Linear Algebra

2021/2022

Учебный год

ENG

Обучение ведется на английском языке

5

Кредиты

Кто читает:

Образовательная программа «Управление цифровым продуктом»

Статус:

Курс обязательный

Когда читается:

1-й курс, 1, 2 модуль

Преподаватели

Глухов Евгений Владимирович

Смирнов Сергей Валерьевич

Course Syllabus

Abstract

In the process of studying the discipline, students will become familiar with theoretical foundations and basic methods in the following topics: systems of linear equations (row operations and Gaussian elimination), vector spaces and subspaces, matrix inversion and determinants, complex numbers and their properties, linear operators (eigenvalues and eigenvectors, diagonalisation), Euclidean spaces (inner product and orthogonality), lines in R^2, planes and lines in R^3, lines and hyper-planes in R^n, quadratic forms (orthogonal diagonalisation), conic sections.

Learning Objectives

• Provide students with an understanding of key concepts and methods of linear algebra for understanding other practical courses, related to data analysis and programming

Expected Learning Outcomes

• Carry out matrix operations, including inverses and determinants.
• Solve systems of linear equations using multiple methods, including Cramer's rule, Gaussian elimination and matrix inversion.
• Comprehend vector spaces (subspaces) and linear transformations.
• Apply linear algebra concepts to model, solve, and analyze real-world situations.
• Communicate mathematics in well-written sentences and to explain the solutions to problems.

Course Contents

• Matrices and systems of linear equations
• Inverse matrix and determinant
• Lines, planes, area and volume
• Complex numbers
• Vector space and linear dependence
• Linear operators
• Euclidean space and orthogonality
• Quadratic forms and conic sections

Assessment Elements

• Test 1
• Test 2
• Homework
• Final exam
  The exam is ONLINE in written form. It is taken on Ms Teams platform. Students are required to join a session 15 minutes before the beginning. The computers must meet the following technical requirements: https://docs.microsoft.com/ru-ru/microsoftteams/hardware-requirements-for-the-teams-app A student is supposed to follow the requirements below: check your computer for compliance with technical requirements no later than 5 days before the exam; sign in with your corporate account (@edu.hse.ru); check your microphone, speakers or headphones, webcam, Internet connection (we recommend connecting your computer to the network with a cable, if possible); prepare the necessary writing equipment, such as pens, pencils, pieces of paper, and others. Disable applications on the computer's task other than the MS Teams application or the browser that will be used to log in to the MS Teams platform. Students are not allowed to: turn off the video camera; use notes, textbooks, and other educational materials; leave the place where the exam task is taken (go beyond the camera's viewing angle); look away from your computer screen or desktop; use smart gadgets (smartphone, tablet, etc.) involve outsiders for help during the exam, talk to outsiders during the examination tasks. Students are allowed to: write on a piece of paper, use a pen for making notes and calculations; use a calculator (not on mobile); turn on the microphone to answer the teacher’s questions; ask a teacher for additional information related to understanding the exam task. A short-term communication failure during the exam is considered to be the loss of a student's network connection with the MS Teams platform for no longer than 1 minute. A student cannot continue to participate in the exam, if there is a long-term communication failure appeared. The retake procedure is similar to the exam procedure. In case of long-term communication failure in the MS Teams platform during the examination task, the student must notify the teacher, record the fact of loss of connection with the platform (screenshot, a response from the Internet provider). Then contact the manager of a program with an explanatory note about the incident to decide on retaking the exam.
• Quizzes

Interim Assessment

• 2021/2022 2nd module
  0.15 * Quizzes + 0.2 * Test 2 + 0.2 * Test 1 + 0.1 * Homework + 0.35 * Final exam

Bibliography

Recommended Core Bibliography

• Elementary linear algebra : applications version, Anton, H., 2019
• Elementary linear algebra : with supplement applications, Anton, H., 2011
• Linear algebra : concepts and methods, Anthony, M., 2012

Recommended Additional Bibliography

• Linear algebra with applications, Leon, S. J., 2002