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# Mathematics for Cognitive Science 2-IKVa-102

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 08:10 M-VII Martina Babinská
Exercise/Lecture Thursday 13:10 M-VII Martina Babinská

## Syllabus

Date Topic References
27.09. The basics of logic and proving methods: propositional logic. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

03.10. The basics of logic and proving methods: propositional + predicate logic. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

04.10. The basics of logic and proving methods: Sets (sets of numbers, set theory, set operations, the laws of set theory) Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

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; Download here; chap. 2, 3, 4.1

11.10. Counting methods for Rows (sum and multiplying) Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

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
03.10. 1. Choose 1 Exercise from the Exercise 2.1 (page 54).

2. Is 0/0 = 0 statement or not? Why?

1 point

1 point

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

## References

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

• 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;

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: 27.10.2017
• goal: self-study motivation
• weight: 15%

WEEKLY EXAMS

• form: 10-15 minutes writing tests
• term: every Thursday at the beginning of the exercise
• goal: regular preparation
• weight: 40%
• note: student can also achieve extra (bonus) points for: weekly homeworks, class work (solving problems and schoolmate’s help) and/or self-activity (lecture preparation… )

MIDDLE TERM EXAM

• form: 90 minutes writing test (student can choose from the offered task sets)
• term: 23.11.2017
• goal: progress definition
• weight: 15%

FINAL EXAM

• form: 90 minutes writing test
• term: January, February 2018
• goal: course output
• weight: 30%

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