# MATA171 Introduction to mathematical analysis 1 (5 cr)

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## 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

- 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 read proofs and follow their logical structure.
- 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.

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### Method 2

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### Teaching (5 cr)

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Lectures (in Finnish) 36 h, exercises

#### Teaching

##### 9/11–10/22/2023 Lectures

##### 11/1–11/1/2023 Exam

##### 11/15–11/15/2023 Exam

### Exam (5 cr)

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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.