Penn State
Fall 2013
Algebra A (MATH 535)
Lectures: M W F 10:10AM –
11:00AM, 112 Sackett
Arriving late to class, leaving
class early, or disrupting class in any way will not be tolerated.
Cellphones must be silenced during lectures.
Please, always include “535” in
the subject of your email messages. You can expect to get an answer by the
end of the next business day.
Office hours: By appointment only, 325 McAllister Building.
We will NOT use ANGEL for this
course. However, I might send you mass email messages through ANGEL.
Textbooks: (suggestions)
Kenneth M. Hoffman and Ray Kunze,
Linear Algebra (Second Edition), Pearson 1971
(The suggested retail price is outrageous: $170
for a four-decade-old book.)
Anthony W. Knapp, Basic Algebra, Birkhäuser 2006
(available
in PDF from the University Libraries)
Peter Petersen, Linear Algebra, Springer 2012
(available
in PDF from the University Libraries)
Contents: Linear Algebra
Vector spaces: Fields. Vector
spaces. Subspaces. Spanning sets. Linearly independent sets. Bases.
Dimension.
Linear transformations: Kernel and image. Matrices. Direct sums and
quotients. Correspondence between linear transformations and matrices.
Matrix operations. Standard homomorphism theorems. Rank-nullity theorem.
Inner products and quadratic
forms: Bilinear functions. Sesquilinear functions. Orthogonal sets and
orthonormal sets. Norms. Schwarz’ inequality and Bessel’s inequality.
Adjoints. Self-adjoint, normal and unitary matrices. Orthogonal
projections and orthogonal complements. The Gram-Schmidt orthogonalization
process. Parseval’s inequality. Diagonalizability of normal operators.
Quadratic forms over the real numbers. Signature. Sylvester’s law.
Positive (semi)definiteness. The spectral theorem.
Theory of endomorphisms of a
finite-dimensional vector space: Determinants. Cramer’s rule.
Multiplicative property of the determinant. Minimal and characteristic
polynomial. Cayley-Hamilton theorem. Modules over a principal ideal
domain. Primary decomposition. Application to finitely generated abelian
groups. If F is a field, F[x] is a principal ideal domain. Rational and
Jordan canonical forms.
Evaluation: Weekly homework
and a final exam.
All
electronic devices must be turned off and stowed away during
examinations. Unauthorized use of any electronic device will result in a
zero score on the examination, no exceptions.
Homework and final exam will each
be worth half of your course grade. Grade
scale: A ≥ 90% > B ≥ 80% > C ≥ 70% > D ≥ 60 % > F. Plus or
minus grades will be given at the instructor's discretion.
Attention
math graduate students: The MATH 535 final exam and the ALGEBRA A
qualifying exam are two distinct examinations.
The final examination will be given during the week from December
16 to December 20, 2013. The final examination may be scheduled on any day
during the final examination period. Do not plan to leave University Park
until after Friday, December 20, 2013. Students who miss or cannot take
the final examination due to a valid and documented reason, such as
illness, may be allowed to take a makeup final examination. Personal
business, such as travel, employment, weddings, graduations, or attendance
at public events such as concerts, sporting events are not valid excuses.
Forgetting the date, time or room of an examination is not a valid excuse.
Students who have taken the original final examination are not permitted
to take a makeup examination.
Academic integrity is the pursuit of scholarly activity in an open, honest
and responsible manner. Academic integrity is a basic guiding principle
for all academic activity at The Pennsylvania State University, and all
members of the University community are expected to act in accordance with
this principle. Consistent with this expectation, the University's Code of
Conduct states that all students should act with personal integrity,
respect other students' dignity, rights and property, and help create and
maintain an environment in which all can succeed through the fruits of
their efforts.
Academic integrity includes a commitment by all members of the University
community not to engage in or tolerate acts of falsification,
misrepresentation or deception. Such acts of dishonesty violate the
fundamental ethical principles of the University community and compromise
the worth of work completed by others.
Academic dishonesty includes, but is not limited to, cheating,
plagiarizing, fabricating of information or citations, facilitating acts
of academic dishonesty by others, having unauthorized possession of
examinations, submitting work of another person or work previously used
without informing the instructor, or tampering with the academic work of
other students. For any material or ideas obtained from other sources,
such as the text or things you see on the web, in the library, etc., a
source reference must be given. Direct quotes from any source must be
identified as such.
Each student in this course is expected to work entirely on her/his own
while taking any exam, to complete assignments on her/his own effort
without the assistance of others unless directed otherwise by the
instructor, and to abide by University and Eberly College of Science
policies about academic integrity and academic dishonesty. Academic
dishonesty can result in assignment of "F" by the course instructors or
"XF" by Judicial Affairs as the final grade for the student.
All Penn State Policies regarding ethics and honorable behavior apply to
this course.
Penn State welcomes students
with disabilities into the University's educational programs.
If you have a disability-related
need for reasonable academic adjustments in this course, contact the
Office for Disability Services (ODS) at 814-863-1807 (V/TTY).
For
further information regarding ODS, please visit the Office for Disability
Services Web site at http://equity.psu.edu/ods/.
In order to receive consideration for course accommodations, you must
contact ODS and provide documentation (see the documentation guidelines
at http://equity.psu.edu/ods/guidelines/documentation-guidelines).
If the documentation supports the need for academic adjustments, ODS will
provide a letter identifying appropriate academic adjustments. Please
share this letter and discuss the adjustments with your instructor as
early in the course as possible. You must contact ODS and request academic
adjustment letters at the beginning of each semester.