(30 intermediate revisions by 2 users not shown)
Line 5: Line 5:
 
__TOC__
 
__TOC__
  
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 20: Line 20:
 
|-
 
|-
 
|Lecture/Exercise
 
|Lecture/Exercise
|Wednesday
+
|Monday
|08:10
+
|13:10 - 14:40
|M-VII
+
|M112 / 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
 
|Thursday
|13:10
+
|14:50 - 16:20
|M-VII
+
|M112 / 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 add all students who sign up for this course in the AiS (Academic Information System). The MS Teams should send you a notification about it. The course will be held in hybrid form, which means: those who can attend it personally will be present in M112 (pavilion of Mathematics, 1st floor, close to the 1st staircase). Those, who cannot participate personally, can use the link in MS Teams. All materials will be in MS Teams (I'll explain it more in the 1st class). 
  
 
== Syllabus ==
 
== Syllabus ==
 
+
<ol>
{| class="alternative table-responsive"
+
<li>Basics of mathematical analysis: functions, differential calculus</li>
!Date
+
<li>Basics of linear algebra: matrices and vectors, operations </li>
!Topic
+
<li>Basics of probability: likely and not likely, unconditional and conditional probability </li>
!References
+
<li>Basics of propositional and predicate logic </li>
|-
+
</ol>
|27.09.
+
|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; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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.
+
Rose-Hulman Institute of Technology: Pearson, 2004; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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.
+
Rose-Hulman Institute of Technology: Pearson, 2004; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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.
+
Rose-Hulman Institute of Technology: Pearson, 2004; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf Download here]; chap. 2, 3, 4.1
+
 
+
|-
+
|11.10.
+
|Counting methods for Rows
+
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
+
Rose-Hulman Institute of Technology: Pearson, 2004; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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
+
}
+
 
+
 
+
== Homework ==
+
 
+
{| class="alternative table-responsive"
+
!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.
+
Rose-Hulman Institute of Technology: Pearson, 2004; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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.
+
Rose-Hulman Institute of Technology: Pearson, 2004; [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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)
+
| 4 points
+
| Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here]; 
+
 
+
|-
+
|30.11
+
|Find non-homogeneous linear system of 5 equations with 5 variables.
+
Use Gaussian Reduction to find the solution of your system.
+
| 4 points
+
| Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here];
+
 
+
|-
+
|07.12
+
|Try to find (google or book(s)) the explanation of the mathematical term: eigenvalue.
+
Choose any matrix and find its eigenvalues.
+
| 4 points
+
| Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here];
+
|}
+
  
 
== 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. [http://ceiucaweb.com.ar/documentos/6-informatica/3er-anio-2do-cuatri/estructura-de-datos/apunte/Discrete_and_Combinatorial_Mathematics_5th_ed_-_R._Grimaldi.pdf 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: 27.10.2017
+
*goal: progress definition
* goal: self-study motivation
+
*weight: 20 % each
* weight: 15%
+
  
WEEKLY EXAMS
+
====ATTENDANCE, ACTIVITY====
*form: 10-15 minutes writing tests
+
*form: classwork (solving problems and schoolmate’s help)
*term: every Thursday at the beginning of the exercise  
+
*term: every lecture and exercise
*goal:  regular preparation  
+
*goal:  regular preparation, cooperation, and virtual-social activity
*weight: 40%
+
*weight: 10%
*note: student can also achieve extra (bonus) points for: weekly homeworks, class work (solving problems and schoolmate’s help) and/or self-activity (lecture preparation… )
+
  
MIDDLE TERM EXAM
+
====FINAL EXAM====
*form: 90 minutes writing test (student can choose from the offered task sets)
+
*term: 23.11.2017
+
*goal: progress definition
+
*weight: 15%
+
 
+
FINAL EXAM
+
 
*form: 90 minutes writing test
 
*form: 90 minutes writing test
*term: January, February 2018
+
*term: January, February 2022
 
*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.
 
 
  
  
== Information list ==
+
<b>OVERALL GRADING:</b>  A > 90%, B > 80%, C> 70%, D > 60%, E > 52%
{{Infolist|2-IKV-102|Course information sheet >}}
+

Latest revision as of 08:53, 16 September 2021

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 Monday 13:10 - 14:40 M112 / MS Teams: FMFI-Mathematics for Cognitive Science Mária Slavíčková
Exercise/Lecture Thursday 14:50 - 16:20 M112 / MS Teams: FMFI-Mathematics for Cognitive Science Mária Slavíčková

How to join the course

I'll add all students who sign up for this course in the AiS (Academic Information System). The MS Teams should send you a notification about it. The course will be held in hybrid form, which means: those who can attend it personally will be present in M112 (pavilion of Mathematics, 1st floor, close to the 1st staircase). Those, who cannot participate personally, can use the link in MS Teams. All materials will be in MS Teams (I'll explain it more in the 1st class).

Syllabus

  1. Basics of mathematical analysis: functions, differential calculus
  2. Basics of linear algebra: matrices and vectors, operations
  3. Basics of probability: likely and not likely, unconditional and conditional probability
  4. Basics of propositional and predicate logic

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 2022
  • goal: course output
  • weight: 30%


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