
10/07/2019 
1 An Introduction to Machine Learning: Methodologies and Practical Implementation
 Đối tượng người học  Audience: anybody in sciences and engineering, including anybody interested in Machine Learning, applied math, life sciences, computer science, electrical engineering, bioengineering, etc, including people outside of academia.
 Kiến thức cần có  Background: calculus, linear algebra, proficiency with some programming (python, MATLAB)
 Giảng viên:
 Kevin Flores, Assistant Professor, Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University
 Erica Rutter, Postdoctoral fellow, Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University
 Hien Tran, Alumni Distinguished Graduate Professor, Director Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University
 Thời gian: June 1721, 2019. Phòng học: Giảng đường 1, từ chiều Thứ ba: B11A
 Tóm tắt:
 What is Machine Learning? “Machine learning teaches computers to do what come naturally to humans and animals: learn from experience. Machine learning algorithms use computational methods to “learn” information directly from data without relying on a predetermined equation as a model. The algorithms adaptively improve their performance as the number of samples available for learning increases” (from MathWorks, Natick, MA)
 In this minilecture series, we will explore the core machine learning concepts and their computational implementation. Several real data, where applicable, will be used to test the numerical implementation.
 Prerequisite: Participants need to bring their own laptops. Programming proficiency (Python, MATLAB)
 Course Timeline: Morning Lecture: 9:00 – 10:15 Break: 10:15 – 10:45 Lecture: 10:45 – 12:00 Afternoon Lecture: 2:00 – 3:15 Break: 3:15 – 3:45 Lecture: 3:45 – 5:00
 Course Topics:
 Monday: ◦ AM (Hien): Bayesian Classifiers, Perceptron, Multilayer Perceptron (Neural Networks)
◦ PM (Erica): TensorFlow, UCI Machine Learning Repository: Iris and Diabetes Data Sets
 Tuesday: ◦ AM (Hien): Support Vector Machines (separable classes, nonseparable classes), Decision Tree
◦ PM (Erica): Tutorial: ScikitLearn, Credit Card Approval Data Sets
 Wednesday: (free day) No Lecture
 Thursday: ◦ AM (Kevin): Convolutional Neural Networks, Computer Vision, Segmentation and Classification
◦ PM (Erica): MNIST Data Set, Imagenet, ISBI cell segmentation
 Friday: ◦ AM (Kevin): Recurrent Neural Networks (RNN), Long ShortTerm Memory (LSTM) Networks, Natural Language Processing (NLP), Time Series Data
◦ PM (Erica): Time series data, sentiment classification, NLP for translation
◦ Optional: Model Evaluation (confusion matrix, loss function, ROC, hypothesis testing), MultiClass, Dimensionality Reduction (TSNE) – MNIST data last layer dimension reduction
2 Stochastic Models in Ecologie and Evolution: Pure jump Markov Processes in Continuous Time
 Giảng viên: Sylvie Méléard, Professor, CMAP, École Polytechnique, France
 Thời gian: July 15–19, 2019. Monday 9:00  11:45, Tuesday  Friday 8:45  11:30. Problem session by Dr. Hoàng Văn Hà: Monday, Wednesday, Friday, 13:30  16:00. Phòng F207
 Tóm tắt: In these lectures, we will give the structure of the pure jump Markov processes with countable values. The prototype is the Poisson process that we will study in details. We will define the infinitesimal generator and prove the Kolmogorov equations. Then we will study two wellknown examples, useful especially for applications in biology: branching processes and birth and death processes describing population dynamics. In both cases, we will give criteria of existence and extinction. Finally, we will study approximations of large populations, showing how these jump processes can be approximated in this case, either by dynamical systems or by stochastic differential equations.

Tài liệu tham khảo:
[1] Modèles aléatoires en écologie et évolution, Mathématiques et Applications 77, SMAI. Springer, 2016. (In French)
Link download: http://www.cmap.polytechnique.fr/IMG/pdf/LIVRE07102013.pdf
[2] L.J.S. Allen. An Introduction to Stochastic Processes with Applications to Biology, Second edition. CRC Press, Chapman & Hall/CRC, 2011.
[3] V. Bansaye, S. Méléard. Stochastic Models for Structured Populations. Mathematical Biosciences Institute Lecture Series 1.4. Springer 2015.
Link download: https://arxiv.org/abs/1506.04165
[4] Ross, Sheldon M. "Stochastic Processes. John Wiley& Sons." New York (1996).
3 An Introduction to Geometric Group Theory
 Giảng viên: NhanPhu Chung, Department of Mathematics, Sungkyunkwan University, Korea.
 Thời gian: August 1214, 2019, 9:0011:00.
 Tóm tắt: I will present finitely generated groups as viewpoints of metric spaces via word lengths and quasiisometries. In this part, I will prove a result of SchwarzcMilnor which is a fundamental observation of geometric group theory. In the second part of the course, I will introduce growth types of finitely generated groups. A landmark result in geometric group theory is Gromov’s theorem stating that a finitely generated group is virtually nilpotent if and only if it has polynomial growth. If time allows I will provide a sketch of Gromov’s proof.
 References
 Tullio CeccheriniSilberstein and Michel Coornaert, Cellular automata and groups, Springer Monographs in Mathematics, SpringerVerlag, Berlin, 2010.
 Pierre de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000.
 Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73.

