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Undergraduate course

Advanced Mathematics and Optimization

Level of Study

Bachelor

Teaching semester

Autumn

Objectives and Content

The course will make students better suited to meeting the demands in mathematics, which they will face in other upper-bachelor and master-level economics courses.

The course deals with linear algebra, the functions of several variables, comparative statistics and optimization with several variables and restrictions. In optimization, the Lagrange and Kuhn-Tucker methods are the main points of focus.

Learning Outcomes

A student who has completed the course should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student can ...

  • comprehend the following conversions and concepts within linear algebra: Addition, subtraction and scalar multiplication of vectors, vector length, distance between vectors and inner product between vectors, lines and planes, hyperplanes in parametric and non-parametric representation, linear independence.
  • give a description of: square shapes, positive and negative semidefinite matrices, convex amounts and functions.
  • distinguish constraint and no constrain optimization problems as well as dynamic and non-dynamic optimization problems.
  • reflect on the necessary conditions for global or local maxima¿s and minima¿s.
  • discuss the application of the envelope theory for optimization problems in economics.

Skills

The student can ...

  • apply addition and multiplication of matrices, the identity matrix, inverse matrix and linear equation system on matrix form. The student should be able to determine the rank of an array to classify linear equation systems. They should also be able to calculate determinants and be able to use Cramer's rules for linear equations.
  • apply partial derivative, total differential, gradient vector and directional derivative as well as implicit derivation, second order partial derivative and hesseian matrix. The student should be able to use comparative statistics on an equation system.
  • apply Lagrange and Kuhn-Tucker methods for solving optimization problems with restrictions.

Required Previous Knowledge

None

Recommended Previous Knowledge

ECON140 or MAT101

Credit Reduction due to Course Overlap

Complete overlap with ECON141

Access to the Course

Open

Teaching and learning methods

Lectures: approx. 36 hours, mathematics tasks: approx. 18 hours, seminars: approx. 18 hours

Compulsory Assignments and Attendance

None

Forms of Assessment

Written exam (4 hours)

Examination Support Material

Mathematical Formula Collection of K. Sydsæter, A. Strøm and P. Berck and calculator. The following simple, non-programmable calculators without graphical display are allowed to be used for written tests:

All models of the type:

  • Casio FX-82, Casio FX-82ES PLUS or Casio FX-82EX
  • Hewlett-Packard HP30
  • Texas Instruments TI-30

The Department of Economics may conduct a sample of aids in the examination room.

Grading Scale

A-F

Assessment Semester

Assessment in teaching semester. Only students who have a valid document of absence will be entitled to take a new exam the following semester.

Course Evaluation

All courses at the Department of Economics are evaluated at the end of each semester.

Exam information

  • For written exams, please note that the start time may change from 09:00 to 15:00 or vice versa until 14 days prior to the exam. The exam location will be published 14 days prior to the exam. Candidates must check their room allocation on Studentweb 3 days prior to the exam.

  • Type of assessment: Written examination

    Date
    02.12.2019, 09:00
    Duration
    4 hours
    Withdrawal deadline
    18.11.2019