Line 19: Line 19:
 
!Lecturer
 
!Lecturer
 
|-
 
|-
|Lecture/Excercise
+
|Lecture/Exercise
|Thursday
+
|Wednesday
|09:50
+
|08:10
|M-112
+
|M-VII
|[[Martina Koronci Babinska|Martina Koronci Babinská]]
+
|[[Martina Babinská|Martina Babinská]]
 
|-
 
|-
|Excercise/Lecture
+
|Exercise/Lecture
 
|Thursday
 
|Thursday
|14:50
+
|13:10
|M-V
+
|M-VII
|[[Martina Koronci Babinska|Martina Koronci Babinská]]
+
|[[Martina Babinská|Martina Babinská]]
 
|}
 
|}
  
Line 39: Line 39:
 
!References
 
!References
 
|-
 
|-
|03.10.
+
|27.09.
 
|Introduction. The basics of logic and proving methods: propositional logic.  
 
|Introduction. 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.
Line 45: Line 45:
  
 
|-
 
|-
|05.10.
+
|03.10.
|The basics of logic and proving methods: 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; [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
  
 
|-
 
|-
|12.10.
+
|04.10.
 
|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: 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.
Line 57: Line 57:
  
 
|-
 
|-
|12.10.
+
|10.10.
|The basics of logic and proving methods: Proofs (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; [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
  
 
|-
 
|-
|19.10.
+
|11.10.
|The basics of mathematical analysis: Functions (definition, graph, characteristics, basic mathematical functions, functions in the real word)
+
|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];
  
 
|-
 
|-
|26.10. I
+
|17.10.
|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 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)
  
 
|-
 
|-
|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, monotonicityboundary, extremes)
|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
+
  
 
|-
 
|-
|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: mathematical function (continuity, limit)  
|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
+
  
 
|-
 
|-
|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
  
 
|-
 
|-
|30.11. I - II
+
|22.11.
|The basics of linear algebra: Matrix and Vector operations, Gaussian Reduction - introduction
+
|The basics of linear algebra: The basic problem of linear algebra (Matrix and Vector)
| Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here]; chap. 2.2, 2.3, 2.4
+
  
 
|-
 
|-
|07.12. I
+
|28.11.
|The basics of linear algebra: Gaussian Reduction practice - various number of solutions
+
|The basics of linear algebra: The basic problem of linear algebra (vector operations, linear combination)
| Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here]; chap. 2.4
+
  
 
|-
 
|-
|07.12. II
+
|29.11.
|The basics of linear algebra: Matrix operations - transposition, multiplication, inverse matrix, determinants
+
|The basics of linear algebra: Matrices (basic operations)
| Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. [https://www.math.ubc.ca/~carrell/NB.pdf Download here]; chap. 3.1, 8.1
+
 
|}
+
|-
 +
|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
 +
}
  
  

Revision as of 09:46, 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. 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; 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; 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; 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; 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; 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

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; 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; 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. 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. 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. Download here;

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: 27.10.2017
  • goal: self-study motivation
  • weight: 15%

WEEKLY EXAMS

  • form: 10-15 minutes writing tests
  • term: every Thursday at the beginning of the exercise
  • goal: regular preparation
  • weight: 40%
  • 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

  • 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
  • term: January, February 2018
  • goal: course output
  • weight: 30%

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


Information list

Course information sheet >