Course Information

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).
In-person direct teaching

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Bc. Martin Chvátal, Ph.D. (seminar tutor)
Ing. Lukáš Kokrda (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Division of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Division of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102, except Wed 18. 9., except Wed 6. 11.

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, except Thu 19. 9., except Thu 7. 11., L. Kokrda
MPM_MAT2/03: Thu 14:00–15:50 VT202, except Thu 19. 9., except Thu 7. 11., L. Kokrda
MPM_MAT2/04: Thu 8:00–9:50 VT204, except Thu 19. 9., except Thu 7. 11., M. Matulová

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 7 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. 6th edition. Harlow: Pearson, 2021. ISBN 1-292-35928-5. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- homework assigments
- midterm project
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Study support

https://is.muni.cz/auth/el/econ/podzim2024/MPM_MAT2/index.qwarp

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
General note: Přednášky jsou dostupné online a ze záznamu.

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Bc. Martin Chvátal, Ph.D. (seminar tutor)
Ing. Lukáš Kokrda (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Division of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Division of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102, except Wed 20. 9., except Wed 8. 11.

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, except Thu 21. 9., except Thu 9. 11., L. Kokrda
MPM_MAT2/03: Thu 12:00–13:50 VT314, except Thu 21. 9., except Thu 9. 11., M. Matulová
MPM_MAT2/04: Thu 14:00–15:50 VT202, except Thu 21. 9., except Thu 9. 11., L. Kokrda
MPM_MAT2/05: Thu 8:00–9:50 VT105, except Thu 21. 9., except Thu 9. 11., M. Matulová

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 7 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. 6th edition. Harlow: Pearson, 2021. ISBN 1-292-35928-5. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- homework assigments
- midterm project
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
General note: Přednášky jsou dostupné online a ze záznamu.

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Bc. Martin Chvátal, Ph.D. (seminar tutor)
Ing. Lukáš Kokrda (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102, except Wed 14. 9., except Wed 2. 11.

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, except Thu 15. 9., except Thu 3. 11., M. Matulová
MPM_MAT2/02: Thu 14:00–15:50 VT204, except Thu 15. 9., except Thu 3. 11., L. Kokrda
MPM_MAT2/04: Thu 10:00–11:50 VT202, except Thu 15. 9., except Thu 3. 11., M. Matulová

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 7 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016, xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- homework assigments
- miterm project
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.
General note: Přednášky jsou dostupné online a ze záznamu.

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Bc. Martin Chvátal, Ph.D. (seminar tutor)
Ing. Lukáš Kokrda (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102, except Wed 15. 9., except Wed 3. 11.

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, except Thu 16. 9., except Thu 4. 11., L. Kokrda
MPM_MAT2/02: Thu 14:00–15:50 VT204, except Thu 16. 9., except Thu 4. 11., M. Chvátal
MPM_MAT2/03: Thu 8:00–9:50 VT105, except Thu 16. 9., except Thu 4. 11., M. Chvátal
MPM_MAT2/04: Thu 10:00–11:50 VT202, except Thu 16. 9., except Thu 4. 11., M. Matulová

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 7 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016, xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- homework assigments
- miterm project
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
General note: Přednášky jsou dostupné online a ze záznamu.

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Bc. Martin Chvátal, Ph.D. (seminar tutor)
Ing. Lukáš Kokrda (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, L. Kokrda
MPM_MAT2/02: Thu 14:00–15:50 VT204, M. Chvátal
MPM_MAT2/03: Thu 8:00–9:50 VT105, M. Chvátal
MPM_MAT2/04: Thu 10:00–11:50 VT202, M. Matulová

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 7 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016, xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- homework assigments
- miterm project
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
General note: Přednášky jsou dostupné online a ze záznamu.

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Ing. Lukáš Kokrda (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, L. Kokrda
MPM_MAT2/02: Thu 14:00–15:50 VT204, M. Matulová
MPM_MAT2/03: Thu 8:00–9:50 VT105
MPM_MAT2/04: Thu 10:00–11:50 VT202

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

there are 7 fields of study the course is directly associated with, display

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016, xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- homework assigments
- miterm project
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further comments (probably available only in Czech)

Study Materials
General note: Přednášky jsou dostupné online a ze záznamu.

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Hanna Demchenko, Ph.D. (seminar tutor)
Mgr. Štěpán Křehlík, Ph.D. (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 10:00–11:50 P102

• Timetable of Seminar Groups:

MPM_MAT2/01: Thu 12:00–13:50 VT202, M. Matulová
MPM_MAT2/02: Thu 14:00–15:50 VT204, M. Matulová
MPM_MAT2/03: Thu 8:00–9:50 VT204, H. Demchenko
MPM_MAT2/04: Thu 10:00–11:50 VT202, Š. Křehlík

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Finance (programme ESF, M-FU)
• Finance (programme ESF, N-FU)
• Business Management (programme ESF, M-EKM)
• Business Management (programme ESF, N-EKM)
• Business Informatics (programme ESF, N-SI)

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016, xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- active participation on the seminars
- homework assigments
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further Comments

Study Materials

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Štěpán Křehlík, Ph.D. (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 11:05–12:45 P102

• Timetable of Seminar Groups:

MPM_MAT2/02: Thu 12:50–14:30 VT204, M. Matulová
MPM_MAT2/03: Thu 14:35–16:15 VT204, M. Matulová
MPM_MAT2/04: Thu 9:20–11:00 VT204, M. Matulová
MPM_MAT2/05: Thu 7:40–9:15 VT204, Š. Křehlík

Prerequisites

Knowledge of calculus and linear algebra according to syllabus of the course BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Finance (programme ESF, M-FU)
• Finance (programme ESF, N-FU)
• Business Management (programme ESF, M-EKM)
• Business Management (programme ESF, N-EKM)
• Business Informatics (programme ESF, N-SI)

Course objectives

The aim of the course is to prepare students to use advanced mathematical apparatus in specialized courses (Financial Mathematics, Microeconomics 2, Macroeconomics 2, etc.) so that they know not only how but also why these mechanisms work.

Learning outcomes

After completion of the course students will be able to:
- Analyze the behavior of economic systems and handle quantitative relationships between economic variables.
- Apply the tools required for static and dynamic economic modelling
- Foster mathematical and geometric intuition for understanding principals of financial mathematics, microeconomics, etc.
- Effectively use available software tools for symbolic and numeric computations

Syllabus

• Topics with links to the respective chapters of Essential mathematics for economic analysis (EMEA) and Further mathematics for economic analysis (FMEA)
• 1. Advanced linear algebra: rank of matrix, linear dependence, eigenvalues and eigenvectors, quadratic forms [FMEA, kap. 1]
• 2. Multivariate calculus: limit, gradient, Hessian, direction derivative, convexity, Taylor polynomial [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Multivariate optimization [FMEA, 3.1-3.2]
• 4. Multivariate optimization with equality constraints [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Multivariate optimization with inequality constraints [FMEA 3.5-3.8]
• 6. Introduction to linear programming [EMEA, 17]
• 7. Implicit function, envelope theorem, comparative statics [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Improper integration [EMEA, 9.7]
• 9. Double integration [FMEA, 4]
• 10. Differential equations I [FMEA, 5]
• 11. Differential equations II [FMEA, 6,7]
• 12. Difference equations [FMEA, 11]

Literature

required literature
• SYDSÆTER, Knut, Peter J. HAMMOND, Arne STRØM and Andrés M. CARVAJAL. Essential mathematics for economic analysis. Fifth edition. Harlow: Pearson, 2016, xvi, 807. ISBN 9781292074610. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info

recommended literature
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods

Theoretical training includes lectures,obligatory seminars in the computer hall.

Assessment methods

The course is ended by an examination. The prerequisite of successful completion of the course is active participation in seminars. The rating is determined by point gain from
-the final and midterm tests
- active participation on the seminars
- homework assigments
Any copying, recording or leaking tests, use of unauthorized tools, aids and communication devices, or other disruptions of objectivity of exams (credit tests) will be considered non-compliance with the conditions for course completion as well as a severe violation of the study rules. Consequently, the teacher will finish the exam (credit test) by awarding grade "F" in the Information System, and the Dean will initiate disciplinary proceedings that may result in study termination.

Language of instruction

Czech

Further Comments

Study Materials

MPM_MAT2 Mathematics

Extent and Intensity

2/2/0. 8 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Mgr. Markéta Matulová, Ph.D. (lecturer)
Mgr. Štěpán Křehlík, Ph.D. (seminar tutor)
Ing. Mgr. Markéta Matulová, Ph.D. (seminar tutor)

Guaranteed by

Ing. Mgr. Markéta Matulová, Ph.D.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Supplier department: Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration

Timetable

Wed 11:05–12:45 P102

• Timetable of Seminar Groups:

MPM_MAT2/02: Thu 12:50–14:30 VT204, M. Matulová
MPM_MAT2/03: Thu 14:35–16:15 VT204, M. Matulová
MPM_MAT2/04: Thu 9:20–11:00 VT204, M. Matulová
MPM_MAT2/05: Thu 7:40–9:15 VT204, Š. Křehlík

Prerequisites (in Czech)

Znalosti z matematické analýzy a lineární algebry v rozsahu předmětu BPM_MATE

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Finance (programme ESF, M-FU)
• Finance (programme ESF, N-FU)
• Business Management (programme ESF, M-EKM)
• Business Management (programme ESF, N-EKM)
• Business Informatics (programme ESF, N-SI)

Course objectives (in Czech)

Po absolvování předmětu budou studenti schopni:
- analyzovat chování ekonomických systémů a pracovat s kvantitativními vztahy mezi ekonomickými proměnnými.
- aplikovat aparát potřebný pro statické i dynamické ekonomické modelování
- používat matematickou intuici a geometrickou představivost, porozumět postupům a vědět nejen jak, ale i proč uvedené mechanismy fungují

Syllabus (in Czech)

• Témata s odkazy do kapitol Essential mathematics for economic analysis (EMEA) a Further mathematics for economic analysis (FMEA)
• 1. Pokročilejší témata teorie matic: hodnost matice, nezávislost, vlastní čísla a vektory, kvadratické formy, definitnost matice [FMEA, kap. 1]
• 2. Funkce více proměnných: Definiční obor, limita, gradient, Hessián, směrové derivace, (kvazi)konvexita, Taylorův polynom [EMEA 11.4-11.8, FMEA 2.1-2.6]
• 3. Optimalizace funkce více proměnných [FMEA, 3.1-3.2]
• 4. Optimalizace s omezením ve formě rovností [EMEA, 14, FMEA, 3.3 - 3. 4]
• 5. Optimalizace s omezením ve formě nerovností [FMEA 3.5-3.8]
• 6. Úvod do lineárního programování [EMEA, 17]
• 7. Implicitní funkce, obálková věta, komparativní statika [FMEA 2.8, EMEA 12, 13.7, 14. 7]
• 8. Nevlastní integrál [EMEA, 9.7]
• 9. Dvojný integrál [FMEA, 4]
• 10. Diferenciální rovnice I [FMEA, 5]
• 11. Diferenciální rovnice II [FMEA, 6,7]
• 12. Diferenční rovnice [FMEA, 11]

Literature

• SYDSÆTER, Knut and Peter J. HAMMOND. Essential mathematics for economic analysis. 3rd ed. Harlow: Prentice-Hall, 2008, xiv, 721. ISBN 9780273713241. info
• SYDSÆTER, Knut. Further mathematics for economic analysis. 2st ed. Harlow: Prentice-Hall, 2008, xi, 616. ISBN 9780273713289. info
• HOY, Michael. Mathematics for economics. 3rd ed. Cambridge, Mass.: MIT Press, 2011, xiv, 959. ISBN 9780262516228. info
• SIMON, Carl P. and Lawrence BLUME. Mathematics for economists. 1st ed. New York: W.W. Norton, 1994, xxiv, 930. ISBN 0393957330. info
• BAUER, Luboš, Hana LIPOVSKÁ, Miloslav MIKULÍK and Vít MIKULÍK. Matematika v ekonomii a ekonomice (Mathematics in Economics and Economy). první vydání. Praha: Grada Publishing, a.s., 2015, 352 pp. ISBN 978-80-247-4419-3. info

Teaching methods (in Czech)

Předmět má přednášky a semináře 2/2. Účast na seminářích je povinná.

Assessment methods (in Czech)

Předmět je ukončen zkouškou, hodnocení se odvozuje z celkového bodového zisku získaného:
- v závěrečném a v průběžných písemných testech (80%)
- za aktivní práci v seminářích a doma (20%)
Jakékoli opisování, zaznamenávání nebo vynášení testů, používání nedovolených pomůcek jakož i komunikačních prostředků nebo jiné narušování objektivity zkoušky (zápočtu) bude považováno za nesplnění podmínek k ukončení předmětu a za hrubé porušení studijních předpisů. Následkem toho uzavře vyučující zkoušku (zápočet) hodnocením v ISu známkou "F" a děkan zahájí disciplinární řízení, jehož výsledkem může být až ukončení studia.

Language of instruction

Czech

Further Comments

Study Materials

• Enrolment Statistics (recent)