Mathematics 2IKV102
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/Excercise  Thursday  09:50  M112  Martina Koronci Babinská 
Excercise/Lecture  Thursday  14:50  MV  Martina Koronci Babinská 
Syllabus
Date  Topic  References 

03.10.  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; Download here; chap. 2.1, 2.2 
05.10.  The basics of logic and proving methods: predicate logic.  Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
RoseHulman Institute of Technology: Pearson, 2004; Download here; chap. 2.4 
12.10.  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 
12.10.  The basics of logic and proving methods: Proofs (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 
19.10.  The basics of mathematical analysis: Functions (definition, graph, characteristics, basic mathematical functions, functions in the real word)  
26.10. I  The basics of mathematical analysis: Basic function's characteristics in the definitions (domain, range, monotonicity, boundaries, extremes, continuity, infimum, supremum).
 
26.10. II  The basics of mathematical analysis: Limit of a function (the real word problem, definition, oneside limit)  Calculus / Gilbert Strang. Massachusetts Institute of Technology: WellesleyCambridge Press. Download here; 
02.11.  The basics of mathematical analysis: The rate of change  derivative (the real word problem, definition, basic functions derivatives, formulas and calculating rules)  Calculus / Gilbert Strang. Massachusetts Institute of Technology: WellesleyCambridge Press. Download here; 
09.11. I  The basics of mathematical analysis: Minimum/maximum problem and Convex/Concave problem in case of derivatives  Calculus / Gilbert Strang. Massachusetts Institute of Technology: WellesleyCambridge Press. Download here;

09.11. II  The basics of mathematical analysis: The Chain Rule  Calculus / Gilbert Strang. Massachusetts Institute of Technology: WellesleyCambridge Press. Download here; 
Homework
Date  Homework  Points  References 

05.10.  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.
RoseHulman Institute of Technology: Pearson, 2004; Download here; 
12.10.  1. Choose 2 Exercises from the Exercise 2.4 (page 100).  1 point / exercise  Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
RoseHulman Institute of Technology: Pearson, 2004; Download here; 
19.10  Find/create the open statement which is possible to prove by mathematical induction.
Prove the statement and use the proof to explain the principle of mathematical induction. 
3 points  
26.10  1. Take the FEV1 Spirometry graph in time (Morning Lecture, slide 27). Based on that graph write as many information as you can.
2. Find the quadratic function characteristics. 
2  4 points
2 points  
02.11  Find derivatives:
1. y = (x + 5)*x^2 2. y = log(2)x – 5x + 7x^5 3. y = sin x / cos x 4. y = (3x + 5^x – 6)/(ln x + e^x) 
4 points  
09.11  Find the local and global extremes of a function. Create the graph of that function: y = x2 / (1 – x2)
(you can check your answer on a page 115) 
Calculus / Gilbert Strang. Massachusetts Institute of Technology: WellesleyCambridge Press. Download here;  4 points 
References
 Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
RoseHulman Institute of Technology: Pearson, 2004. Download here;
 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: 27.10.2017
 goal: selfstudy motivation
 weight: 15%
WEEKLY EXAMS
 form: 1015 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 selfactivity (lecture preparation… )
MIDDLE TERM EXAM
 form: 90 minutes writing test (student can choose from the offered task sets)
 term: 16.11.2017
 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.