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Riadok 1: Riadok 1:
 
{{CourseHeader
 
{{CourseHeader
     | code = 2-IKV-102
+
     | code = 2-IKVa-102
     | title = Mathematics
+
     | title = Mathematics for Cognitive Science
 
}}
 
}}
 
__TOC__
 
__TOC__
Riadok 19: Riadok 19:
 
!Lecturer
 
!Lecturer
 
|-
 
|-
|Lecture/Excercise
+
|Lecture/Exercise
|Thursday
+
|Wednesday
|09:50
+
|11:30
|M-112
+
|M-X
|[[Martina Koronci Babinska|Martina Koronci Babinská]]
+
|[[Martina Babinská|Martina Babinská]]
 
|-
 
|-
|Excercise/Lecture
+
|Exercise/Lecture
 
|Thursday
 
|Thursday
|14:50
+
|13:10
|M-V
+
|M-II
|[[Martina Koronci Babinska|Martina Koronci Babinská]]
+
|[[Martina Babinská|Martina Babinská]]
 
|}
 
|}
  
Riadok 38: Riadok 38:
 
!Topic
 
!Topic
 
!References
 
!References
 +
|-
 +
|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.
 
|03.10.
|Introduction. The basics of logic and proving methods: propositional logic.  
+
|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.
 
|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
  
 
|-
 
|-
|05.10.
+
|04.10.
|The basics of logic and proving methods: predicate logic.
+
|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.
 
|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, 2.3
  
 
|-
 
|-
|12.10.
+
|10.10.
|The basics of logic and proving methods: Sets (sets of numbers, set theory, set operations, the laws of set theory)
+
|The basics of logic and proving methods: Quantifiers, its negations and truth values
 
|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. 2.4
  
 
|-
 
|-
|12.10.
+
|11.10.
|The basics of logic and proving methods: Proofs (constructive, direct, contrapositive, contradiction, biconditional, mathematical induction)  
+
|Mathematical Induction and counting with rows (sum and multiplication)
 
|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. 4.1
  
 
|-
 
|-
|19.10.
+
|17.10.
|The basics of mathematical analysis: Functions (definition, graph, characteristics, basic mathematical functions, functions in the real word)
+
|The basics of mathematical analysis: mathematical function vs dependency (definition, mathematical functions in the real world )
 +
| Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
  
 
|-
 
|-
|26.10. I
+
|18.10.  
|The basics of mathematical analysis: Basic function's characteristics in the definitions (domain, range, monotonicity, boundaries, extremes, continuity, infimum, supremum).
+
|The basics of mathematical analysis: mathematical function (graph vs. formula, constant and linear mathematical functions)
 
+
| Slides from the lecture,  https://www.khanacademy.org/math/algebra/algebra-functions
  
 
|-
 
|-
|26.10. II
+
|24.10.  
|The basics of mathematical analysis: Limit of a function (the real word problem, definition, one-side limit)  
+
|The basics of mathematical analysis: mathematical function (quadratic function)  
|Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  chap. 1.1, 1.2, 1.3, 2.1
+
|Slides from the lecture,  https://www.khanacademy.org/math/algebra/algebra-functions
  
 
|-
 
|-
|02.11.
+
|25.10.  
|The basics of mathematical analysis: The rate of change - derivative (the real word problem, definition, basic functions derivatives, formulas and calculating rules)
+
|The basics of mathematical analysis: extremes, monotonicity, boundary
|Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  chap. 2.2, 2.3, 2.4, 2.5
+
|Slides from the lecture,  https://www.khanacademy.org/math/algebra/algebra-functions
  
 
|-
 
|-
|09.11. I
+
|31.10.  
|The basics of mathematical analysis: Minimum/maximum problem and Convex/Concave problem in case of derivatives
+
|The basics of mathematical analysis: calculus (the rate of change, derivative definition, derivative in the real world)
|Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  chap. 3.2, 3.3, 3.4
+
  
 
|-
 
|-
|09.11. II
+
|07.11.  
|The basics of mathematical analysis: The Chain Rule
+
|The basics of mathematical analysis: calculus (derivative counting rules)
|Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  chap. 4.1
+
  
 
|-
 
|-
|16.11. I
+
|08.11.  
|The basics of mathematical analysis: The Chain Rule + Minimum/maximum problem - counting exercise
+
|The basics of mathematical analysis: calculus (maximum and minimum problem, convex and concave problem)
|Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. [https://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf Download here];  chap. 4.1 
+
  
 
|-
 
|-
|16.11. II
+
|14.11.  
|The basics of linear algebra: Linear equations - the basic problem of linear algebra, Matrix and Vector definition
+
|The basics of mathematical analysis: calculus (the chain rule, functions’ characteristics in a view of derivative)
| Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here]; chap. 2.1, 2.2, 3.1
+
  
 
|-
 
|-
|23.11. I
+
|15.11.  
|Repeating class
+
|Repeating and practicing class
  
 
|-
 
|-
|23.11. II
+
|21.11.
 
|Middle term writing test
 
|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
 +
 
|}
 
|}
  
Riadok 119: Riadok 159:
 
!References
 
!References
 
|-
 
|-
|05.10.
+
|23.09.
|1. Choose 1 Exercise from the Exercise 2.1 (page 54).
+
|1. Find and explain IDEAL NUMBERS
2. Is 0/0 = 0 statement or not? Why?
+
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
 
| 1 point
1 point
+
2 points
|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.
+
|03.10.
|1. Choose 2 Exercises from the Exercise 2.4 (page 100).
+
|1. Chapter 2.1 / Exercise 2.1 / PROBLEM 4
| 1 point / exercise
+
2. Chapter 2.1 / Exercise 2.1 / PROBLEM 5
|Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
+
| 1 point
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];
+
1 point
 +
| Discrete and combinatorial mathematics: An applied introduction  
  
 
|-
 
|-
|19.10
+
|04.10.
| Find/create the open statement which is possible to prove by mathematical induction.
+
|1. Find (google) DE MORGAN’S LAWS. What does these laws represent? How can we prove them?
Prove the statement and use the proof to explain the principle of mathematical induction.
+
2. Help developers: The problem of REPEATING TASKS
| 3 points
+
  
|-
+
Repeating task is a task created from its parent task every few (n) days.  
|26.10
+
Repeating rules have the next parameters:
| 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
+
  
|-
+
+ Date of the last repeat
|02.11
+
| Find derivatives:
+
1. y = (x + 5)*x^2
+
  
2. y = log(2)x – 5x + 7x^5
+
+ Maximum number of repeats
  
3. y = sin x / cos x
+
+ Number of days for repeat (n) (“repeat task every 5 days”)
  
4.  y = (3x + 5^x – 6)/(ln x + e^x)
+
+ 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)
 +
| -
 +
 
 +
|-
 +
|11.10.
 +
|1. EXERCISE 4.1, PAGE 208, PROBLEM 1/Choose two of problems a-d
 +
2. EXERCISE 4.1, PAGE 208, PROBLEM 8
 
| 4 points
 
| 4 points
 +
2 points
 +
| Discrete and combinatorial mathematics: An applied introduction
  
 
|-
 
|-
|09.11
+
|17.10.
| Find the local and global extremes of a function. Create the graph of that function: y = x2 / (1 – x2)
+
|Based on the graph (see slides from the lecture) describes the
(you can check your answer on a page 115)
+
changes which can be caused if a
 +
man: is not smoking OR is smoking
 +
OR quit smoking during his life.
 +
Write as many information as you
 +
can.
 
| 4 points
 
| 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]; 
+
| Slides from the lecture
 +
 
 +
|-
 +
|18.10.
 +
|Find the graph and a general formula for an absolute value function.
 +
| 2 points
 +
|
 +
 
 +
|-
 +
|24.10.
 +
|Find the graph, domain, range, axis intercepts
 +
and vertex of a quadratic function:
 +
r: R → R, y = (x + a) 2 + b
 +
| 2 points
 +
|
  
 
|}
 
|}
Riadok 171: Riadok 244:
  
 
* 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];
Riadok 182: Riadok 256:
 
* 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: What does mathematics mean for me? What am I expecting from this course?  
* term: 27.10.2017
+
* term: 06.12.2018
 
* 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 Wednesday at the beginning of the exercise  
 
*goal:  regular preparation  
 
*goal:  regular preparation  
*weight: 40%
+
*weight: 20%
*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… )
+
 
 +
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
 
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: 21.11.2017
 
*goal: progress definition
 
*goal: progress definition
 
*weight: 15%
 
*weight: 15%
Riadok 201: Riadok 280:
 
FINAL EXAM
 
FINAL EXAM
 
*form: 90 minutes writing test
 
*form: 90 minutes writing test
*term: January, February 2018
+
*term: January, February 2019
 
*goal: course output   
 
*goal: course output   
 
*weight: 30%
 
*weight: 30%

Verzia zo dňa a času 10:31, 25. október 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 11:30 M-X Martina Babinská
Exercise/Lecture Thursday 13:10 M-II Martina Babinská

Syllabus

Date Topic References
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: Quantifiers, its negations and truth values Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 2.4

11.10. Mathematical Induction and counting with rows (sum and multiplication) Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.

Rose-Hulman Institute of Technology: Pearson, 2004; chap. 4.1

17.10. The basics of mathematical analysis: mathematical function vs dependency (definition, mathematical functions in the real world ) Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
18.10. The basics of mathematical analysis: mathematical function (graph vs. formula, constant and linear mathematical functions) Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
24.10. The basics of mathematical analysis: mathematical function (quadratic function) Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
25.10. The basics of mathematical analysis: extremes, monotonicity, boundary Slides from the lecture, https://www.khanacademy.org/math/algebra/algebra-functions
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
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

2. Chapter 2.1 / Exercise 2.1 / PROBLEM 5

1 point

1 point

Discrete and combinatorial mathematics: An applied introduction
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)

-
11.10. 1. EXERCISE 4.1, PAGE 208, PROBLEM 1/Choose two of problems a-d

2. EXERCISE 4.1, PAGE 208, PROBLEM 8

4 points

2 points

Discrete and combinatorial mathematics: An applied introduction
17.10. Based on the graph (see slides from the lecture) describes the

changes which can be caused if a man: is not smoking OR is smoking OR quit smoking during his life. Write as many information as you can.

4 points Slides from the lecture
18.10. Find the graph and a general formula for an absolute value function. 2 points
24.10. Find the graph, domain, range, axis intercepts

and vertex of a quadratic function: r: R → R, y = (x + a) 2 + b

2 points

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: 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 >