# MATA132 How to Prove It? (4 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023

## 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

## Additional information

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

**Grading scale:**

0-5

**Language:**

Finnish

**Study methods:**

Lectures 28 h (in Finnish), exercises

#### Teaching

##### 8/28–8/28/2020 Exam

##### 3/23–5/20/2021 Lectures

##### 5/26–5/26/2021 Exam

##### 6/9–6/9/2021 Exam

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

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