# MATA132 How to Prove It? (4 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

Mathematical reasoning and logic. Direct proof, proof by contradiction and proof by induction. Negating statements. Sets, functions, and cardinality.

## Learning outcomes

The student
• knows the basics of logic, set theory and functions
• understands why statements are proved in mathematics
• knows basic proof methods (direct proof, proof by contradiction, proof by induction) and is able to apply them
• can negate mathematical statements
• knows how to read, write and evaluate proofs

The study module is recommended for students that have completed Calculus 1-3 before taking Introduction to mathematical analysis 1-4.

## Description of prerequisites

Good command of the long mathematics curriculum of high school.

## Study materials

Richard Hammack: Book of proof

J. Franklin, A. Daoud: Proof in Mathematics, An introduction

## Completion methods

### Method 1

Description:
Final exam and exercises.
Evaluation criteria:
Final exam and exercises.
Time of teaching:
Period 4
Select all marked parts

### Method 2

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

### Teaching (4 cr)

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

Lectures 28 h (in Finnish), exercises

x

### Exam (4 cr)

Type:
Exam
0-5
Language:
English, Finnish
Study methods:

Independent study and final exam.

Study materials:

Richard Hammack: Book of proof

J. Franklin, A. Daoud: Proof in Mathematics, An introduction