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Unit information: Optimisation in 2021/22

Unit name Optimisation
Unit code MATH30017
Credit points 20
Level of study H/6
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Dr. Tadic
Open unit status Not open
Pre-requisites

MATH10011 Analysis and MATH10015 Linear Algebra

Either MATH10012 ODEs, Curves and Dynamics or good familiarity with partial derivatives, gradients, Hessians and Jacobians

MATH20015 Multivariable Calculus and Complex Functions is also desirable but not essential

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

Unit Aims

The aim of this unit is to make students acquainted with the main concepts, ideas, methods, tools and techniques of the mathematical optimisation.

Unit Description

Optimisation can be described as the processes of selecting a best solution (or a decision) out of available alternatives. As such, optimisation is involved in a number of human activities and almost all branches of natural sciences.

For example, investors seek to create portfolios avoiding excessive risk and achieving high return rates. Manufactures aim to maximize the efficiency of their production processes. Engineers adjust parameters to optimise the performance of their designs. Physical systems tend to a state of a minimum energy. Molecules in an isolated system tend to react with each other until the total potential energy is minimized. Rays of light follow paths minimising their travel time.

Mathematically speaking, optimisation is the process of minimising (or maximizing) a multivariable function subject to constraints on its variables.

Intended Learning Outcomes

At the end of the unit, the students should:

  • understand the basic theoretical aspects of optimisation problems.
  • understand the numerical methods for optimisation problems and their properties.
  • be able to solve simple optimisation problems by hand.
  • be able to solve (relatively) simple optimisation problems numerically.

Teaching Information

The unit will be taught through a combination of

  • synchronous online and, if subsequently possible, face-to-face lectures
  • asynchronous online materials, including narrated presentations and worked examples
  • guided asynchronous independent activities such as problem sheets and/or other exercises
  • synchronous weekly group problem/example classes, workshops and/or tutorials
  • synchronous weekly group tutorials
  • synchronous weekly office hours

Assessment Information

80% Timed, open-book examination 20% Coursework: computing assignments

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH30017).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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