# Schedule of Classes

## Additional Information on Select Fall 2015 Courses

MATH 3010 – Seminar in problem solving techniques
Instructor: Pieter Allaart, Joseph Iaia
W 5:00 - 5:50 PM

Are you good at math and enjoy a challenge? Try taking the Putnam exam and MATH 3010!
The Putnam exam is an exam for undergraduate math majors given every year in December. In the one hour course MATH 3010, we will discuss strategies for solving some of the typical problems that come up on the Putnam exam. These are often fairly challenging problems and not for the faint of heart, so bring your best math skills and your thinking cap for a challenge and some fun for a class team. More details, visit our William Lowell Putnam Competition page.

MATH 4060 – Foundations of Geometry
Instructor: William Cherry
TR 3:30 - 4:50 PM
Prerequisites: MATH 3000; Prior or concurrent enrollment in either MATH 3510 or MATH 3610 is strongly recommended.
Texts: Robin Hartshorne, Geometry: Euclid and Beyond, Springer Verlag, 2005; ISBN 9780387986500. Euclid's Elements, The Thomas L. Heath translation edited by Dana Densmore, Green Lion Press, 2002. ISBN 9781888009194
Course Website: wcherry.math.unt.edu/math4060
Early interest in geometry was almost certainly motivated by a desire to improve building techniques and to be able to create interesting shapes for temples, altars, toys, and machines. Scholars in ancient Greece "abstracted" the study of shapes into an idealized form. The most widely read textbook in history is a geometry text by Euclid known as the Elements. Thousands of years later, much of what we learn in high school geometry is based on the ideas in Euclid's text. Euclid's goal was to create a logical foundation for idealized geometry. He wanted to provide proofs for geometric facts based on as few axioms as possible. The course will begin with a careful study of parts of Euclid and an exploration of what he was trying to do and why. The course will then move on to the contributions of 19th and 20th century scholars who built on Euclid's work. The second half of the course will look at alternative geometries where the so-called parallel postulate need not hold.
The course will emphasize the role of proof in geometry, its historical development, and the philosophical implications that proof had on the development of scientific thought. Students will begin by reading Euclid and continually develop their own proof writing skills and geometric intuition.

MATH 4090 - Senior Seminar (CANCELLED)
Instructor: Lior Fishman
TR 11:00 AM - 12:20 PM

Text: Diophantine Approximation – W. M. Schmidt (any edition will be fine)
Prerequisites: Senior standing, Math 2700, Math 3410, Math 3510, Math 3610 and at least one of Math 3680 or Math 4610. Note however, that for the Fall 2015 topic, the Math 3410, 3680, and 4610 prerequisites are not essential, and students without those course prerequisites who wish to enroll may do so by seeing Rita Sears in GAB 443.
The main objective of this course is to introduce and prepare students for math research in the 21st century. Senior seminar is a new CAPSTONE option intended primarily for math majors who are considering continuing their mathematics education in graduate school. By examining a mathematical topic of contemporary interest, students will be introduced to the culture and techniques of mathematical research and will get a better sense of what is involved in a graduate mathematics education. In Fall 2015, we shall explore Diophantine approximation theory, starting with classical results and methods such as Dirichlet’s and Minkowski’s theorems, continued fractions and Farey series. We shall then read recently published research papers in the field. Students will be required to present selected topics in class, preparing them for independent study and presentations. Students interested in computer programing will be encouraged to explore some questions relating to the course’s material, and the data gathered may help us formulate and hopefully even prove some conjectures.
Other Capstone options for math majors: Math 3850 (Mathematical modeling) will be offered in Spring '16 and also meets the UNT Capstone requirement. TNT students will meet UNT’s Capstone requirement by taking EDSE 4618.

MATH 4430 - Introduction to Graph Theory
Instructor: Elizabeth Drellich
TR 12:30 PM - 1:50 PM

Text: "A First Course in Graph Theory" by Chartrand and Zhang
When you send an email, how many computers must it go through before it reaches your friend's inbox?
Why does the mail truck drive that particular route around the neighborhood?
How many telephone poles can get knocked down without your house losing electricity?
And of course, how many people are you away from Kevin Bacon?
All of these questions are Graph Theory questions. In Graph Theory a graph is a collection of vertices or nodes connected by edges. These vertices might represent computers, houses, telephone poles, people, or any number other real world objects. The goal of the class is to survey the introductory concepts in the eld, including, but not limited to, distance in a graph (the email question), Euler paths (the mail truck), vertex connectivity (the telephone pole question) as well as many classic problems like the four color theorem and the bridges of Konigsberg:

Can Snowball cross all seven bridges exaclty once and end where she started?

MATH 5210 - Numerical Analysis - Scientific Computation
Instructor: Jianguo (Jay) Liu
TR 3:30 PM - 4:50 PM
Prerequisites: Advanced linear algebra and multivariable calculus. Computer programming experience will be helpful.
This course (one of the two courses) will prepare you for the Applied Mathematics Qualifying Exam. It will cover the fundamentals of matrix computation and optimization including the following topics:

• Error analysis and sensitivity analysis
• Design of computer programs
• Matrix decompositions and iterative methods for linear systems
• Optimality conditions for optimization
• Data fitting
• Monte Carlo simulation
• A few case studies will be presented, including image deblurring and data classification.

MATH 6150 - Functional Analysis
Instructor: Bunyamin Sari
TR 11:00 AM - 12:20 PM

Text: No text required
This course is an introduction to Functional Analysis and to common functional analytic techniques in Analysis. Since the basic principles of functional analysis (Hahn-Banach, Open mappings, etc.) are covered in Real Analysis series, we will only give a short review of those. Then we will cover the basics of

1. Weak and weak* topologies, and duality
2. Bases and basic sequences
3. Structure of Hilbert and the classical Banach spaces $C(K)$$c_0$, $\ell_p$, $1\le p\le\infty$.
4. The algebra of bounded linear operators

The material is likely to be somewhat adjusted depending on participants' background and interests.
No textbook is required. Royden's book that is used in Real Analysis is still useful because it covers some of the material. Some recommended texts (there are plenty other, however)

•  B. Bollobas, Linear Analysis
•  N. Carothers, A short course on Banach space theory
•  Fabian et al, Banach space theory
•  Conway, A course in Functional Analysis

Grading will be based on attendance and a class presentation. Each participant selects a project and writes a short but concise exposition (less than 5 pages or so) and present in class. In most cases, a project consists of presenting a single theorem, or explaining a widely used notion. I will meet with you in the second week to help you select a project that is likely be helpful to your own thesis research. I will provide references and clear instructions on what to include in the project.

MATH 6610 – Topology and Geometry
Instructor: Mariusz Urbanski
TR 3:30 PM - 4:50 PM

Text: "Theory of Dimensions; Finite and Infinite" by R. Engelking.
The course will cover basic properties of ( finite) topological dimension in the class of separable metrizable spaces. These will include three defi nitions/characterizations of topological dimension: small inductive one, large inductive, and covering dimension. Also, a characterization by partitions will be given. Furthermore: zero-dimensional spaces, the countable sum theorem, Cartesian product theorem, universal space, compacti cation, and embedding theorem will be proved. It will be shown that the dimension of Rn is equal to n. The most transparent properties of topological dimension under continuous maps, with various additional hypotheses, will be established.
Also selected topics from the theory of transfi nite topological dimension will be covered. In particular small and large, now differing, transfi nite dimensions will be treated. Countable-dimensional and strongly countable-dimensional spaces will be introduced and studied. Basic theorems will be proved. The class of Smirnov spaces will be defi ned and its dimension-wise properties will be dealt with.
If time permits, Hausdor dimension will be introduced and its relations to topological dimension will be emphasized. If still some time is left (rather unlikely) transfi nite Hausdor dimension will be dealt with.
The textbook is: "Theory of Dimensions; Finite and In finite" by R. Engelking. It can be purchesed directly from the publisher Heldermann Verlag at http://www.heldermann.de/SSPM/sspmcovr.htm
The grades will determined by attendance and activity of students in the classroom.

# Catalog Course Descriptions

View the Course Descriptions from the University Catalog