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|-
 
|-
 
|Lecture/Exercise
 
|Lecture/Exercise
|Wednesday
+
|Tuesday
 
|08:10
 
|08:10
|M-VII
+
|M-I
 
|[[Martina Babinská|Martina Babinská]]
 
|[[Martina Babinská|Martina Babinská]]
 
|-
 
|-
 
|Exercise/Lecture
 
|Exercise/Lecture
 
|Thursday
 
|Thursday
|13:10
+
|11:30
|M-VII
+
|M-III
 
|[[Martina Babinská|Martina Babinská]]
 
|[[Martina Babinská|Martina Babinská]]
 
|}
 
|}
Line 39: Line 39:
 
!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; [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
  
 
|-
 
|-
|03.10.
+
|26.09.
|The basics of logic and proving methods: propositional + 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
  
 
|-
 
|-
|04.10.
+
|01.10.
|The basics of logic and proving methods: Sets (sets of numbers, set theory, set operations, the laws of set theory)
+
|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. 3.1, 3.2
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|10.10.
+
|03.10.
|The basics of logic and proving methods: Proving methods (constructive, direct, contrapositive, contradiction, biconditional, 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. 2, 3, 4.1
+
Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2
  
 
|-
 
|-
|11.10.
+
|08.10.
|Counting methods for Rows
+
|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; [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
  
 
|-
 
|-
|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.  
 
+
|-
+
|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.
 
|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.
 
|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];
 
 
|}
 
|}
  
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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 229: 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: 23.11.2017
+
*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 >