Courses and Schedules

Schedule of Classes

Current Course Descriptions

Fall 2012

Math 4010 / 5010 - Introduction to Metamathematics / Mathematical Logic and Set Theory I
Instructor: Dr. John Krueger (jkrueger@unt.edu)
Lectures: Monday, Wednesday, Friday; 10:00 -10:50 AM; LANG 318
Course objective: This course is an introduction to mathematical logic for junior or senior level undergraduate students or graduate students who are interested in abstract mathematics, algebra discrete math or theoretical computer science. We will study first-order logic, which is a formal language in mathematical theories can be expressed, together with axioms of deduction which captures the essence of mathematical proofs. Then we study the model theory of first-order logic, which provides a way of describing how mathematical structures can be used to interpret a formal language.
       After developing the basic theory of computability, we are led to the fascinating incompleteness theorems, which set inherent limitations on what can be done in mathematics. Any theory strong enough to develop elementary number theory contains statements which can neither be proven nor disproven. And it is impossible to prove in mathematics that mathematics itself is a consistent theory.  COURSE FLIER

Math 6810 - Probability
Instructor: Dr. Pieter Allaart  (Pieter.Allaart@unt.edu)
Lectures: Monday, Wednesday, Friday; 11:00 -11:50 AM; GAB 201
Degree plan information: This course fulfills the analysis breadth requirement.
Prerequisite: None for the first semester, but measure theory (Math 5320) is required for the second semester. Some prior knowledge of probability will be helpful. Students interested in this course who have not taken a class at the level of Math 4610/5810 are encouraged to meet with Dr. Allaart before the summer.
Textbooks: TBD
Course objective: The goal of this two-semester sequence is primarily to develop the mathematical machinery needed to study mathematical finance. However, as an old proverb goes, the journey is more important than the destination! This means that we will not rush to get to the finance part as soon as possible, but we will take ample time to attend to the mathematical details. After a brief review of basic probability (1-2 weeks, as needed), we will examine the mother of all stochastic processes: Brownian motion, and discover some of its remarkable properties. This will be followed by the more general notions of martingales and Markov processes. After that, we will have all the necessary tools to introduce the stochastic integral, which leads to a whole new kind of calculus. This is, in a nutshell, the synopsis of the first semester. In the second semester we will look at applications of stochastic calculus, particularly in finance. That requires the introduction of two major mathematical results: the martingale representation theorem and the Girsanov change-of-measure theorem.
Grading: There will be no homework or exams. Your grade will be based on two substantial in-class presentations (30-50 minutes each).

Spring 2012

Math 6710 - Quantitative & Computational Biology
Instructor: Rajeev Azad (Rajeev.Azad@unt.edu)
Lectures: Tuesday & Thursday 11:00 AM – 12:20 PM, GAB 438
Office hours: 1:30 – 3:00 PM Tuesday (GAB 434) & Thursday (LSC A316) or by appointment
Recommended textbooks: The course content will be based on selected Bioinformatics textbooks considering diverse background of the prospective students and with no expectation of the prior exposure to this interdisciplinary area. The recommended textbooks are Biological Sequence Analysis by Durbin et al., Bioinformatics and Functional Genomics by Pevsner, and Statistical Methods in Bioinformatics by Ewens & Grant. New research developments will also be covered in this course, based mainly on research articles and review papers.
Course objective: The aim of this course is to familiarize students with state-of-the-art methodologies in Bioinformatics and Computational Biology, and help them understand how to apply these techniques to solving biological and biomedical problems. This course will include the following topics:
• An introduction to probability and probabilistic models for interpreting biological sequence data
• Markov chain models, hidden Markov models, profile hidden Markov models
• Genome architecture, genome assembly, gene prediction, protein topology prediction
• Pairwise and multiple sequence alignment
• Molecular phylogeny
• Genome evolution: vertical and horizontal modes of gene transfer
• Microarray and next generation sequencing data analysis
• Metagenomics: gene detection and phylogenetic classification
• Human genome variations: detection of structural variations and copy number variations, identification of disease-associated genes
Course outcomes: Appreciation of the interdisciplinary approaches to solving problems in biology; understanding of the essence of computational and mathematical methods in biology and medicine; familiarization with principles and models underlying standard bioinformatics methods/algorithms; practical experience of using bioinformatics tools for sequence analysis; development of skills to write simple computer programs for interpreting biological data.
Grading: Based on in-class discussions, in-class presentation, homework assignments and final project presentation.
 

Course Descriptions

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