Math 797 - Networks and Spectral Graph Theory

 

Outline & objective

Graphs and networks have been successfully used in a variety of fields (e.g., machine learning, data mining, image analysis, sensor networks, social sciences, etc.) that are confronted with the analysis and modeling of high-dimensional datasets. Analysis tools originally developed for Euclidean spaces and regular lattices are now being transferred to the general settings of graphs and networks in order to analyze geometric and topological structures, and data and signals measured on them. In this course, we shall discuss a variety of important theories and interesting applications employing spectral graph analysis of and on graphs and networks. Topics include: graph Laplacians, their eigenvalues and eigenvectors for structural/morphological analysis; wavelets on graphs; random walks and diffusion on graphs; spectral clustering; community detection; etc. The last part will cover some topics about deep learning on graph neural networks. The objective of the course is to present a broad spectrum of network analysis concepts and techniques, clarify their mathematical foundations and demonstrate their practical applicability. The lectures will give theoretical discussion on network concepts and present efficient algorithms and techniques for their analysis, while students will work on practical examples of applying network analysis within their coursework. Except for some basic knowledge of programming language (e.g. Python, Java, C/C++, or Matlab), there are no specific prerequisites for the course. However, students will benefit from a solid knowledge in graph theory, probability theory and statistics, and linear algebra. The main part of the coursework consists of a substantial course project. Students will be encouraged to submit a report describing their course project to the preprint server arXiv.org or make their work publicly available. All students will have the opportunity to present their project in front of their peers. Students are encouraged to work in groups of three, while other sizes of groups will be allowed only in special cases.

Fall  2019         

                                           

                 Math 331- Ordinary Differential Equtions

   MATH 331 All sections

Spring  2019         

                 (M537-Introduction to Math Finance)

Fall 2018         

   MATH 797DE                      

                 (M537-Introduction to Math Finance)

Spring 2018         

Fall 2017         

Spring 2017          

Fall  2016          

                                      (Ordinary Differential Equations for Sciences and Engineers)
   MA 331 -section 4

Spring  2014          

                                      (Ordinary Differential Equations for Sciences and Engineers)
   MA 331 -section 6

Fall  2013          

Spring  2013          

Fall  2012          

                                      (Ordinary Differential Equations for Sciences and Engineers)
   MA 331 -section 4

Spring  2012          

Fall 2011          

                                      (Ordinary Differential Equations for Sciences and Engineers)
   MA 331 -section 1

Spring  2011          

Fall 2010           (Multivariable Differential Calculus)
   MA 233 -section 6

                                      (Ordinary Differential Equations for Sciences and Engineers)
   MA 331 -section 1

  Spring 2010       Probability theorey,    Advanced Calculus

Spring 2009          Multivariable Differential Calculus, Advanced Calculus

Fall 2008           (Multivariable Differential Calculus)

Spring 2008        (Multivariable Differential Calculus)

Fall      2007        (Integral Calculus)

Spring 2007        (Calculus III & Linear Algebra)

Fall      2006        (Probability and Statistics)

Spring 2006        (Calculus II & Linear Algebra)

Fall      2005        (Calculus I & II)

Spring 2005        (Survey of Calculus)                                                               

Fall      2004        (Pre-calculus: Algebra/ Trigonometry)

Spring 2004        (Pre-Calculus: Trigonometry)

Fall      2003        (Pre-Calculus: Algebra)

Spring 2003        (Intermediate Algebra)

Fall      2002        (Basic Algebra)