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**MATH 3420 - Differential Equations 2Instructor: Joseph IaiaTR 11:00 AM - 12:20 PMCourse Description:**

In this course we will discuss the solutions of the most well-known partial differential equations (PDEs) - the heat equation, wave equation, and laplace equation. We will solve these equations on intervals and rectangles by the method of separation of variables. We will also discuss Fourier series and see how these are used in solving many linear PDEs. We will also discuss the Fourier transform and the solution of the heat and wave equations on the entire real line. We will prove existence and uniqueness of solutions for a wide variety of linear equations. We will discuss polar coordinates and spherical coordinates and use them to solve the laplace equation in a disk and in a ball. If time permits we will study Bessel's equation and also first order linear equations.

At the end of this course students will be able to calculate the Fourier series of a function and be able to use the separation of variables technique to solve various linear PDEs on intervals and rectangles. Students will also be able to calculate the Fourier transform of a function and use it to solve various linear PDEs on the real line. In addition students will be able to write the laplace equation in polar coordinates and spherical coordinates.

**MATH 3850 – Mathematical ModelingInstructor: Jay Liu**MATH 1720 and MATH 2700 (may be taken concurrently) or consent of instructor.

This course serves as a bridge between the study of mathematics and the applications of mathematics to various fields. It affords the students an early opportunity to see how the pieces of an applied problem fit together. Students will be motivated to investigate meaningful and practical problems from common experiences encompassing many academic disciplines, including mathematical sciences, chemical and physical sciences, economics, engineering, life sciences, management sciences, and operations research.

Math 3850 will be counted as a capstone course and as a upper-level math for the math minor or as math elective 3350 or higher for the math major.

Contact: Dr. Jianguo Liu, jgliu@unt.edu or 940-565-4703

**MATH 4060 – Foundations of Geometry****Instructor: William Cherry****MWF: 9:00 AM - 9:50 AM****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 4500/5600 - TopologyInstructor: Dr. Lior FishmanUndergraduate Prerequisite: **MATH 3610 (Real analysis II)

The course’s main aim is to discover and explore connections between Point Set Topology, Measure Theory and Number Theory. After establishing a solid background in Topology, we shall review some important notions from Measure Theory, an important foundation for advanced graduate study in analysis and probability. We shall then study selected chapters from John C. Oxtoby’ book: Measure and Category: A Survey of the Analogies between Topological and Measure Spaces. This will allow us to understand how the concept of topology provides an important tool for us to better understand real analysis, and working with the real line gives us a concrete and familiar place to work with the new topological concepts introduced in the course. Highlights of the course will include the Baire Category Theorem, a beautiful topological tool that enables one to prove a variety of existence theorems, and the PoincarĂ© Recurrence Theorem, which provides certain criteria for a physical system to eventually return to a state close to its initial state. We will also explore important and interesting sets, such as the Cantor Set.

For undergraduate students, particularly those considering attending graduate school in pure mathematics, or in programs in probability, statistics, or financial mathematics which also include a theoretical component, Math 4500 provides you with the tools and foundations to prepare you for more advanced study of analysis, probability, and geometry. For graduate students, Math 5600 reinforces your knowledge of real analysis and provides ideal preparation for UNT’s core sequences in measure theory and topology.

**MATH 4980: Financial Math****Instructor: Dr. Huguette Tran****MWF**** 1:00- 1:50 PM****Text:** Mathematics for Finance - 2nd edition by Marek Capinski, ISBN13: 978-0857290816**Prerequisites**: MATH 1720 and MATH 3680. (MATH 3680 may be taken concurrently with MATH 4980)

This course covers fundamental concepts of financial mathematics and their applications in calculating present and future values, annuities and variable cash flows, yield rates, and valuation of stocks, bonds and other securities. The course will also provide an introduction to financial instruments, including options, contracts, and hedging, and the concept of no–arbitrage as it relates to financial mathematics.

Students who meet the prerequisites and have an interest in financial mathematics are welcome to enroll (whether they plan to complete the actuarial certificate). Students interested in a career in actuarial science are encouraged to take this course to be familiar with the topics covered in Exam FM/2.

**MATH 5470 - Differential Equations 2Instructor: Joseph IaiaMWF 9:00 AM - 9:50 AM**

In this course we will discuss the solutions of the most well-known partial differential equations (PDEs) - the heat equation, wave equation, and laplace equation. We will begin with a discussion of the Laplace equation - the maximum principle, the Hopf boundary point lemma, the mean value property, Green's formulas, and the solution of the Dirichlet problem in the ball and upper half space. We will discuss the Perron method for solving the Dirichlet problem for a more general bounded domain in Euclidean n space. Next we will turn to the heat equation and the heat kernel. We will solve the initial value problem for the heat equation in Euclidean

**MATH 6110 - Topics in Automorphic FormsInstructor: Olav RichterMW 11:00 AM - 12:20 PM**

Please follow the link below to learn more about this course

http://www.math.unt.edu/~richter/teach/S15-6110.html

**MATH 6510 – Topics in AlgebraInstructor: Charles ConleyMW 2:00 PM - 3:20 PM**

The goal of this seminar will be to give the flavor of various different types of representation theory by means of examples. The link below gives some possible topics, each of which might take anywhere from two to five weeks. However, if anyone would like to see a particular topic covered, I will do my best to cover it. We do not have to stick to my list of topics if there is interest in something else. There will be no formal text for the course, but “Representation Theory” by Fulton and Harris may be useful.

http://www.math.unt.edu/~conley/6510/6510s15.pdf

View the Course Descriptions from the University Catalog