Study Guide

Objective

The student learns fundamental mathematical concepts, principles, tools (including computing environments) and terminology of statistics, probability and optimization for professional studies.

Content

Theory of statistics and probability
- Numerical and graphical description of data
- Probability, probability rules and theorems, probability distribution
- Modeling, parameter estimation
- Model selection, decision theory
- Analysis task types

Optimization, differential calculus and numerical computation
- Objective function
- Critical points, extrema
- Types of optimization problems
- Limit, derivative, partial derivative, differentiation rules
- Iterative gradient-based optimization methods, derivative-free methods

Location and time

Spring term 2025, Lapland University of Applied Sciences, Rantavitikka campus (Rovaniemi, Jokiväylä 11)

Materials

Study material is available as an eBook and on the Moodle learning platform.

Teaching methods

Lessons and exercises

Exam schedules

The number and date of exams will be agreed on during the course. Resit is possible by the end of the next term.

Completion alternatives

Studying independently is possible. All exercises must be returned in time to be evaluated.

Evaluation scale

H-5

Assessment criteria, satisfactory (1)

Assessment criteria - grade 1
The student knows the concepts of probability, statistics, and optimization and is able to solve basic problems.

Assessment criteria, good (3)

Assessment criteria - grade 3
The student understands the concepts of probability, statistics, and optimization and is able to solve varied problems related to applications of probability, statistics, and optimization.

Assessment criteria, excellent (5)

The student understands the concepts of probability, statistics, and optimization and is able to apply methods of probability, statistics, and optimization in solving and handling new types of problems.

Assessment methods and criteria

Evaluation is based on exercises (homework) and/or exams. The emphasis on these will be agreed upon at the beginning of the course.

Assessment criteria, fail (0)

Student doesn't meet the basic requirements of grade 1.

Assessment criteria, satisfactory (1-2)

Student knows the basic concepts of probability, statistics, and optimization, and is able to solve basic problems.

Assessment criteria, good (3-4)

Student understands more complicated concepts of probability, statistics, and optimization, and is capable of solving versatile exercises. Student uses correct mathematical language and can create logical solutions.

Assessment criteria, excellent (5)

Student is capable of applying concepts of probability, statistics, and optimization to new problems and solve them in exact mathematical language.