(Course schedule)
 
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__TOC__
 
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The lectures will provide students with basics of propositional and
+
The lectures will provide students with the basics of propositional and
predicate logic, linear algebra, mathematical analysis, and probability that are important for
+
predicate logic, linear algebra, mathematical analysis, and the probability that are important for
 
the study of informatics and its role in (computational) cognitive science. At the same time,
 
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
 
students will learn about mathematical culture, notation, way of thinking and expressing
Line 21: Line 21:
 
|Lecture/Exercise
 
|Lecture/Exercise
 
|Wednesday
 
|Wednesday
|11:30
+
|14:00 - 15:30
|M-X
+
|MS Teams: FMFI-Mathematics for Cognitive Science
|[[Martina Babinská|Martina Babinská]]
+
|[https://sluzby.fmph.uniba.sk/ludia/slavickova1 Mária Slavíčková]
 
|-
 
|-
 
|Exercise/Lecture
 
|Exercise/Lecture
|Thursday
+
|Wednesday
|13:10
+
|15:45 - 17:15
|M-II
+
|MS Teams: FMFI-Mathematics for Cognitive Science
|[[Martina Babinská|Martina Babinská]]
+
|[https://sluzby.fmph.uniba.sk/ludia/slavickova1 Mária Slavíčková]
 
|}
 
|}
 +
 +
==How to join the course==
 +
I'll use your e-mail addresses from the Academic Information System (AiS) and I add you to the course.  You should find an e-mail concerning the first meeting, please, accept it (no later than 21.9.2020, if not, first check the spam. If you'll not be successful, send me an e-mail). As a student at Comenius University, you have access to MS Office 365 for free. If you are a student on mobility without access to MS Office 365, you can join the lectures via the web. 
  
 
== Syllabus ==
 
== Syllabus ==
 
+
<ol>
{| class="alternative table-responsive"
+
<li>Basics of logic and proving methods: propositional logic, predicate logic, the sets of numbers, proofs. </li>
!Date
+
<li>Basics of mathematical analysis: functions, differential calculus</li>
!Topic
+
<li>Basics of linear algebra: matrices and vectors, operations.Looking forward to meeting you in the lessons </li>
!References
+
<li>Basics of probability: likely and not likely, unconditional and conditional probability </li>
|-
+
</ol>
|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: Proving methods (constructive, direct, contrapositive, contradiction, biconditional, mathematical induction)
+
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2, 3, 4.1
+
 
+
|-
+
|11.10.
+
|Counting methods for Rows (sum and multiplying)
+
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
+
Rose-Hulman Institute of Technology: Pearson, 2004;
+
 
+
|-
+
|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.
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|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.
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|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
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2. Chapter 2.1 / Exercise 2.1 / PROBLEM 5
+
| 1 point
+
1 point
+
| -
+
 
+
|-
+
|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)
+
| -
+
|}
+
  
 
== References ==
 
== References ==
  
* Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
+
* Discrete structures with contemporary applications / Stanoyevitch A. CRC Press, Taylor & Francis Group, 2011.
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];
+
* A First Course in Real Analysis. Second Edition. / Protter, M.H. & Morrey, C.B. Springer-Verlag , 1991.
* Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];
+
* Basics of Mathematical Functions: https://www.khanacademy.org/math/algebra/algebra-functions
* Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here];
+
* [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Calculus] / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press.  
* Artificial Intelligence: A Modern Approach / Stuart Russell and Peter Norvig. The USA: Pearson, 2010. [http://dai.fmph.uniba.sk/courses/ICI/russell-norvig.AI-modern-approach.3rd-ed.2010.pdf Download here];
+
* [https://www.math.ubc.ca/~carrell/NB.pdf Fundamentals of Linear Algebra] / James B. Carrell. Canada: University of British Colombia, 2005.
 +
* Artificial Intelligence: A Modern Approach / Stuart Russell and Peter Norvig. The USA: Pearson, 2010.
  
 
== Course grading ==
 
== Course grading ==
 
<b>To be classified student has to achieve at least 50% of every activity:</b>
 
<b>To be classified student has to achieve at least 50% of every activity:</b>
  
PROJECT 
+
====THREE EXAM TESTS:====
* form: essay, presentation, song or movie
+
*form: 60 minutes writing test
* topic: What does mathematics mean for me? What am I expecting from this course?
+
*terms: to be announced
* term: 06.12.2018
+
*goal: progress definition
* goal: self-study motivation
+
*weight: 20 % each
* weight: 15%
+
  
WEEKLY EXAMS AND HOMEWORK
+
====ATTENDANCE, ACTIVITY====
*form: 10-15 minutes writing tests
+
*form: classwork (solving problems and schoolmate’s help)
*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
 
*term: every lecture and exercise
*goal:  regular preparation, cooperation and social activity
+
*goal:  regular preparation, cooperation, and virtual-social activity
*weight: 20%
+
*weight: 10%
 
+
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
+
====FINAL EXAM====
 
*form: 90 minutes writing test
 
*form: 90 minutes writing test
*term: January, February 2019
+
*term: January, February 2021
 
*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.
 
 
 
== Information list ==
 
{{Infolist|2-IKV-102|Course information sheet >}}
 

Latest revision as of 19:01, 16 September 2020

Mathematics for Cognitive Science 2-IKVa-102

The lectures will provide students with the basics of propositional and predicate logic, linear algebra, mathematical analysis, and the 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 14:00 - 15:30 MS Teams: FMFI-Mathematics for Cognitive Science Mária Slavíčková
Exercise/Lecture Wednesday 15:45 - 17:15 MS Teams: FMFI-Mathematics for Cognitive Science Mária Slavíčková

How to join the course

I'll use your e-mail addresses from the Academic Information System (AiS) and I add you to the course. You should find an e-mail concerning the first meeting, please, accept it (no later than 21.9.2020, if not, first check the spam. If you'll not be successful, send me an e-mail). As a student at Comenius University, you have access to MS Office 365 for free. If you are a student on mobility without access to MS Office 365, you can join the lectures via the web.

Syllabus

  1. Basics of logic and proving methods: propositional logic, predicate logic, the sets of numbers, proofs.
  2. Basics of mathematical analysis: functions, differential calculus
  3. Basics of linear algebra: matrices and vectors, operations.Looking forward to meeting you in the lessons
  4. Basics of probability: likely and not likely, unconditional and conditional probability

References

  • Discrete structures with contemporary applications / Stanoyevitch A. CRC Press, Taylor & Francis Group, 2011.
  • A First Course in Real Analysis. Second Edition. / Protter, M.H. & Morrey, C.B. Springer-Verlag , 1991.
  • Basics of Mathematical Functions: https://www.khanacademy.org/math/algebra/algebra-functions
  • Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press.
  • Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005.
  • Artificial Intelligence: A Modern Approach / Stuart Russell and Peter Norvig. The USA: Pearson, 2010.

Course grading

To be classified student has to achieve at least 50% of every activity:

THREE EXAM TESTS:

  • form: 60 minutes writing test
  • terms: to be announced
  • goal: progress definition
  • weight: 20 % each

ATTENDANCE, ACTIVITY

  • form: classwork (solving problems and schoolmate’s help)
  • term: every lecture and exercise
  • goal: regular preparation, cooperation, and virtual-social activity
  • weight: 10%

FINAL EXAM

  • form: 90 minutes writing test
  • term: January, February 2021
  • goal: course output
  • weight: 30%


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