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|-
 
|-
 
|Lecture/Exercise
 
|Lecture/Exercise
|Wednesday
+
|Tuesday
|11:30
+
|08:10
|M-X
+
|M-I
 
|[[Martina Babinská|Martina Babinská]]
 
|[[Martina Babinská|Martina Babinská]]
 
|-
 
|-
 
|Exercise/Lecture
 
|Exercise/Lecture
 
|Thursday
 
|Thursday
|13:10
+
|11:30
|M-II
+
|M-III
 
|[[Martina Babinská|Martina Babinská]]
 
|[[Martina Babinská|Martina Babinská]]
 
|}
 
|}
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!References
 
!References
 
|-
 
|-
|27.09.
+
|24.09.
|Introduction, The basics of logic and proving methods: propositional logic.  
+
|Introduction. The set of numbers, cardinality, the set theory.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004;chap. 2.1
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 3
  
 
|-
 
|-
|03.10.
+
|26.09.
|The basics of logic and proving methods: primitive vs. compound statement, conjunction, disjunction, implication, biconditional. Its truth values and negations
+
|The basics of logic: statement vs. sentence.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004;chap. 2.1
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|04.10.
+
|01.10.
|The basics of logic and proving methods: Proving methods in propositional logic, Sets (sets of numbers, cardinality of a set, custom and general sets)
+
|The basics of logic: primitive vs. compound statement, conjunction, disjunction, implication, biconditional, quantifiers.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2.2, 2.3
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|10.10.
+
|03.10.
|The basics of logic and proving methods: Quantifiers, its negations and truth values
+
|The basics of logic: Negation. Logical Equivalence. Contradiction and tautology.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2.4
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|11.10.
+
|08.10.
|Mathematical Induction and counting with rows (sum and multiplication)
+
|Mathematical Rows: Sum and multiplication. Mathematical notation.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1
 
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1
  
 
|-
 
|-
|17.10.
+
|10.10.
|The basics of mathematical analysis: mathematical function vs dependency (definition, mathematical functions in the real world )
+
|Proving methods in mathematics: Constructive proof, direct proof and mathematical Induction. Indirect/contrapositive proof. Contradiction.  
 
+
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
|-
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1
|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 ==
 
 
{| class="alternative table-responsive"
 
!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)
 
 
 
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)
 
| -
 
 
|}
 
|}
  
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* Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
* Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
 
Rose-Hulman Institute of Technology: Pearson, 2004. [https://www.scribd.com/doc/119851254/Discrete-and-Combinatorial-Mathematics-An-Applied-Introduction-5th-Ed-R-Grimaldi-Pearson-2004-WWW Download here];  
 
Rose-Hulman Institute of Technology: Pearson, 2004. [https://www.scribd.com/doc/119851254/Discrete-and-Combinatorial-Mathematics-An-Applied-Introduction-5th-Ed-R-Grimaldi-Pearson-2004-WWW Download here];  
 +
* Basics of Mathematical Functions: https://www.khanacademy.org/math/algebra/algebra-functions
 
* Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  
 
* Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  
 
* Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here];
 
* Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here];
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PROJECT   
 
PROJECT   
 
* form: essay, presentation, song or movie
 
* form: essay, presentation, song or movie
* topic: What does mathematics mean for me? What am I expecting from this course?  
+
* topic: Me and Mathematics: what does mathematics mean for me?  
* term: 06.12.2018
+
* term: 05.12.2019
 
* goal: self-study motivation
 
* goal: self-study motivation
 
* weight: 15%
 
* weight: 15%
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WEEKLY EXAMS AND HOMEWORK
 
WEEKLY EXAMS AND HOMEWORK
 
*form: 10-15 minutes writing tests
 
*form: 10-15 minutes writing tests
*term: every Wednesday at the beginning of the exercise  
+
*term: every Tuesday at the beginning of the exercise  
 
*goal:  regular preparation  
 
*goal:  regular preparation  
*weight: 20%
+
*weight: 25%
 
+
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
 
MIDDLE TERM EXAM
 
*form: 90 minutes writing test (student can choose from the offered task sets)
 
*form: 90 minutes writing test (student can choose from the offered task sets)
*term: 21.11.2017
+
*term: 12.11.2019
 
*goal: progress definition
 
*goal: progress definition
 +
*weight: 15%
 +
 +
ATTENDANCE, ACTIVITY (bonus points. max 15%)
 +
*form: class work (solving problems and schoolmate’s help)
 +
*term: every lecture and exercise
 +
*goal:  regular preparation, cooperation and social activity
 
*weight: 15%
 
*weight: 15%
  
 
FINAL EXAM
 
FINAL EXAM
 
*form: 90 minutes writing test
 
*form: 90 minutes writing test
*term: January, February 2019
+
*term: January, February 2020
 
*goal: course output   
 
*goal: course output   
 
*weight: 30%
 
*weight: 30%
 +
  
 
<b>OVERALL GRADING:</b>  A > 90%, B > 80%, C> 70%, D > 60%, E > 52% points.
 
<b>OVERALL GRADING:</b>  A > 90%, B > 80%, C> 70%, D > 60%, E > 52% points.

Latest revision as of 09:49, 10 October 2019

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 Tuesday 08:10 M-I Martina Babinská
Exercise/Lecture Thursday 11:30 M-III Martina Babinská

Syllabus

Date Topic References
24.09. Introduction. The set of numbers, cardinality, the set theory. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 3

26.09. The basics of logic: statement vs. sentence. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2

01.10. The basics of logic: primitive vs. compound statement, conjunction, disjunction, implication, biconditional, quantifiers. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2

03.10. The basics of logic: Negation. Logical Equivalence. Contradiction and tautology. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2

08.10. Mathematical Rows: Sum and multiplication. Mathematical notation. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

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

10.10. Proving methods in mathematics: Constructive proof, direct proof and mathematical Induction. Indirect/contrapositive proof. Contradiction. Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

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

References

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

Rose-Hulman Institute of Technology: Pearson, 2004. 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: Me and Mathematics: what does mathematics mean for me?
  • term: 05.12.2019
  • goal: self-study motivation
  • weight: 15%

WEEKLY EXAMS AND HOMEWORK

  • form: 10-15 minutes writing tests
  • term: every Tuesday at the beginning of the exercise
  • goal: regular preparation
  • weight: 25%

MIDDLE TERM EXAM

  • form: 90 minutes writing test (student can choose from the offered task sets)
  • term: 12.11.2019
  • goal: progress definition
  • weight: 15%

ATTENDANCE, ACTIVITY (bonus points. max 15%)

  • form: class work (solving problems and schoolmate’s help)
  • term: every lecture and exercise
  • goal: regular preparation, cooperation and social activity
  • weight: 15%

FINAL EXAM

  • form: 90 minutes writing test
  • term: January, February 2020
  • goal: course output
  • weight: 30%


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


Information list

Course information sheet >