# Mathematics for Cognitive Science 2-IKVa-102

## Contents

The lectures will provide students with basics of propositional and predicate logic, linear algebra, mathematical analysis, and probability that are important for the study of informatics and its role in (computational) cognitive science. At the same time, students will learn about mathematical culture, notation, way of thinking and expressing oneself.

## Course schedule

Type | Day | Time | Room | Lecturer |
---|---|---|---|---|

Lecture/Exercise | Tuesday | 08:10 | M-I | Martina Babinská |

Exercise/Lecture | Thursday | 11:30 | M-III | Martina Babinská |

## Syllabus

Date | Topic | References |
---|---|---|

24.09. | Introduction. The set of numbers, cardinality, the set theory. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 3 |

26.09. | The basics of logic and proving methods: statement vs. sentence. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2 |

01.10. | The basics of logic and proving methods: primitive vs. compound statement, conjunction, disjunction, implication, biconditional, quantifiers. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2 |

03.10. | The basics of logic and proving methods: Negation. Logical Equivalence. Contradiction and tautology. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2 |

08.10. | Mathematical Rows: Sum and multiplication. Mathematical notation. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1 |

10.10. | Proving methods in mathematics: Constructive proof, direct proof and mathematical Induction. Indirect/contrapositive proof. Contradiction. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1 |

## References

- Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004. Download here;

- Basics of Mathematical Functions: https://www.khanacademy.org/math/algebra/algebra-functions
- Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. Download here;
- Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. Download here;
- Artificial Intelligence: A Modern Approach / Stuart Russell and Peter Norvig. The USA: Pearson, 2010. Download here;

## Course grading

**To be classified student has to achieve at least 50% of every activity:**

PROJECT

- form: essay, presentation, song or movie
- topic: What does mathematics mean for me? What am I expecting from this course?
- term: 06.12.2018
- goal: self-study motivation
- weight: 15%

WEEKLY EXAMS AND HOMEWORK

- form: 10-15 minutes writing tests
- term: every Wednesday at the beginning of the exercise
- goal: regular preparation
- weight: 20%

ACTIVITY

- form: class work (solving problems and schoolmate’s help)
- term: every lecture and exercise
- goal: regular preparation, cooperation and social activity
- weight: 20%

MIDDLE TERM EXAM

- form: 90 minutes writing test (student can choose from the offered task sets)
- term: 21.11.2017
- goal: progress definition
- weight: 15%

FINAL EXAM

- form: 90 minutes writing test
- term: January, February 2019
- goal: course output
- weight: 30%

**OVERALL GRADING:** A > 90%, B > 80%, C> 70%, D > 60%, E > 52% points.