3106 Math Building
Course Assistant: Summer Lu
Prerequisites: MATH240 or MATH461 (Linear Algebra)
Examinations and grading:
There will be one midterms and one final exam.
The final grade will include the homeworks, the two exams, and class participation.
- Course notes .
- Course advertisement.
- First handout:
with first problem set, due Tuesday, 13 September 2016.
- Second Problem Set,
due Tuesday, 27 September 2016.
- Third Problem Set,
due Thursday, 20 October 2016.
- Fourth Problem Set,
due Tuesday, 22 November 2016.
- Fifth Problem Set,
due Thursday, 8 December 2016.
- Midterm Exam,
(with solutions), Thursday, 27 October 2016.
- The Final Exam is in the regularly scheduled time, 10:30-12:30, Saturday 17 December
in Room 0104 Kirwan Building.
There will be no required text for the course,
but Vince's recommended book is a general-purpose
reference. The last sections of Lay's book give a good
exposition of some of the basic linear algebra we discuss
at the beginning. Please let me know if you know of some
other useful books on the subject. (The literature is vast.)
Materials will be distributed and posted as they are written.
- Mathematics for Computer Graphics, Fourth Edition,
by John Vince,
Springer Undergraduate Topics in Computer Science,
- Linear Algebra and its applications, Fourth edition,
by David C. Lay, Addison Wesley, ISBN 13:978-0-321-38517-8
(1994, 1997, 2006, 2012)
- Practical Linear Algebra: A Geometry Toolbox,
by Gerald Farin and Dianne Hansford,
CRC Press, ISBN 978-1-4665-7956-9 (2014)
- Applied Geometry for Computer Graphics and CAD,
Second Edition, by Duncan Marsh, Springer Undergraduate Mathematics Series,
ISBN 2-85433-801-6 (1999,2005)
Nigel Hitchin's course notes,
available from his website.
- Projective geometry, both real and complex
- Conic sections and quadric surfaces
- How topology makes data types complicated
- Geometric transformations
- One-parameter groups and matrix exponentials
- Complex numbers and quaternions
- Representing lines in 3-space by Plucker coordinates
There will be no makeups for quizzes or midterms. If illness,
a death in the family, car trouble or a faulty alarm clock cause you
to miss a midterm -- that is the midterm or section quiz you will
drop. So do not decide an earlier midterm or quiz is going to be your
bad score -- if you miss a later one, then that is going to be your
bad score. When you have compelling reasons for missing an exam, share
them with me or your TA.
**If you know BEFORE an exam that you have a conflict, contact Dr. Goldman
and the Course Assistant in advance.
In this case, it is sometimes possible to arrange an early exam.**
Late homework will not be accepted. Here are two reasons:
we want to use resources well (it is much more time consuming to grade
homework when it is late), and you will learn better if you do the
work on time. If you have any questions about policy, please consult
the Course Assistant.
In case of an emergency that closes the University
for an extended period of time (for example, due to inclement
weather), be sure to access your email for instructions from me. Also
check the University's home page.
You are expected to come to class, do the homework, and most important of all
be actively engaged in trying to understand. Two tips for success: Don't fall behind. Make
friends. Help each other (especially after trying alone first).
Attendance is extremely important, since much of the material is not covered in the books.
If your religion dictates that you cannot take
an exam or hand in assigned work on a particular date, then contact me
at the beginning of the semester to discuss alternatives. You are
responsible for making these arrangements at the beginning of the
On each paper, students must
write by hand and sign the following pledge:
``I pledge on my honor that I have not given or received any unauthorized assistance on this examination (or assignment).''
If you have some disability related to testing under the
usual timed, in-class conditions, you may contact the office of
Disabled Students Services (DSS) in Shoemaker. If they assess you as
meriting private conditions and/or extra time, then you may arrange to
take your tests at DSS, with extra time as they indicate. You must
arrange this well in advance of a test (in particular: no
retakes). Click to Disability Support Services for further
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19 November 2015