Time: Wednesdays 5:30 – 8:20 PM

Classroom: PKH 109 

Instructor: Prof. Shipman, PKH 437 

Office Hours : Tues., Wed. 4:15–5:15 PM, Thur. 10-10:45 AM and by appt.  

Phone: (817) 272-2606   

E-mail: bshipman@uta.edu  

Undergraduate real analysis, calculus, and matrix algebra

Our study will integrate geometric, algebraic, and analytic methods, both continuous and discrete, in analyzing a rich class of dynamical systems known as the Toda lattice. Each concept will be built up from familiar ideas, with a view toward connecting advanced mathematics with topics taught at the secondary and junior college levels, both for the enrichment of current and future teaching careers and for the development of a versatile and practical grasp on the mathematics. As an introduction to the ideas and techniques of the Toda lattice, the course will begin with a geometric and algebraic study of mechanical oscillations and related systems.
       The Toda lattice originated in 1967 from a physical problem describing interactions among particles arranged along a line. The discovery a few years later that the equations of motion may be written in a special matrix form led to a variety of mathematical abstractions of the original system. This opened up a realm of algebraic and geometric techniques in describing the dynamics, singular behaviors, and global structures of these systems. In particular, the flows may be organized via the discrete structures of objects known as moment polytopes. Topics of study will include mechanical oscillations, Hamiltonian systems, Toda lattice hierarchies, matrix factorizations, projective spaces, compactification, group actions, and moment polytopes.

Weekly Schedule
The concepts will be developed through interactive class work, homework, and team projects. Each class will incorporate interactive lessons together with group work on related problems. This will lead to homework for the week designed solidify and extend the ideas; the homework will be handed out at the end of class. If you miss a class, please send me an e-mail for the homework assignment. At each class meeting, class members will present solutions to selected homework problems for discussion. The assignments will include individual and team projects.

The course grade will be based on participation, presentations, homework and projects.  Each in-class presentation and each written problem to be handed in will be given a score out of 20 points based on clarity of the explanations and thoughtfulness of the solution. It is important to attend every class meeting and participate in the group work and discussions.  At the beginning of the semester, you will have a score of 100% for participation.  Five points will be deducted for every absence after the first.  There will be no exams.  A final project will be submitted in place of a final exam.

Presentations and homework:  60%
Participation:  15%
Final Project:  25%

Jan 20               First class 

Mar 13-21          Spring Break 

Apr  2                Last day to drop a class
May  5               Last class

May 12              Final Project Due

Drop Policy:
The last day to drop the course is Friday, April 2. Please refer to the University drop policy for details on withdrawing from a class. 
 

Americans With Disabilities Act:
The University of Texas at Arlington is on record as being committed to both the spirit and letter of federal equal opportunity legislation; reference Public Law 92-112 - The Rehabilitation Act of 1973 as amended. With the passage of federal legislation entitled Americans with Disabilities Act (ADA), pursuant to section 504 of the Rehabilitation Act, there is renewed focus on providing this population with the same opportunities enjoyed by all citizens.

The instructor will provide "reasonable accommodations" to students with disabilities, so as not to discriminate on the basis of that disability. It is the student’s responsibility to informing the instructor of his or her need for accommodation by providing authorized documentation through designated administrative channels.  Information regarding specific diagnostic criteria and policies for obtaining academic accommodations can be found at www.uta.edu/disability.   Also, you may visit the Office for Students with Disabilities in room 102 of University Hall or call them at (817) 272-3364.

Academic Integrity:
It is the philosophy of The University of Texas at Arlington that academic dishonesty is a completely unacceptable mode of conduct and will not be tolerated in any form. All persons involved in academic dishonesty will be disciplined in accordance with University regulations and procedures. Discipline may include suspension or expulsion from the University.

"Scholastic dishonesty includes but is not limited to cheating, plagiarism, collusion, the submission for credit of any work or materials that are attributable in whole or in part to another person, taking an examination for another person, any act designed to give unfair advantage to a student or the attempt to commit such acts." (Regents’ Rules and Regulations, Series 50101, Section 2.2)

Student Support Services Available:
The University of Texas at Arlington supports a variety of student success programs to help you connect with the University and achieve academic success. These programs include learning assistance, developmental education, advising and mentoring, admission and transition, and federally funded programs. Students requiring assistance academically, personally, or socially should contact the Office of Student Success Programs at 817-272-6107 for more information and appropriate referrals.