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)
Time: MoTuWeTh 12:00PM - 2:00PM - Room SEC 202 - 7/7/2008 to 8/14/2008
Instructor: Michael Friedberg
Prerequisites: Math 4377 or Consent of instructor
Text(s): Hoffman-Kunze, 'Linear Algebra,' Second Edition, Prentice-Hall.
Description: Canonical forms: eigenvalues, eigenvectors, Cayley-Hamilton Theorem, diagonalization, triangulation, Primary (Cyclic ) Decomposition Theorem, Jordan form. Inner product spaces: inner products, orthonormal systems, projections, normal operators, unitary operators, Spectral Theory.

Online courses

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.

Math 5336 - Section: 26846 - Discrete Mathematics (6/2/2008 - 7/3/2008)
MATH 5336 Discrete Mathematics (section# 26846 )
Time: On line course (6/2/2008 to 7/3/2008)
Instructor: Klaus Kaiser
Prerequisites: Consent of instructor
Text(s): 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)
Time: MoTuWeTh 1:00PM - 2:00PM - Room AH 301 - 6/3/2011 to 8/14/2008
Instructor: Dinesh Singh
Prerequisites: 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)
Time: MoTuWeTh 12:00PM - 2:00PM - Room PGH 350 - 6/2/2008 to 7/3/2008
Instructor: Klaus Kaiser
Prerequisites: Graduate standing.
Text(s):

Logic for Applications by Anil Nerode and Richard A. Shore, Second Edition, Graduate Texts in Computer Science, Springer Verlag. (ISBN 0-387-94893-7)
Description:

Propositional Logic, Predicate Logic (Chapter I, 1-6; Chapter II, 1-8). If time permits: Ultraproducts of Relational Systems.

More information is available through my website:
http://math.uh.edu/~klaus

Math 6397 - Section: 25205 - Time Series Analysis (7/7/2008 - 8/14/2008 )
MATH 6397: Time series analysis (secton#25205) )
Time: MoTuWeTh 10:00AM - 12:00PM - Room SEC 203 - 7/7/2008 to 8/14/2008
Instructor: G. Johnson
Prerequisites:  
Text(s):  
Description: 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.

How to enroll course:

  1. Log in to My UH (People Soft)
  2. Click on "UH Self-Service"
  3. Click on "Enrollment," select "add classes" and choose semester you would like to enroll.
  4. Enter specific section number to add class (example: if you like to add Math 4377, you will enter the section number 19884)
  5. continue add more courses if needed and continue to finish the enrollment process.