Math 2000: Discrete Mathematics
Instructor: Professor Anne Shepler
TR 11:00 - 12:20
Prerequisites: MATH 1710 (may be taken concurrently)
Introduction to proof writing, logic, sets, relations and functions, induction and recursion, combinatorics and counting techniques, discrete probability, graphs and trees. The course includes an exploratory project on misuses of logic in modern society and current scientific research.
Math 2000 is a new Discovery course intended for math majors entering UNT in Fall 2013 or later. Students who began at UNT prior to Fall 2013 should consult an advisor before enrolling in Math 2000.
Math 3520: Abstract Algebra II and Math 5900.717: Introduction to Modern Algebra
Instructor: Professor Joseph Kung
TR 12:30 - 1:50
Prerequisites: MATH 3510
This is the optional second semester of MATH 3510 Abstract Algebra I.
We will cover more advanced topics. We will begin with error-detecting codes like the international standard book number ISBN-code and use dihedral groups to make better ISBN-like codes. After that, we will do permutation groups with two main topics: counting under group actions and Wielandt's proof of the first Sylow theorem. We will then consider how Sylow's theorem works in groups of symmetries of sets (the "symmetric group of permutations") and vector spaces (the general linear group). Then we will do double cosets! We'll use them to give Frobenius's proof of the first Sylow theorem. This will take up the first two-thirds of the course.
In the second half, we will do ring theory, focusing on polynomial and power series rings. We will introduce the basic concepts of ideal theory and apply them to ideals in polynomial rings and do a little bit of algebraic geometry. This will be done using Gröbner basis theory.
Pre-requisites: The pre-requisites is MATH 3510. This is a continuation of that course. We will assume basic knowledge of group and ring theory (denitions and elementary properties covered in MATH 3510).
Grading: There will be homework, two-hour test during the semester, and a final.
Textbook: We will use the textbook from the rst semester 3510 as a required text: Allan Clark, Elements of abstract algebra, Dover, New York, ISBN 0-486-64725-0
For the ring theory, a recommended (not required) text is David Cox, John Little, Donal O'Shea, Ideals, varieties, and algorithms: An introduction to computational algebraic geometry and commutative algebra, Springer, Paperback edition, ISBN 1-44-192257-1.
Questions? Ask the instructor (or his cat). Joseph Kung, GAB 471B. Email: firstname.lastname@example.org
Math 4500/5600: Introduction to Topology
Instructor: Professor Lior Fishman
TR 11:00 - 12:20
Undergraduate prerequisite: MATH 3610; Graduate prerequisite: None
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 Poincaré 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, amusingly illustrated in the figure below.
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: Professor Huguette Tran
MWF 9:00 - 9:50
Prerequisites: MATH 1720, MATH 3680
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 or not 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.
Text book: Mathematics for Finance - 2nd edition by Marek Capinski
View the Course Descriptions from the University Catalog