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Spring 2022                                                     

                 Math 697U- Stochastic Processes and Applications


Fall  2021         


                  Math 605- Advanced Probability


                  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

  MATH 331 Section 5 and Section 7

Spring  2019         


                 (M537-Introduction to Math Finance)

   MATH 537

Fall 2018         

                      (M797DE-Dynamical Systems and Ergodic Theory)

   MATH 797DE                      

                 (M537-Introduction to Math Finance)

   MATH 537

Spring 2018         

                      (Stat 515-Section 3)
    STAT 515

Fall 2017         

                      (M331-Ordinary Differeential Equations)
   MATH 331-Sect 2    MATH 331-Sect 5

Spring 2017          

                      (FR- Financial Mathematics and Risk Management)
   MATH 797-FR

Fall  2016          

                      (ST-Adv. Stochastic Calculus)
   MATH 797-SC

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

Spring  2014          

                                  (Introduction to Math. Finance)
   MATH 441

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

Fall  2013          

                                   (Advanced Finanical Math)
   Math 797 FM

Spring  2013          

                                   (Advanced Probability)
   STAT 605

Fall  2012          

                                  (Introduction to Math. Finance)
   MATH 441

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

Spring  2012          

                                   (Introduction to Math. Finance)
   MATH 441

Fall 2011          

                                   (Stochastic differential equations)
   MA 797P-01

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

Spring  2011          

                                   (Advanced Probability)
   STAT 605

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