# MATA171 Introduction to mathematical analysis 1 (5 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Inequalities, functions, supremum and infimum (least upper bound and greatest lower bound), completeness of real number system, limit of a sequence and the algebraic properties of limit, monotonic sequences.

In this study-module, students practice reading and writing mathematics. They learn basics of logic and practice proving mathematical statements.

## Learning outcomes

The student
• knows the epsilon-definition for the limit of a number sequence, and can prove simple statements using that definition.
• is able to use the algebraic properties of limit to study the convergence of sequences
• knows how to apply the convergence criteria for monotonic sequences
• is familiar with the definitions of supremum and infimum, and can determine the supremum and infimum of a given set
• can use inequalities to estimate the size of a given expression
• is familiar with the basic terminology associated to functions
• can produce simple proofs

## Description of prerequisites

Good command of the long mathematics curriculum of high school.

## Study materials

The contents of the study-module correspond to:

D. Brannan: A first course in mathematical analysis, chap. 1-2, or

P. Fitzpatrick: Advanced Calculus, chap. 1-2.

## Completion methods

### Method 1

Description:
Final exam and exercises. The weekly exercises are handed in and graded. To attend the final exam, the students must receive enough bonus-points from the exercises (the exact amount is mentioned in the teaching schedule).
Evaluation criteria:
Final exam and weekly exercises.
Time of teaching:
Period 1
Select all marked parts

### Method 2

Description:
Final exam.
Evaluation criteria:
Final exam score.
Select all marked parts
Parts of the completion methods
x

### Teaching (5 cr)

Type:
Participation in teaching
0-5
Language:
Finnish
Study methods:

Lectures (in Finnish) 36 h, exercises

x

Type:
Exam