# 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 | Wednesday | 11:30 | M-X | Martina Babinská |

Exercise/Lecture | Thursday | 13:10 | M-II | Martina Babinská |

## Syllabus

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

27.09. | Introduction, The basics of logic and proving methods: propositional logic. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004;chap. 2.1 |

03.10. | The basics of logic and proving methods: primitive vs. compound statement, conjunction, disjunction, implication, biconditional. Its truth values and negations | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004;chap. 2.1 |

04.10. | The basics of logic and proving methods: Proving methods in propositional logic, Sets (sets of numbers, cardinality of a set, custom and general sets) | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2.2, 2.3 |

10.10. | The basics of logic and proving methods: Proving methods (constructive, direct, contrapositive, contradiction, biconditional, mathematical induction) | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2, 3, 4.1 |

11.10. | Counting methods for Rows (sum and multiplying) | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; |

17.10. | The basics of mathematical analysis: mathematical function vs dependency (definition, mathematical functions in the real world ) | |

18.10. | The basics of mathematical analysis: mathematical function (graph vs. formula, basic mathematical functions, basic characteristics) | |

24.10. | The basics of mathematical analysis: mathematical function (quadratic function, monotonicity, boundary, extremes) | |

25.10. | The basics of mathematical analysis: mathematical function (continuity, limit) | |

31.10. | The basics of mathematical analysis: calculus (the rate of change, derivative definition, derivative in the real world) | |

07.11. | The basics of mathematical analysis: calculus (derivative counting rules) | |

08.11. | The basics of mathematical analysis: calculus (maximum and minimum problem, convex and concave problem) | |

14.11. | The basics of mathematical analysis: calculus (the chain rule, functions’ characteristics in a view of derivative) | |

15.11. | Repeating and practicing class | |

21.11. | Middle term writing test | |

22.11. | The basics of linear algebra: The basic problem of linear algebra (matrix and vector) | |

28.11. | The basics of linear algebra: The basic problem of linear algebra (vector operations, linear combination) | |

29.11. | The basics of linear algebra: Matrices (basic operations) | |

05.12. | The basics of linear algebra: Matrices (Gaussian Reduction) | |

06.12. | The basics of linear algebra: Matrices (advanced operations) | |

12.12. | The basics of linear algebra: Matrices (eigenvalues, eigenvectors) | |

13.12. | The basics of probability: Introduction (probability in the real world, definition) | |

13.12. | The basics of probability: Introduction (counting basics) | |

20.12. | Repeating and practicing |

## Homework

Date | Homework | Points | References |
---|---|---|---|

23.09. | 1. Find and explain IDEAL NUMBERS
2. Decide, if the statement is true or false ∀ y ∈ R ∃ x ∈ R: y = x^2 ∃ x ∈ R ∀ y ∈ R: y = x^2 ∃ y ∈ R ∀ x ∈ R: y = x^2 ∃ x ∈ R ∃ y ∈ R: y = x^2 |
1 point
2 points |
- |

03.10. | 1. Chapter 2.1 / Exercise 2.1 / PROBLEM 4
2. Chapter 2.1 / Exercise 2.1 / PROBLEM 5 |
1 point
1 point |
- |

04.10. | 1. Find (google) DE MORGAN’S LAWS. What does these laws represent? How can we prove them?
2. Help developers: The problem of REPEATING TASKS Repeating task is a task created from its parent task every few (n) days. Repeating rules have the next parameters: Date of the last repeat Maximum number of repeats Number of days for repeat (n) (“repeat task every 5 days”) Number of already repeated tasks (how many times had been task already repeated) What condition have developer put to the computer to repeat parent task every requested day? Find Symbolic form of your solution |
2 points
5 points (in two weeks) |
- |

## References

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

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

- 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.