Drukuj sylabusAlgebra (in English)
Informacje ogólne
| Kod przedmiotu: | 121001-D |
| Kod Erasmus / ISCED: |
11.1
|
| Nazwa przedmiotu: | Algebra (in English) |
| Jednostka: | Szkoła Główna Handlowa w Warszawie |
| Grupy: |
Courses for QME - bachelors Major courses for QME - bachelors Przedmioty obowiązkowe na programie SLLD-MIS |
| Punkty ECTS i inne: |
6.00 (zmienne w czasie)
|
| Język prowadzenia: | angielski |
| Efekty uczenia się: |
Wiedza: A student should know: Definition and properties of a field of complex numbers. Definition and properties of linear spaces. Algebraic operations on matrices. Techniques of solving systems of linear equations. Definition and properties of linear mappings. Definition of eigenvalues and eigenvectors of a matrix of a linear mapping. A student should know: Definition of inner product, induced norm, a metric induced by a norm. Definition and properties of finitely dimensional unitary space (Hermitian vector space). Definition and properties of orthogonal projection on linear subspace. A student should know: Definition and properties of convex sets, convex functions and their applications. Definition and properties of cones and dual cones. Relations between cones and orderings. Applications of cones in optimization. Umiejętności: A student should be able to: Interpret (draw) simple subsets of a complex plain. Calculate n-th roots of an arbitrary complex number. Construct basis of a linear space and a linear subspace. Find a matrix of a linear mapping. Solve a system of linear equations. Calculate eigenvalues and eigenvectros of linear mapping. A student should be able to: Calculate inner product of vectors, cosine of an angle given by two vectors, check for orthogonality of two vectors. Construct orthogonal and orthonormal basis of a linear space. Calculate an orthogonal projection of a vector onto a linear subspace. A student should be able to: Check for convexity of a given set. Draw multi-facet convex sets in two and three dimensional spaces. Draw cones and dual cones in two dimensional space. Kompetencje społeczne: Developing the practice and culture of doing mathematics. Developing precise and logical reasoning. Developing ability to unaided mathematical reasoning (proofs). Working with algebraic techniques in mathematical analysis, statistics, econometrics and decision making. Developing ability to read professional papers in economics. Developing ability to do professional economic and managerial analysis. Developing ability to create mathematical models of complex economic processes. Understanding the distinction between mathematical elements of a model and economic content of a model. Providing knowledge used further while studying probability theory, optimization techniques and advanced economics. Developing creative thinking. |
Zajęcia w cyklu "Semestr zimowy 2024/25" (w trakcie)
| Okres: | 2024-10-01 - 2025-02-14 |
 
PN WT ŚR CZ WYK
CW
PT |
| Typ zajęć: |
Ćwiczenia, 30 godzin
Wykład, 30 godzin
|
|
| Koordynatorzy: | (brak danych) | |
| Prowadzący grup: | Maria Ekes | |
| Lista studentów: | (nie masz dostępu) | |
| Zaliczenie: |
Przedmiot -
Ocena
Wykład - Ocena |
|
| Skrócony opis: |
The lecture material includes elements of linear algebra: linear spaces, linear representations, billinear functionals including scalar products and also elements of convex analysis. |
|
| Pełny opis: |
The purpose of the course is presentation of selected topics from linear algebra in the context of mathematical analysis and economic modeling. The course can be treated as a basis for more advanced courses on growth theory and optimal control theory. |
|
| Literatura: |
Literatura podstawowa: * Howard Anton, Chris Rorres, Elementary Linear Algebra (10th edition), Wiley 2011,(selected chapters) * Thomas W. Judson, Abstract Algebra -- Theory and Applications, 2012, (selected chapters), * Matthias Beck, Gerald Marchesi, and Dennis Pixton A First Course in Complex Analysis, 2002-2006 (selected chapters) * Stephen Boyd, Lieven Vandenberghe, Convex Optimization (selected chapters) Literatura uzupełniająca: Jim Hefferon, Linear Algebra, http://joshua.smcvt.edu/linearalgebra |
|
| Uwagi: |
Kryteria oceniania: egzamin tradycyjny-pisemny: 50.00% kolokwium: 40.00% inne: 10.00% |
|
Zajęcia w cyklu "Semestr letni 2023/24" (zakończony)
| Okres: | 2024-02-24 - 2024-09-30 |
PN WT ŚR WYK
CW
CZ PT |
| Typ zajęć: |
Ćwiczenia, 30 godzin
Wykład, 30 godzin
|
|
| Koordynatorzy: | (brak danych) | |
| Prowadzący grup: | Maria Ekes | |
| Lista studentów: | (nie masz dostępu) | |
| Zaliczenie: |
Przedmiot -
Ocena
Wykład - Ocena |
|
| Skrócony opis: |
The lecture material includes elements of linear algebra: linear spaces, linear representations, billinear functionals including scalar products and also elements of convex analysis. |
|
| Pełny opis: |
The purpose of the course is presentation of selected topics from linear algebra in the context of mathematical analysis and economic modeling. The course can be treated as a basis for more advanced courses on growth theory and optimal control theory. |
|
| Literatura: |
Literatura podstawowa: * Howard Anton, Chris Rorres, Elementary Linear Algebra (10th edition), Wiley 2011,(selected chapters) * Thomas W. Judson, Abstract Algebra -- Theory and Applications, 2012, (selected chapters), * Matthias Beck, Gerald Marchesi, and Dennis Pixton A First Course in Complex Analysis, 2002-2006 (selected chapters) * Stephen Boyd, Lieven Vandenberghe, Convex Optimization (selected chapters) Literatura uzupełniająca: Jim Hefferon, Linear Algebra, http://joshua.smcvt.edu/linearalgebra |
|
| Uwagi: |
Kryteria oceniania: egzamin tradycyjny-pisemny: 50.00% kolokwium: 40.00% inne: 10.00% |
|
Zajęcia w cyklu "Semestr zimowy 2023/24" (zakończony)
| Okres: | 2023-10-01 - 2024-02-23 |
PN WT ŚR CZ PT |
| Typ zajęć: |
Ćwiczenia, 30 godzin
Wykład, 30 godzin
|
|
| Koordynatorzy: | (brak danych) | |
| Prowadzący grup: | (brak danych) | |
| Lista studentów: | (nie masz dostępu) | |
| Zaliczenie: |
Przedmiot -
Ocena
Wykład - Ocena |
|
| Skrócony opis: |
The lecture material includes elements of linear algebra: linear spaces, linear representations, billinear functionals including scalar products and also elements of convex analysis. |
|
| Pełny opis: |
The purpose of the course is presentation of selected topics from linear algebra in the context of mathematical analysis and economic modeling. The course can be treated as a basis for more advanced courses on growth theory and optimal control theory. |
|
| Literatura: |
Literatura podstawowa: * Howard Anton, Chris Rorres, Elementary Linear Algebra (10th edition), Wiley 2011,(selected chapters) * Thomas W. Judson, Abstract Algebra -- Theory and Applications, 2012, (selected chapters), * Matthias Beck, Gerald Marchesi, and Dennis Pixton A First Course in Complex Analysis, 2002-2006 (selected chapters) * Stephen Boyd, Lieven Vandenberghe, Convex Optimization (selected chapters) Literatura uzupełniająca: Jim Hefferon, Linear Algebra, http://joshua.smcvt.edu/linearalgebra |
|
| Uwagi: |
Kryteria oceniania: egzamin tradycyjny-pisemny: 50.00% kolokwium: 40.00% inne: 10.00% |
|
Właścicielem praw autorskich jest Szkoła Główna Handlowa w Warszawie.
