MAT 220: Vector Geometry and Algebra
Stony Brook University - Spring 2017
The course covers the following topics:
Vectors and vector algebra. Dot product. Cross product and triple product.
Complex numbers and quaternions and their geometric interpretations.
symmetry, similarity transformations, affine transformations on a plane and
n 3-space. Analytical geometry. Vector equations of lines and planes. Curves
and surfaces of degree two. The basic notions of projective geometry.
No preliminary knowledge of advanced mathematics is required.
Level 4 on the mathematics placement examination, or permission by
Tuesdays and Thursdays 4:00pm - 5:20pm in Physics P112
Ph.D. 1974, Doctor Phys-Mat.Sci. 1983, both from Leningrad State
Arrived at Stony Brook in 2007.
Office: Math Tower 5-110
Phone: (631) 632-8286
Email: oleg.viro AT math.stonybrook.edu
Web page: www.math.stonybrook.edu/~oleg
Research fields: Topology and Geometry,
especially low-dimensional topology
and real algebraic geometry.
Tuesdays and Thursdays 5:40pm - 6:50pm in Math Tower 5-110.
Arrived at Stony Brook in 2004
Office: Math Tower 4-122
Email: jean-francois.arbour AT stonybrook.edu
Homework sets will be typically assigned weekly and due on Thursdays in
class. They will be posted on the blackboard site. Late homework will not
be accepted. However, grades for homework assignments may be dropped in
cases of documented medical problems or similar difficulties.
There will be two in-class midterms; the first midterm will be on Th, 3/9. The date of the second midterm will be announced later.
Final Exam: Monday, May 15, 2:15pm-5:00pm
Grades will be based on the following scheme: Homework -- 10%; Quizes --
10%, Midterms -- 20% each; Final Exam 40%.
The basic arithmetic of complex numbers: addition,
subtraction, multiplication, conjugation, division, moduli, absolute value and
argument, trigonometric form of a complex number. Geometry of
Quaternions. Quaternion units, scalars and vectors,
multiplication, conjugation, division, absolute value, unit quaternions.
Vectors and vector operations. The basic operations with vectors.
Linear dependence. Bases and dimension. Arithmetic vector spaces $\mathbb
R^n$. Applications to geometric problems.
Multiplications: dot and cross products. Algebraic properties and
geometry of them, distance and dot product, projections to lines and
planes, volume and triple product.
Analytic geometry of lines and planes. Line on a plane, their
vector and coordinate equations. Various types of equations. Formulas for distances.
Transformations: isometries. Types of isometries of plane and
3-space. Their classification. Applications to geometric problems.
Similarity transformations. Classification. Relation to complex
Affine transformations. Affine invariants. Center of masses.
Polyhedra and their plane sections.
Conic sections. Ellipse, parabola, hyperbola. Equations, focal
and directorial properties.
Quadratic surfaces. Cylinders, cones, ellipsoids, paraboloids,
Projective lines. Double ratio.
Projective geometry. Duality.
If you have a physical, psychological, medical, or learning disability that
may impact your course work, please contact Disability Support
or call (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.
Students who require assistance during emergency evacuation are encouraged
to discuss their needs with their professors and Disability Support
Services. For procedures and information go to the Evacuation
Guide for People with Physical Disabilities.
Each student must pursue his or her academic goals honestly and be
personally accountable for all submitted work. Representing another
person's work as your own is always wrong. Faculty are required to report
any suspected instances of academic dishonesty to the Academic Judiciary.
For more comprehensive information on academic integrity, including
categories of academic dishonesty, please refer to the academic judiciary
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.