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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 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: Quantifiers, its negations and truth values Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2.4

11.10. Mathematical Induction and counting with rows (sum and multiplication) Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1

17.10. The basics of mathematical analysis: mathematical function vs dependency (definition, mathematical functions in the real world ) Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
18.10. The basics of mathematical analysis: mathematical function (graph vs. formula, constant and linear mathematical functions) Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
24.10. The basics of mathematical analysis: mathematical function (quadratic function) Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
25.10. The basics of mathematical analysis: extremes, monotonicity, boundary Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
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

Discrete and combinatorial mathematics: An applied introduction
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”)

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)

-
11.10. 1. EXERCISE 4.1, PAGE 208, PROBLEM 1/Choose two of problems a-d

2. EXERCISE 4.1, PAGE 208, PROBLEM 8

4 points

2 points

Discrete and combinatorial mathematics: An applied introduction
17.10. Based on the graph (see slides from the lecture) describes the

changes which can be caused if a man: is not smoking OR is smoking OR quit smoking during his life. Write as many information as you can.

4 points Slides from the lecture
18.10. Find the graph and a general formula for an absolute value function. 2 points
24.10. Find the graph, domain, range, axis intercepts

and vertex of a quadratic function: r: R → R, y = (x + a) 2 + b

2 points