Mathematical Tools for Research, using R

April 3-7, 2017

Application form
Application deadline: 08.03.17

Course description


The goal of this course is to provide the course participants with knowledge of the essential mathematical tools needed for understanding methodologies used in a wide variety of research areas. The course has the parallel aim of familiarizing participants with the programming language R, which provides a perfect practical tool to illustrate the mathematical concepts taught in the course.
 
The course “Mathematical Tools for Research, using R" aims to refresh mathematical concepts which are required for the understanding and the application of recent developments in the methodology of empirical research. It covers the fundamentals of Mathematics (functions, linear algebra, calculus and optimization); focusing on the understanding of the concepts. Instead of pursuing a formal approach, this course aims to familiarize the participants with what we consider essential and useful mathematical knowledge. In this way we hope to remove the commonly experienced uncertainty when students are dealing with mathematical concepts and expositions in their research.

A crucial aspect of this workshop is the active use of the open-source programming language R. Since its introduction in the nineties R has become a de-facto standard for research computing. As such, this workshop combines communicating mathematical concepts with an introduction and the active application of R: both are learnt in parallel.

The course sessions basically comprise two parts that are continuously alternating; the “theoretical part” covers the mathematical explanations while the “applied part” re-elaborates and reinforces the theoretical part by actively using R. Thus the course lays the foundation for advanced empirical research methodology by covering the theoretical background as well as providing the participants with an active knowledge of R.


Course prerequisites

The only pre-requisite for the workshop is the motivation to learn (or to repeat) the fundamentals of Mathematics and R. Familiarity with R is not a prerequisite. In case you wish to work on your own computer, downloading and installing R (http://cran.r-project.org) and Rstudio (http://rstudio.org) prior to the course is strongly suggested. Participants are encouraged to play around with the software before the course in order to get a feeling for it. 

Preliminary timetable

 Monday
3.4.2017
Tuesday
4.4.2017
Wednesday
5.4.2017
Thursday
6.4.2017
Friday
7.4.2017
9.00 – 12.00

 

13.00 –16:00
 

Introduction to Mathematics and R

 

·   The language and notation of Mathematics

 

·   The language and notation of R

 

 

Functions and their properties

 

·   An anthology of functions

 

·   Drawing functions in R

 

·   Properties of functions

 

 
 

Linear algebra

 

·   Linear functions

 

·  Matrices and vectors

 

·   Manipulating matrices and vectors

 

·  Special matrix transformations, such as rotation and projection

 

·  Eigenvalues and eigenvectors

 

·  Singular value decomposition

 

 

 
 

Calculus

 

·  Derivatives of scalar functions

 

· Derivatives of vector and matrix functions

 

· Second derivatives

 

·  Intepretation of derivatives

 

·  Introduction to optimization of a function of a single variable

 

·  Integration and its practical meaning

 
 

Optimization (continued)

 

·  Optimization of a function of two or more variables

 

·  Optimization of vector-valued functions

 

·  Gradient-based methods of optimization

·  Gradient-free algorithms for optimization

·  Regression analysis as an optimization problem: least-squares and maximum likelihood estimation

 

 
 

Mathematical applications (preliminary list, can be extended/ substituted on demand)

 

·  Generalized linear models

 

·  Principal component analysis

 

·  Factor analysis and structural equation modelling

 

·  Cluster analysis

 

·  Network analysis

General summary and discussion

 

 

 

Reading list

A copy of the companion workshop notes will be provided to the participants:
  • Greenacre, M. and Nenadić, O. (2015): “Mathematical Tools for Social Scientists: An Introduction with R”, forthcoming.

Optional literature:

  • Sydsæter, K., Hammond, P. and Strom, A. (2012): “Essential Mathematics for Economic Analysis”, 4th ed., Pearson.
  • Sydsæter, K., Hammond, P., Seierstad, A. and Strom, A. (2008): “Further Mathematics for Economic Analysis”, 2nd ed., Pearson.
  • Dalgaard, P. (2008): “Introductory Statistics with R”, Springer.

Course presenters


Michael Greenacre is professor of Statistics at the Universitat Pompeu Fabra, Barcelona., specializing in multivariate data analysis, principally in the social and environmental sciences. Apart from more than 60 published articles in international journals (see http://www.researcherid.com/rid/D-7401-2013) he has written five books on correspondence analysis and related methods and co-edited four books (with Jörg Blasius) on data visualization. He has given short courses in 15 countries in Europe, north and south America, Africa and Australia.

Oleg Nenadić is presently Akademischer Rat at the University of Göttingen and has been a visiting professor at the universities of Göttingen and Erfurt. His interest lies in Applied Statistics across various disciplines such as Economics, Social Sciences and Biology, and his main focus is on Computational Statistics with the statistical software environment R (http://www.r-project.org). He is author of a number of R-packages and has given workshops on R on four continents