R program offers a powerful tool for analyzing and visualizing data, and in recent years it became very popular among (not only) ecologists. It offers great freedom in handling, analysing and visualizing any type of data, however, it also comes up with steep learning curve of S language and frustration from frequent error messages. This practical course should teach students the basic of R program operation and data visualization.

All materials are available on http://bit.ly/r-ecol The main goal is to teach students basic skills of using R program, and prepare them for more advanced courses where R will be used for data analysis and visualization. College of Life Science Main Campus David Zeleny 35 Tuesday 2,3,4 EEB5082 3 Half Department of Lifescience, Institute of Ecology and Evolutionary Biology http://ecology.lifescience.ntu.edu.tw/english/index.htm

There are three chapters in this course. Chapter one covers the Cartesian Tensors, which are extensive used in the courses of Elasticity, Plasticity, Fluid mechanics, Piezoelasticity, and etc. Chapter two includes three parts. The first part introduces the existence and uniqueness theory for the 1st order ordinary differential equation (ODE) and 1st order system of ODE. The second part covers the solution of 1st order linear system of ODE, which is particular useful for the course of Dynamics. The third part of this chapter is designed to the solution of linear 2nd order ODE with unknown source functions. We introduces the concept of Dirac delta function, generalized functions, adjoint operators, Fredholm alternative theorem, Green�fs functions and modified Green�fs functions and the integral representation of the solution of 2nd order ODE. Finally, Chapter 3 also includes three parts. The 1st part introduces the classification of linear 2nd order PDE. The 2nd introduces the Green�fs function and the integral representation of solution of 2nd order linear PDEs. Free space Green�fs functions are solved first for infinite domain and then method of images are introduced for solving some simple finite domain PDE problems. The 3rd part introduces the eigenvalue problem of self-adjoint boundary value problems of 2nd order PDE, and the full/partial eigenfunction expansion for solving the linear 2nd order BVP or IBVP. Also included in this part are the Maximum-Minimum principle and unique theorems for Laplace/Poisson equation and Heat equation. This course is aimed to let the graduate students own required knowledge in applied mathematics, which has applications in all aspects of mechanics, electricity and applied science. College of Social Engineering Main Campus Mao Kuen Kuo,U Lei 98 Tuesday 2 Friday 34 AM7006 3 Half Graduate Institute of Applied Mechanics http://www.iam.ntu.edu.tw/English/EN-homepage/homepage-Frameset.htm

This is a mathematical analysis course for doctoral and master students in economics. The course aims to
prepare you for advanced courses in economics and your future research. The material includes some basic
concepts in set theory, real analysis, convexity and optimization. Given the time constraint, the focus of the
course is not to have an extensive coverage of mathematical concept and theorem, but rather to give you a
decent training in abstract reasoning and theorem proving. Course Outlines
Sets and Functions
1. Sets
2. Functions
3. Cardinality
3. Rational Numbers
Real Numbers and Metric Space
1. Real Numbers
2. Metric Space
3. Convergence
4. Cauchy Sequence
Topology
1. Open Sets and Closed Sets
2. Continuous Functions
3. Compactness
4. Existence of Optima
Covexity and Optimization
1. Convexity
2. Duality
3. Karush_Kuhn_Tucker Theorem
Linear Algebra
1. Vector Space
2. Matrix Algebra
3. Eigenvalues and Eigenvectors
College of Social Science Main Campus *Restrict to graduate students.
*Ten classes only, from Aug. 28 to Sept. 8, Monday to Friday, 9:10-12:10
Chien-Chiang Wang 80 ECON7009 2 Half Graduate Institute of Economics http://www.econ.ntu.edu.tw/db/new2011/index.asp?l=english

The course is intended for students who have basic knowledge of probability such as random variables, distribution functions, generating functions and their basic properties. The basic concepts of risk analysis and their stochastic nature will be presented. The methodology presented in the course will broaden students’ knowledge area and show new applications of the probabilistic techniques in risk phenomena. Institute of Mathematics ans Statistics (IME) São Paulo main campus 1. Probability aspects of risk. 2. Distributions of total insurance paid in one year. 3. Principles of calculation of the premiums. 4. Exchanges of risk and re-insurance. Nikolai Valtchev Kolev 60 MAE5890 8 https://www.ime.usp.br/en

The joint development of areas such as discrete mathematics, probability, operational research and computer theory is continuous and relevant. The solution of theoretical and applied problems in these areas can be given in terms of a probabilistic modeling that arises from physics as well as the analysis of engineering systems or areas such as economics, biology, engineering, neuroscience. The tools used in such modeling include Markov chains, martingales, stochastic optimization, coupling and combinatorics. Introduce and apply probability topics such as Markov chains, coupling and Poisson approaches through concrete examples such as those from the stochastic models for information theory, engineering, combinatorics, biology, neuroscience and other areas of application of Probability and Stochastic Processes. Institute of Mathematics ans Statistics (IME) São Paulo main campus 1. Discrete Probability Models; 2. Markov chains; 3. Recurrence and ergodicity; 4. Coupling and limiting behavior; 5. Martingales; 6. Renewal processes; 7. Contemporary Topics: Variable Range, Poisson Approximations, Reliability Theory, and Queue Theory Fabio Prates Machado, Luiz Renato Goncalves Fontes, Miguel Natalio Abadi 50 MAE5703 8 The evaluation will consist of the score’s average of tests and lists of exercises. https://www.ime.usp.br/en