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|The basics of logic and proving methods: propositional logic.  
 
|The basics of logic and proving methods: propositional logic.  
 
|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. 2.1
  
 
|-
 
|-
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|The basics of logic and proving methods: propositional + predicate logic.  
 
|The basics of logic and proving methods: propositional + predicate logic.  
 
|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. 2.2, 2.4
  
 
|-
 
|-
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|The basics of logic and proving methods: Sets (sets of numbers, set theory, set operations, the laws of set theory)
 
|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.
 
|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
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 3.1, 3.2
  
 
|-
 
|-
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|The basics of logic and proving methods: Proving methods (constructive, direct, contrapositive, contradiction, biconditional, mathematical induction)  
 
|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.
 
|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
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2, 3, 4.1
  
 
|-
 
|-
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|Counting methods for Rows (sum and multiplying)
 
|Counting methods for Rows (sum and multiplying)
 
|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;
  
 
|-
 
|-
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|-
 
|-
 
|03.10.
 
|03.10.
|1. Choose 1 Exercise from the Exercise 2.1 (page 54).
+
|1.  
2. Is 0/0 = 0 statement or not? Why?
+
2.  
 
| 1 point
 
| 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];
 
 
|}
 
|}
  
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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];  
 
* 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];

Revision as of 15:08, 27 September 2018

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 Wednesday 08:10 M-VII Martina Babinská
Exercise/Lecture Thursday 13:10 M-VII Martina Babinská

Syllabus

Date Topic References
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;chap. 2.1

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;chap. 2.2, 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; 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; 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. 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

Date Homework Points References
03.10. 1.

2.

1 point

References

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

Rose-Hulman Institute of Technology: Pearson, 2004. Download here;

  • Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge 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: 06.12.2018
  • goal: self-study motivation
  • weight: 15%

WEEKLY EXAMS AND HOMEWORK

  • form: 10-15 minutes writing tests
  • 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
  • goal: regular preparation, cooperation and social activity
  • weight: 20%

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

  • form: 90 minutes writing test
  • term: January, February 2019
  • goal: course output
  • weight: 30%

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


Information list

Course information sheet >