Course Syllabus

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Course Description

Linear algebra is a branch of mathematics that focuses on linear equations, linear transformations, vector spaces and matrices. Its far-reaching impact extends across disciplines like physics, engineering, computer science, and economics, with practical applications spanning image processing, signal processing, modeling of earth and nature phenomena, computer graphics, machine learning, economic models and beyond.

This course will cover fundamental concepts of linear algebra from a mathematical perspective, including systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality, least squares, and symmetric matrices. It has a hands-on format where a major focus is placed on mathematical application of concepts and problem solving. In addition, students will have the opportunity to participate in field studies to learn how professionals from academia and industry utilize linear algebra in their work.

The course will cover the following modules (modules 6-7 will be covered if time allows):

Learning Objectives

By the end of this course, students will be able to:

• Apply fundamental concepts of linear algebra during mathematical reasoning
• Identify and provide examples of expressions that include systems of linear equations, vectors and matrices
• Solve systems of linear equations using various methods
• Perform matrix operations
• Analyze mathematical expressions and describe solutions to linear systems
• Develop the ability to communicate mathematical ideas clearly and effectively, using appropriate mathematical notation and language.

Faculty

Frida Svelander, Lic. Advanced Engineering Mathematics.
Frida has a background in modeling, research and software development within physics and data science applications. She is also the CEO and founder of her own consulting company FEEM Solutions, helping companies and organizations with strategy, computation and analysis for a healthy and sustainable society. She teaches part time at Stockholm School of Economics, and has previously taught mathematics at KTH Royal Institute of Technology and Chalmers University of Technology. She worked with R&D at Elekta Instruments, Fraunhofer-Chalmers Centre for Industrial Mathematics and a consulting company in the energy sector.

Readings

Linear Algebra and Its Applications, 6th edition, by  David C. Lay, Steven R. Lay, Judi J. McDonald
Chapters 1-7

Field Studies

We will have two course-integrated field studies to learn how linear algebra is utilized in academic research and industry work.

The field studies will include:

1. A city walk at the university areas close to the DIS school building, including Kungliga Tekniska Högskola (Royal Institute of Technology) and Stockholm University (SU) including exercises in the intersection between linear algebra and exploring the Stockholm city map.
2. Visiting the newly built Forskaren office close to Karolinska University Hospital, where we will have fika with a researcher in machine learning for radiotherapy treatments and learn about his research.

Guest Lecturers

Guest lecturers may be invited to talk about topics of particular interest to the students.

Approach to Teaching

The course consists of interactive lectures, class exercises, and problem-solving individually or in group. Discussion of applications is included, especially during field studies.

DIS Accommodations Statement 

Your learning experience in this class is important.  If you have approved academic accommodations with DIS, please make sure to give your DIS accommodations letter to the teacher within two weeks from the start of classes. If you can think of other ways we can support your learning, please don't hesitate to talk to the teacher. If you have any further questions about your academic accommodations, contact Academic Support acadsupp@dis.dk. 

Expectations of the Students

• You should participate actively during lectures, discussions, group work, and exercises.
• Laptops may be used for note‐taking, fact‐checking, or assignments in the classroom, but only when indicated by the instructor. At all other times, laptops and electronic devices should be put away during class meetings.
• Readings must be done prior to the class session. 
• In addition to completing all assignments and exams, you need to be present, arrive on time, and actively participate in all classes and field studies to receive full credit. Your final grade will be affected, adversely, by unexcused absences and lack of participation. Your participation grade will be reduced by 10 points (over 100) for every unexcused absence. Remember to be in class on time!
• Classroom etiquette includes being respectful of other opinions, listening to others and entering a dialogue in a constructive manner.
• You are expected to ask relevant questions in regards to the material covered.
• Excuses for any emergency absences must be given beforehand. It is the responsibility of the student to make up any missed coursework.

Evaluation

To be eligible for a passing grade in this class, all of the assigned work must be completed.

You are expected to turn in your solutions to all examining elements on the due date. If a a solution is turned in after the due date, your grade on that element will be reduced by 10 points (over 100) for each day the submission is late. 

Grading

Preparation for class: Before each class you will do your own readings in the course book, watch videos, and answer to a quiz in Canvas. You are required to complete all quizzes and and obtain at least 50% correct answers. This will make sure that you are prepared for class. 

Active participation: Includes attendance, preparation for lectures and other sessions, active participation in learning activities, class discussions, group work and problem solving. It also includes active participation during field studies and presentation of reflections on how they are related and relevant within the context of the course.

Assignments:  Homework problems will be posted on Canvas. Students are allowed to work in groups to complete their homework. A pdf scan or clear photo of their work must be submitted on Canvas. Late submissions of homework will be deducted by 10 points for each day the homework is late.

Project: A small project that can be made individually or (preferably) in group will be handed-out by the middle of the semester. The project will be of applied nature, and later to be presented in class. 

Final exam + oral presentation: At the end of the semester, you will take an exam that covers all topics from the course. You are expected to work on your own. The exam can be made from home, and you will have to be prepared to present your solutions to the teacher in a follow-up oral presentation. 

Academic Regulations

Please make sure to read the Academic Regulations on the DIS website. There you will find regulations on:

• Course Enrollment and Grading
• Academic Expectations and Honor Code

DIS - Study Abroad in Scandinavia - www.DISabroad.org