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{{CourseHeader
 
{{CourseHeader
     | code = 2-IKV-102
+
     | code = 2-IKVa-102
     | title = Mathematics
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     | title = Mathematics for Cognitive Science
 
}}
 
}}
 
__TOC__
 
__TOC__
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!Lecturer
 
!Lecturer
 
|-
 
|-
|Lecture/Excercise
+
|Lecture/Exercise
|Thursday
+
|Tuesday
|09:50
+
|08:10
|M-112
+
|M-I
|[[Martina Koronci Babinska|Martina Koronci Babinská]]
+
|[[Martina Babinská|Martina Babinská]]
 
|-
 
|-
|Excercise/Lecture
+
|Exercise/Lecture
 
|Thursday
 
|Thursday
|14:50
+
|11:30
|M-V
+
|M-III
|[[Martina Koronci Babinska|Martina Koronci Babinská]]
+
|[[Martina Babinská|Martina Babinská]]
 
|}
 
|}
  
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!References
 
!References
 
|-
 
|-
|03.10.
+
|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; [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
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 3
  
 
|-
 
|-
|05.10.
+
|26.09.
|The basics of logic and proving methods: predicate logic.  
+
|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; [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
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|10.10.
+
|01.10.
|The basics of logic and proving methods: the sets of numbers, rationality and irrationality of numbers
+
|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; [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
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|12.10.
+
|03.10.
|The basics of logic and proving methods: mathematical induction
+
|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; [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
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
|}
+
  
 
== Homework ==
 
 
{| class="alternative table-responsive"
 
!Date
 
!Homework
 
!Points
 
!References
 
 
|-
 
|-
|05.10.
+
|08.10.
|1. Choose 1 Exercise from the Exercise 2.1 (page 54).
+
|Mathematical Rows: Sum and multiplication. Mathematical notation.  
  2. Is 0/0 = 0 statement or not? Why
+
| 1 point
+
  1 point
+
 
|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; [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];
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1
  
 
|-
 
|-
|12.10.
+
|10.10.
|1. Choose 2 Exercises from the Exercise 2.4 (page 100).
+
|Proving methods in mathematics: Constructive proof, direct proof and mathematical Induction. Indirect/contrapositive proof. Contradiction.  
| 1 point / exercise
+
 
|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; [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];
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1
 +
 
 
|}
 
|}
  
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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. [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];  
+
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];
Line 101: Line 90:
 
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: 27.10.2017
+
* term: 05.12.2019
 
* goal: self-study motivation
 
* goal: self-study motivation
 
* weight: 15%
 
* weight: 15%
  
WEEKLY EXAMS
+
WEEKLY EXAMS AND HOMEWORK
 
*form: 10-15 minutes writing tests
 
*form: 10-15 minutes writing tests
*term: every Thursday at the beginning of the exercise  
+
*term: every Tuesday at the beginning of the exercise  
 
*goal:  regular preparation  
 
*goal:  regular preparation  
*weight: 40%
+
*weight: 25%
*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
 
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: 16.11.2017
+
*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 2018
+
*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 >