Line 181: | Line 181: | ||

| 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]; | ||

+ | |- | ||

+ | |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]; | ||

|- | |- |

## Revision as of 12:54, 11 December 2017

# Mathematics 2-IKV-102

## Contents

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/Excercise | Thursday | 09:50 | M-112 | Martina Koronci Babinská |

Excercise/Lecture | Thursday | 14:50 | M-V | Martina Koronci Babinská |

## Syllabus

Date | Topic | References |
---|---|---|

03.10. | 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 |

05.10. | The basics of logic and proving methods: predicate logic. | Discrete and combinatorial mathematics: An applied introduction / Ralph P. Grimaldi.
Rose-Hulman Institute of Technology: Pearson, 2004; Download here; chap. 2.4 |

12.10. | 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 |

12.10. | The basics of logic and proving methods: Proofs (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 |

19.10. | The basics of mathematical analysis: Functions (definition, graph, characteristics, basic mathematical functions, functions in the real word) | |

26.10. I | The basics of mathematical analysis: Basic function's characteristics in the definitions (domain, range, monotonicity, boundaries, extremes, continuity, infimum, supremum).
| |

26.10. II | The basics of mathematical analysis: Limit of a function (the real word problem, definition, one-side limit) | Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. Download here; chap. 1.1, 1.2, 1.3, 2.1 |

02.11. | The basics of mathematical analysis: The rate of change - derivative (the real word problem, definition, basic functions derivatives, formulas and calculating rules) | Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. Download here; chap. 2.2, 2.3, 2.4, 2.5 |

09.11. I | The basics of mathematical analysis: Minimum/maximum problem and Convex/Concave problem in case of derivatives | Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. Download here; chap. 3.2, 3.3, 3.4 |

09.11. II | The basics of mathematical analysis: The Chain Rule | Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. Download here; chap. 4.1 |

16.11. I | The basics of mathematical analysis: The Chain Rule + Minimum/maximum problem - counting exercise | Calculus / Gilbert Strang. Massachusetts Institute of Technology: Wellesley-Cambridge Press. Download here; chap. 4.1 |

16.11. II | The basics of linear algebra: Linear equations - the basic problem of linear algebra, Matrix and Vector definition | Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. Download here; chap. 2.1, 2.2, 3.1 |

23.11. I | Repeating class | |

23.11. II | Middle term writing test | |

30.11. I - II | The basics of linear algebra: Matrix and Vector operations, Gaussian Reduction - introduction | Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. Download here; chap. 2.2, 2.3, 2.4 |

07.12. I | The basics of linear algebra: Gaussian Reduction practice - various number of solutions | Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. Download here; chap. 2.4 |

07.12. II | The basics of linear algebra: Matrix operations - transposition, multiplication, inverse matrix, determinants | Fundamentals of Linear Algebra / James B. Carrell. Canada: University of British Colombia, 2005. Download here; chap. 3.1, 8.1 |

## 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.