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A Mathematical Introduction to Machine Learning, 7.5 Credits

Swedish name: Matematisk introduktion till maskininlärning

This syllabus is valid: 2022-07-25 and until further notice

Course code: 5MA206

Credit points: 7.5

Education level: First cycle

Main Field of Study and progress level: Mathematics: First cycle, has at least 60 credits in first-cycle course/s as entry requirements

Grading scale: VG Pass with distinction, G Pass, U Fail

Established by: Faculty Board of Science and Technology, 2022-03-02


The course addresses the fundamental mathematical and statistical methods and models used within the field of machine learning. Its purpose is to provide a mathematical foundation for advanced level courses in machine learning and artificial intelligence, as well as to introduce machine learning applications within academia and industry. The course is comprised of two modules.

Module 1 (4,5 hp): Theory and problem solving
This module addresses fundamental statistical models, statistical learning and maximum likelihood estimation, with an emphasis on supervised learning. Several commonly used models are introduced, and their mathematical properties are discussed, for instance linear regression and classification models, neural networks, support vector machines, as well as models for unsupervised learning. Furthermore, evaluation and validation of models are addressed.

Module 2 (3 hp): Computer assignments
This module addresses the implementation of commonly occuring machine learning models, as well as investigating their properties.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

  • account for the foundations of statistical decision theory
  • account for the theoretical foundations of model evaluation
  • describe common machine learning problems in mathematical terms

Skills and abilities

  • derive properties of statistical models commonly used in machine learning
  • implement basic models and evaluation strategies
  • use existing software packages to solve relevant machine learning problems
  • evaluate the precision and generality of trained models 

Judgment and approach

  • determine suitable methods for various machine learning problems

Required Knowledge

The course requires courses in Mathematics, minimum 60 ECTS or at least two years of university studies and both cases require courses in linear algebra, multivariate calculus, mathematical statistics and computer programming, or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.

Form of instruction

The teaching in Module 1 takes the form of lectures and lessons. The teaching in Module 2 takes the form of supervised lab work.

Examination modes

Module 1 is assessed through a written examination. Module 2 is assessed through written lab reports. For Module 1, one of the following judgements is awarded: Fail (U), Pass (G) or Pass with distinction (VG). For Module 2, one of the following judgements is awarded: Fail (U),or Pass (G). For the course as whole, one of the following grades is awarded: Fail (U), Pass (G) or Pass with distinction (VG). The grade for the whole course is determined by the judgement given for Module 1. To pass the whole course, all modules must have been passed. The grade is only set once all compulsory modules have been assessed.

Deviations from the syllabus examination form can be made for a student who has a decision on pedagogical support due to disability. Individual adaptation of the examination form shall be considered based on the student's needs. The examination form is adapted within the framework of the expected learning outcomes of the course syllabus. At the request of the student, the course coordinator, in consultation with the examiner, must promptly decide on the adapted examination form. The decision shall then be communicated to the student.

A student who has been awarded a passing grade for the course cannot be re-assessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfer
All students have the right to have their previous education or equivalent, and  their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be addressed to Student ser-vices/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university,, and in the Higher Education Ordinance (chapter 6). If denied, the application can be ap-pealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics.

In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.