Kenneth Hoffman, Ray Kunze: Linear Algebra, Prentice Hall, third Edition.

Chapter 1, Chapter 2, Chapter 3 (3.1-3.4), Chapter 4.

Course Description: The general theory of Vector Spaces and Linear Transformations will be developed in an axiomatic fashion.
There will be a Midterm and a Final. Homework will be assigned regularly and discussed in class.

Grading: Two tests, each worth 30%, and a Final, worth 40%

Required textbook: Kenneth Hoffman, Ray Kunze: Linear Algebra, Prentice Hall, third Edition.

Recommended book: "Linear algebra" by S. Lipschutz from the Schaum's Outline Series, published by McGraw Hill Book Company.

This course is a continuation of MATH 4377 which was taught from the same text.

Topics to be covered include Determinants, Elementary Canonical Forms, and the Rational and Jordan Forms.

During the first two lectures we will overview problems from 4377, to help those students who attended the course before the summer to refresh the basic material.

The main emphasis of the course is to teach the concepts of eigenvalues and eigenvectors and the sparse representation of matrices by means of Canonical Rational and Jordan forms. Students are expected to learn who to derive these new representations of matrices/linear operators. The course becomes more computational and less theoretical compared to MATH 4377.

There will be three exams, all sectional, given every other week with homework given every odd week. The final exam will be the third of the three exams. Roughly, 60% of your grade will be contributed by the aggregate of the exam grades and 40% from the homework. Homework will be customizable to allow for earning bonus points, to help you offset unexpected losses during exams. I recommend the following auxiliary helper book: "Linear algebra" by S. Lipschutz from the Schaum's Outline Series, published by McGraw Hill Book Company. This book contains a synopsis of the theory and a good number of solved and practice problems.

Victor Katz, A History of Mathematics: An Introduction, 3rd (or 2nd Ed.), Addison-Wesley, 2009 (or 1998).

and lecture notes.

This course is designed to provide a college-level experience in history of mathematics. Students will understand some critical historical mathematics events, such as creation of classical Greek mathematics, and development of calculus; recognize notable mathematicians and the impact of their discoveries, such as Fermat, Descartes, Newton and Leibniz, Euler and Gauss; understand the development of certain mathematical topics, such as Pythagoras theorem, the real number theory and calculus.

Aims of the course: To help students
to understand the history of mathematics;
to attain an orientation in the history and philosophy of mathematics;
to gain an appreciation for our ancestor's effort and great contribution;
to gain an appreciation for the current state of mathematics;
to obtain inspiration for mathematical education,
and to obtain inspiration for further development of mathematics.

On-line course is taught through Blackboard Vista, visit http://www.uh.edu/webct/ for information on obtaining ID and password.

The course will be based on my notes. The textbook is used for extra reading, do homework or do project.

In each week, from Monday to Thursday, two chapters of my notes will be posted per day in Blackboard Vista. Daily homework and reading assignment may be posted in Blackboard Vista, including a project.

In each weak, turn all your homework once by Sunday midnight through Blackboard Vista.

There is no exam.

Grading: 30% homework, 70% projects.

Remark: This is a topics course. If you want to apply the credits toward your degree requirement, before enrollment, you need to contact Dr. Charles Peters to make a petition and get an approval.

Required Text:

Recommended reading:

Analysis by Steven R. Lay, 4th ed.

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.

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

Required Text:

Recommended reading:

Course Description:

Course Topics:

Specific Course Requirements:

Project assignments and Grading

Required Text:

Recommended reading:

Victor Katz, A History of Mathematics: An Introduction, 3rd (or 2nd Ed.), Addison-Wesley, 2009 (or 1998).

and lecture notes.

This course is designed to provide a college-level experience in history of mathematics. Students will understand some critical historical mathematics events, such as creation of classical Greek mathematics, and development of calculus; recognize notable mathematicians and the impact of their discoveries, such as Fermat, Descartes, Newton and Leibniz, Euler and Gauss; understand the development of certain mathematical topics, such as Pythagoras theorem, the real number theory and calculus.

Aims of the course: To help students
to understand the history of mathematics;
to attain an orientation in the history and philosophy of mathematics;
to gain an appreciation for our ancestor's effort and great contribution;
to gain an appreciation for the current state of mathematics;
to obtain inspiration for mathematical education,
and to obtain inspiration for further development of mathematics.

On-line course is taught through Blackboard Vista, visit http://www.uh.edu/webct/ for information on obtaining ID and password.

The course will be based on my notes. The textbook is used for extra reading, do homework or do project.

In each week, from Monday to Thursday, two chapters of my notes will be posted per day in Blackboard Vista. Daily homework and reading assignment may be posted in Blackboard Vista, including a project.

In each weak, turn all your homework once by Sunday midnight through Blackboard Vista.

There is no exam.

Grading: 30% homework, 70% projects.

Instructor shall provide classroom notes based on:

• An Introduction to Frames and Riesz Bases, Ole Christensen. Birkhauser Verlag. 2002,
• Frames for Undergraduates, D. Han, K. Kornelsen, D. Larson & E. Weber. American Mathematical Society (Student Library Volume 40). 2008.ed.

This course is designed to introduce graduate students-from mathematics, physics and engineering- to some interesting aspects of Frame Theory with possible applications if time permits.

This will largely be a reading course with plenty of hands on practical
insights. Class participation will lead to award of grades

This course aims in:

1. Prepare students who have attended MATH 6320 and 6321 for their qualifying exam in Real Analysis.
2. Teach proving techniques to students who only had a senior undergraduate course in Mathematical Analysis and help them acquire proving skills. It will also help this group of students to review Analysis by learning some fundamental results and how to use them without having to learn the proofs of these results.

We survey Analysis by solving problems. So, from day one each student prepares for a discussion on the solution of certain problems that can be found in the textbooks used for MATH 6320 and 6321 in the Fall 08 and Spring 09 semesters, or in handouts. We will also work on preliminary exams in our and other departments. There will be no homework that you need to submit for grading. Grades will be assigned based on your active participation in the class. Instead every day before class you will need to review the problems we will discuss in the class and attempt to solve them. During the class we discuss the solution of each problem (hopefully of all of them) and jointly explore ways to solve the problem. Primarily we will be focusing on: Pinning down the objectives that lead to the solution and see how we can achieve those.

Students who have attended graduate Real Analysis will have the opportunity to practice and guide junior students in problem solving. Junior graduate students will have the opportunity to acquire proving skills without the work lead that a regular semester graduate course requires. The latter group of students should view this course as a summer camp on problem solving and some freestyle exploration of analysis. Overall I want you to enjoy the course and the time you spend in the classroom or working for it. I will primarily (but not exclusively) draw problems from D.L. Cohn's "Measure Theory", from G. Folland's "A course in Real Analysis" or from Rudin's classic "Real and Complex Analysis". At the end of each class you will know the problems we will work on the next class. To participate in the discussion you will need to work on those problems on your own or with your friends. Team work is encouraged.

The course will cover the use of technology in the modern classroom. Every student in the class will be loaned a laptop with all of the necessary software for the course. Topics will include:

* An introduction to PDF Annotator, Mimio notebook, OneNote, wincopy, Camtasia, and Wink 2.0.

* An introduction to the creation and online dissemination of streaming materials, through a standard web server or services like YouTube.

* Practical use of winplot, geogebra, Matlab, R, Excel, and some available JavaScript programs and Java applets.

* The use of Horizon Wimba to host live online sessions, and an overview of other available software.

* An introduction to simple programming in Javascript, Matlab and R.

The course will have a relaxed pace and will hopefully be fun. I do not intend to give any exams. There will be assignments that will help you gain confidence using the different software, and hopefully you will find some of these tools useful in the future.