Mathematics for Cognitive Science 2IKVa102
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  MX  Martina Babinská 
Exercise/Lecture  Thursday  13:10  MII  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.
RoseHulman 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.
RoseHulman 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.
RoseHulman 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.
RoseHulman 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.
RoseHulman 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 )  
18.10.  The basics of mathematical analysis: mathematical function (graph vs. formula, constant and linear mathematical functions)  
24.10.  The basics of mathematical analysis: mathematical function (quadratic function)  
25.10.  The basics of mathematical analysis: extremes, monotonicity, boundary  
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”) + Number of already repeated tasks (how many times had been task already repeated)

2 points
5 points (in two weeks) 
 
11.10.  1. EXERCISE 4.1, PAGE 208, PROBLEM 1/Choose two of problems ad
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 
References
 Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
RoseHulman Institute of Technology: Pearson, 2004. Download here;
 Basics of Mathematical Functions: https://www.khanacademy.org/math/algebra/algebrafunctions
 Calculus / Gilbert Strang. Massachusetts Institute of Technology: WellesleyCambridge 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: selfstudy motivation
 weight: 15%
WEEKLY EXAMS AND HOMEWORK
 form: 1015 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.