Measure and Integral Theory 360-MS2-1TM

Educational profile: general academic

Form of studies: full-time

Compulsory subject

Field: exact and natural sciences, discipline: mathematics

Year of study: 1, semester: 1

Pre-props: none

lecture 30 hours exercises 30 hours

Didactic methods: lectures, calculating exercises, consultations, work on literature, solving homework, discussions in problem groups.

ECTS credits: 6

Balance of student workload:

participation in lectures 15x2h = 30h

participation in exercises 15x3h = 30h

preparation for classes 10x3h = 30h

completing solving tasks started during the exercises and preparing notes at home after the classes (lectures, exercises) 7x2h = 14h

participation in consultations 12x1h = 12h

preparation for the exam and participation in it 16h + 4h = 20h

preparation for tests 3x4h = 12h

solving homework 6x2h = 12h

Quantitative indicators

student workload related to classes requiring the direct participation of an academic teacher: 76 hours, 3 ECTS

Type of course

obligatory courses

Prerequisites (description)

Objectives and objectives of the course: After completing the course, the student should: understand the difference, and more precisely the advantage of the Lebesgue integral over the Riemann integral; see and distinguish metric structures, including structures on family sets; know and be able to use the basic theorems about crossing the boundary into the integral and the Radon-Nikodym theorem; as well as understand the basic literature on the subject, including the ability to independently deepen and expand knowledge in a given field.

Course coordinators

Bartosz Kwaśniewski

Learning outcomes

Understands differences and the advantage of the Lebesgue integral over the Riemann integral; knows the basic properties of the Lebesgue integral. He knows the basic theorems about crossing the boundary under the sign of the integral and the Radon-Nikodym theorem; understand the Radon-Nikodym derivative. He can calculate integrals of simple functions with respect to abstract measures. He can distinguish between metric structures, including structures on families of sets. He can apply the basic theorems about crossing the limit into the integral sign.

KA7_WG03, KA7_UW02, KA7_UW07

Assessment criteria

General form of credit: exam and tests

Bibliography

P. Halmos, Measure theory, van Nostrand, Princeton, 1956.

S. Łojasiewicz, Wstęp do teorii funkcji rzeczywistych, PWN, 1987

W. Rudin, Analiza rzeczywista i zespolona, PWN, Warszawa, 2009.

A. Birkholc Analiza matematyczna. Funkcje wielu zmiennych, PWN 1986.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 360-MS2-1TM in USOSweb