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  08:10  MVII  Martina Babinská 
Exercise/Lecture  Thursday  13:10  MVII  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.
RoseHulman Institute of Technology: Pearson, 2004; Download here; chap. 2.1, 2.2  
03.10.  The basics of logic and proving methods: propositional + predicate logic.  Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
RoseHulman Institute of Technology: Pearson, 2004; Download here; chap. 2.4  
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.
RoseHulman Institute of Technology: Pearson, 2004; Download here; chap. 3.1, 3.2  
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.
RoseHulman 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.
RoseHulman Institute of Technology: Pearson, 2004; Download here;  
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
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Homework
