Mathematical Methods (SL_105)
About Study Course
Objective
This course aims at providing mathematical background for further calculus-based learning of statistics. The main objective of this course is to allow students to understand mathematical concepts that are necessary to follow proofs and reasoning in subsequent courses. Students are not expected to spend much time understanding proofs of calculus theorems, but rather to build intuition of fundamental ideas of calculus and linear algebra, and their role and application in statistics.
Prerequisites
Students must have the necessary mathematical background to understand key statistical techniques and their derivation, if they involve concepts covered in the course. In addition, good knowledge of high school algebra as well as understanding of the notion of a function and its graph.
Learning outcomes
• the student is able to demonstrate deeper knowledge, understands and explains the concepts of limit, derivative, integral, infinite series;
• recognizes and uses the notation of matrices and determinants;
• independently utilize basic methods to do computations involving mathematical objects studied in the course;
• qualitatively describes examples of the practical application of mathematical objects studied in the course, understands how to use them in the research.
• student independently uses limit concept and limit laws to predict the behaviour of a given function;
• finds derivative and indefinite integral of a function, computes definite integral;
• performs computations with matrices and determinants;
• applies rules and methods of mathematical objects studied in the course to solve a practical problem related to these objects.
Students have an comprehension of how calculus generalize pre-calculus mathematics using the limit process and how that can be further integrated to other real-world situations if necessary. Students are competent formulate their tasks into mathematical problems and choose the appropriate method to solve them.
