Senior and Graduate Math Course Offerings 2008 Summer
Undergraduate courses
Math 4377 - Section: 19884 - Advanced Linear Algebra (6/2/2008 - 7/3/2008)
MATH 4377: Advanced Linear Algebra (section# 19884 )
Time:
MoTuWeTh 12:00PM - 2:00PM - Room SR 140 - 6/2/2008 to 7/3/2008
Instructor:
David Blecher
Prerequisites:
Consent of instructor
Text(s):
If you are taking the second semester too (which I am not teaching), get "Linear Algebra", 2nd Edition, by K. Hoffman and R. Kunze(Publisher: Pearson/Prentice-Hall).
However my lectures will be based largely "Linear Algebra done right", 2nd Edition, by S. Axler (Springer), and this book is inexpensive.
Description:
This class falls in the category of those math courses focussing on
theorems and proof, requiring a lot of abstract logical reasoning. However amongst such classes, this is one of the easiest: the proofs and concepts are not difficult. This material is foundational for most branches of mathematics, and for related sciences and engineering.
Syllabus: Systems of linear equations and matrices,
Vector spaces, linear independence,
subspaces, direct sums, finite-dimensional spaces and
bases and dimension. Linear operators and their matrices,
null spaces and ranges, invertibility. Eigenvalues and Eigenvectors,
polynomials with real and complex coefficients,
polynomials of operators, diagonal and triangular matrices.
Inner-product spaces, orthonormal bases, orthogonal projections,
adjoints. Selfadjoint and normal operators, the spectral theorem,
positive operators, the polar decomposition, square roots,
generalized eigenvectors, the characteristic polynomial,
Jordan form. Trace, determinant, change of basis, volume.
Math 4378 - Section: 19886 - Advanced Linear Algebra (7/7/2008 - 8/14/2008 )
MATH 4378: Advanced Linear Algebra (section# 19886)
Math 5331 - Section: 26845 - Linear Algebra W/ Applications (6/2/2008 - 7/3/2008 )
MATH 5331: Linear Algebra W/ Applications (section# 26845 )
Time:
On line course (6/2/2008 to 7/3/2008)
Instructor:
Garret Etgen
Prerequisites:
Three semesters of calculus or consent of instructor
Text(s):
Description:
Systems of linear equations, matrices, vector spaces, linear independence and linear dependence, determinants, eigenvalues; applications of linear algebra.
Math 5333 - Section: 19920 - Analysis (6/2/2008 - 7/3/2008)
MATH 5333: Analysis (section# 19920 )
Time:
On line course (6/2/2008 to 7/3/2008)
Instructor:
M. Ru
Prerequisites:
Consent of instructor
Text(s):
Analysis by Steven R. Lay, 4th ed.
Description:
On-line course through webct.
This is the rigorous theorem/proof-type course in analysis.
The goal of the
course is to teach students mathematical reasoning and the construction of
proofs in the environment of real numbers.
Topics covered include the topology of the Reals, convergence and
limits, and
the proofs of well-known calculus theorems such as the Mean
Value Theorem, the Intermediate Value Theorem, the Inverse
Function Theorem, and the Fundamental Theorem of Calculus.
Discrete Mathematics and Its Applications, Kenneth H. Rosen, sixth
edition, McGraw Hill, ISBN-13 978-0-07-288008-3, ISBN-10 0-07-288008-2.
Plus: My own Notes on the Zermelo-Fraenkel Axioms and Equivalence of Sets.
Description:
Chapter 1, Chapter 2 (2.1-2.3), Chapter 4 (4.1-4.3), Chapter 8
The Zermelo Fraenkel Axioms; Equivalence of Sets in form of my notes.
More information is available through my website:
http://math.uh.edu/~klaus
Graduate Courses
Math 6395 - Section: 25206 - Linear Algebra in Engineering and Science ( 6/3/2011 - 8/14/2008 )
MATH 6395 Linear algebra in engineering and science (section# 25206)
Basic knowledge of vector spaces, linear transformations and matrices. Most of the theory shall be developed in the class.
Text(s):
Linear Algebra: Peter J. Olver and Cheri Shakiban. Prentice Hall 2005
Description:
This course shall teach methods and algorithms that are derived from first
principles for problems in the real world. Besides a quick introduction to
basic linear algebra the course shall describe applications side by side
with the development of the theory. Topics shall be chosen from: Inner
product spaces * *with applications of the concepts of minimization and
least squares and orthogonality. Linear systems. Eigenvalues with
applications to linear dynamical systems governed by ordinary differential
equations and iterative systems, such as Markov chains and numerical
solution algorithms. Aspects of numerical linear algebra. Discrete Fourier
Series and the Fast Fourier Transform. Compression and Noise Removal
Boundary value problems in one dimension. Time permitting other topics may
be added.
Math 6397 - Section: 25190 - Logic with Applications ( 6/2/2008 - 7/3/2008 )
MATH 6397 Logic with applications (section# 25190)
This course is a study of a method of analyzing time dependent data with the intent to
make predictions based upon the analyzes. There is neither a text nor reference book,
nor are any such allowed. The definitions and problems will be provided as needed. The
style of the class is Socratic, in that the students are expected to provide answers to
questions and problems raised and present their solutions to the class. If time permits
the problem of predicting solar activity, using monthly mean sunspot numbers, will be
addressed.
