Mathematics & Statistics

Please see the teaching timetable for teaching times and locations!

Student

 

Data Mining by GUHA (3 ECTS)

GUHA (General Unary Hypotheses Automaton) is a method of automatic generation of hypotheses based on empirical data, thus a method of data mining. The course covers the scope of descriptive data mining in general, the GUHA method in particular and the software implementation LISpMiner.

 

  • Language of instruction: English

  • Number of ECTS: 3

  • Course code: MAT-63816

  • Discipline: Mathematics

  • Level of studies: intermediate / advanced

  • Learning outcomes: After this course, students understand the idea of descriptive data mining and the logica foundations of the Guha method and are able to analyze real life matrix form data by the related LISpMiner Software.

  • Evaluation: Exam and a project work

  • Teacher responsible: Esko Turunen

  • Min-max number of students: 10-24

    In questions concerning course content, please contact Esko Turunen: esko.turunen(a)tut.fi

Introduction to R (2 ECTS)

R is one of the most widely used software for statistics and data science. In this course, the students will have the chance to become familiar with basic R objects, operations, visualizations tools and programming. The course will have in-class and online components. The online material (more information here: http://www.uta.fi/cast/events/Ronline.html) should be done before the first day of the course or between the two in-class days of the course. The second in-class day of the course will offer the chance to get a deeper knowledge about R and to analyze own data.

  • Language of instruction: English

  • Number of ECTS: 2

  • Course code: LUOYY027

  • Discipline: Statistics

  • Level of studies: Basic

  • Learning outcomes: After the course the student is familiar with the R environment. Further, the student is familiar with the basic R operations and objects, data exploration and data visualization.

  • Evaluation: Pass/fail

  • Teacher responsible: Paulo Canas Rodrigues

  • Min-max number of students: 10-20

    In questions concerning course content, please contact Paulo Canas Rodrigues: paulo.rodrigues(a)uta.fi

Introduction to Statistics (5 ECTS)

Knowledge about statistical methods and data analysis is of great importance in almost any field of research. In this course, general concepts of statistics will be provided so that the students can be able to independently carry out a small scale empirical research with the statistical software R.

  • Language of instruction: English

  • Number of ECTS: 5

  • Course code: MTTTP1

  • Discipline: Statistics

  • Level of studies: Basic

  • Learning outcomes: After the course, the student should be familiar with the basic concepts of statistics, ranging from descriptive statistics to basic inference (confidence intervals and hypothesis testing) and linear models (linear a logistic regression).

  • Working schedule:

    • Basic concepts

      1. What is statistics?
      2. Statistical research and its phases of work
      3. Population and sample
      4. Types of variables and scales of measurement
    • Descriptive statistics
      1. What is data?
      2. summary statistics (mean, median, quartiles, standard deviation and variance)
      3. Plotting the data (scatter plot, histogram, QQ-plot and boxplot)
      4. Contingency tables
    • Basics of statistical inference
      1. Basic concepts of probability
      2. Probability distributions (Binomial and Normal)
      3. Basic concepts in sampling theory
      4. Confidence intervals (mean and difference of means in independent samples)
      5. Hypothesis testing (mean and equality of means in independent samples, type I and type II-errors and p-values)
      6. Introduction to some non-parametric tests
    • Linear models
      1. Introduction to linear regression
      2. Basics of logistic regression
      3. Basics of Analysis of Variance (ANOVA)
  • Evaluation: Pass/fail

  • Teacher responsible: Paulo Canas Rodrigues

  • Min-max number of students: 10-20

    In questions concerning course content, please contact Paulo Canas Rodrigues: paulo.rodrigues(a)uta.fi

Inverse Problems (5 ECTS)

The course is aimed for students who need to solve inverse and ill-conditioned problems in their work. The participants will learn how to approach a numerical inverse problem in which the data can be predicted via an advanced mathematical forward model and a priori information is needed in finding the solution. In particular, they will learn about the following topics: (1) applications involving inverse problems, (2) forward modeling, (3) inversion methods, (4) statistical approach and prior models, and (5) computed examples (Matlab).

 

  • Language of instruction: English

  • Number of ECTS: 5

  • Course code: MAT-62006

  • Discipline: Mathematics

  • Level of studies: Advanced. The course will be particularly useful for postgraduate-level students who apply mathematical modelling and imaging methodology in their work.

  • Prerequisites: Calculus courses, linear algebra basics, principles of ordinary and partial differential equations.

  • Working methods: This two-week inverse problems course will consist of ten daily lectures (20 h), four exercise sessions (8 h), exam (4 h) and a project work (8 h). The focus will be on numerical inverse problems which today arise in various fields of science and engineering including, for example, applied physics, biomedical and biological imaging, geophysics and signal processing. The emphasis will be on forward modelling, regularization approaches and statistical methods. Each lecture will consists of both theoretical viewpoints and computational examples. A careful demonstration of each example will be given in the exercise sessions. The methods will be also utilized in the project work. Matlab will be used as the programming platform.

  • Evaluation: Exam, exercises and project work

  • Teacher responsible: Sampsa Pursiainen

  • Course material: Jari Kaipio and Erkki Somersalo, Statistical and Computational Inverse Problems, Springer, New York, 2004.

  • Teaching: The course will be organized by the Finnish Centre of Excellence in Inverse Modelling and Imaging.

  • Min-max number of students: 10-24

    In questions concerning course content, please contact Sampsa Pursiainen: sampsa.pursiainen(a)tut.fi