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)
Grade Method: REG/P-F/AUD.
Lectures: Tuesday-Thursday 2:00 -- 3:15, 0104 Kirwan Hall

Professor: Bill Goldman (
Office: 3106 Math Building
Phone: 301-405-5124
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 materials:

Recommended references:
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, ISBN 978-1-4471-6289-6
  • 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, ``Projective Geometry," available from his website.

Course highlights:
  • 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

Administrative Policies:
  • Makeups: 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.**
  • Deadlines: 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.
  • Emergency closures: 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.
  • Expectations/philosophy: 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.
  • Religious observances: 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 semester.
  • Academic Integrity: 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).''
  • Disabilities: 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 information.
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Last modified: 19 November 2015