Official course description for:
Full info last published 14/05-19

Linear Algebra and Optimisation

Course info
Language:
English
ECTS points:
7.5
Course code:
BSLIALO1KU
Offered to guest students:
yes
Offered as a single subject:
yes
Price (single subject):
10625 DKK (incl. vat)
Programme
Level:
Bachelor
Programme:
Bachelor of Science in Data Science
Staff
Course manager
Associate Professor
Course semester
Semester
Efterår 2019
Start
26 August 2019
End
31 January 2020
Abbreviation
20192
Exam
Exam type
ordinær
Internal/External
ekstern censur
Grade Scale
7-trinsskala
Exam Language
GB
Abstract

This is a course in mathematics covering linear algebra and analysis (calculus) of functions of several variables. These are perhaps the two areas of mathematics that have found most uses in practical applications. In particular, the course equips the student with mathematical tools necessary for analysis of big data.

Description

Linear algebra and analysis (calculus) of functions of several variables are perhaps the two areas of mathematics that have found most uses in practical applications. In particular, the course equips the student with mathematical tools necessary for analysis of big data.

The topics covered in the linear algebra part of the course include systems of linear equations, matrices, determinants, vector spaces, bases, dimension, and eigenvectors. The topics covered in the calculus part include partial derivatives, gradients, Lagrange multipliers and multiple integrals. A number of applications of the material will be covered in the course, including least squares analysis and Google’s PageRank algorithm.

Formal prerequisites
As the course is mandatory for 1st semester Data Science students mathematics corresponding to the Danish A-level with an average mark of at least 6 on the Danish 7-point marking scale is a prerequisite.
Intended learning outcomes

After the course, the student should be able to:

  • Solve systems of linear equations and multivariable optimisation problems.
  • Define the basic concepts of linear algebra and multivariable calculus, e.g., eigenvalues or directional derivative.
  • Compute the essential constructions of linear algebra and multivariable calculus, such as the inverse of a given matrix or the gradient of a function.
  • Apply the tools of linear algebra and calculus to solve small mathematical problems.
  • Construct small proofs using the axioms of vector spaces
Learning activities

14 weeks of lectures and exercises. At the exercise sessions the students will solve and present solutions to mathematical problems. The mandatory assignments are of the form of mathematical problems. The solutions must be submitted in written form.

Mandatory activities
There are 6 mandatory assignments, out of which 5 must be approved for the student to qualify for the exam. The deadlines are evenly distributed over the semester (approximately one every 2 weeks), exact dates will be posted on learnit the first week of the semester. If a mandatory assignment is not approved the first time, the student will be allowed to resubmit one week after the first deadline. 

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

Ordinary exam
Exam type:
A: Written exam on premises, external (7-trinsskala)
Exam variation:
A22: Written exam on premises with restrictions. Restrictions may concern which software and which books you may use.
Exam description:

The exam is a 4 hour written exam

1. Solutions submitted hand written on paper. 
2. Access to aid in the form of books, own notes, e-books, also on laptops and iPads is permitted. 
3. Use of internet including email and social media is not permitted. 
4. Use of any other hardware or software such as MatLab or pocket calculators is not permitted 
5. Any form of communication between students or with the outside world is not permitted.