Линейная алгебра и геометрия

Бакалавриат 2020/2021

Лучший по критерию «Новизна полученных знаний»

Статус: Курс обязательный (Программа двух дипломов НИУ ВШЭ и Лондонского университета "Прикладной анализ данных")

Направление: 01.03.02. Прикладная математика и информатика

Кто читает: Департамент больших данных и информационного поиска

Где читается: Факультет компьютерных наук

Когда читается: 1-й курс, 1-4 модуль

Формат изучения: без онлайн-курса

Преподаватели: Калеева Галина Анатольевна, Мажуга Андрей Михайлович, Медведь Никита Юрьевич

Язык: английский

Кредиты: 10

Контактные часы: 144

Full Syllabus Ask Question

Abstract

The course introduces students to the elements of linear algebra and analytic geometry provides the foundations for understanding some of the main concepts of modern mathematics. There is a strong emphasis in this course on complete proofs of almost all results. We will approach the subject from both a practical point of view (learning methods and acquiring computational skills relevant for problem-solving) and a theoretical point of view (learning a more abstract and theoretical approach that focuses on achieving a deep understanding of the different abstract concepts). Topics covered include matrix algebra, systems of linear equations, permutations, determinants, complex numbers, fields, abstract vector spaces, bilinear and quadratic forms, Euclidean spaces, some elements of analytic geometry, linear operators. It took mathematicians at least two hundred years to comprehend these objects. We plan to accomplish this in one year. There is no formal prerequisites for this course. However, a reasonable knowledge of some of the fundamentals of high school mathematics such as: working with rational and real numbers, fractions, basic algebraic manipulations, geometry, and some trigonometry is assumed. Familiarity with basic mathematical concepts (sets, functions and etc.) is a plus. Calculus is not required for this course.

Learning Objectives

Students will understand the mathematical concepts and terminology involved in linear algebra and analytic geometry.
Students will gain an acceptable level of computational proficiency involving the procedures in linear algebra and analytic geometry.
Students will understand the axiomatic structure of some mathematical objects and learn to construct simple proofs.
Students will be able to apply his or her knowledge to some applications of linear algebra and analytic geometry.
Students will be introduced to abstract mathematical reasoning and the art of reading, writing and understanding rigorous mathematical proofs.

Expected Learning Outcomes

Student will be able to use computational techniques and algebraic skills essential for the study of systems of linear equations, matrix algebra, complex numbers, vector spaces, bilinear and quadratic forms, eigenvalues and eigenvectors, orthogonality and diagonalization, etc.
Students will be able to critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra and analytic geometry.
Students will be able to work collaboratively with peers and instructors to acquire mathematical understanding and to formulate and solve problems and present solutions.

Course Contents

Matrices and Matrix Algebra.
Systems of Linear Equations.
Permutations.
Determinants.
Fields and Complex Numbers.
Vector Spaces.
Bilinear and Quadratic Forms.
Euclidean Spaces.
Analytic Geometry.
Linear Operators.

Assessment Elements

1st module In-class Written Test
Written work up to 90 minutes.
3rd module In-class Written Test
Written work up to 90 minutes.
2nd module In-class Oral Test
4th module In-class Oral Test
2nd module Written Exam
Written work up to 160 minutes. The exam may be carried out online via distance learning platforms.
4th module Written Exam
The exam may be carried out online via distance learning platforms. Письменный экзамен, длительность 100 минут. Можно пользоваться калькуляторами (нельзя телефоном). Выолненная работа фотографируется/ сканируется прикрепляется в гугл форме. Ссылка на гугл форму в чате Zoom
1st semester Quizzes
The average grade of all the quizzes in the 1st semester.
2nd semester Quizzes
The average grade of all the quizzes in the 2nd semester.
1st semester Homework assignments
The average grade of all the homework assignments in the 1st semester.
2nd semester Homework assignments
The average grade of all the homework assignments in the 2nd semester.

Interim Assessment

Interim assessment (2 module)
The cumulative course grade for the first semester, C_1, is obtained without rounding by the following formula: C_1 = 5/16*O_1 + 4/16*W_1 + 4/16*Q_1 + 3/16*H_1. The intermediate course grade for the i-th semester, I_1, is obtained by the following formula: I_1 = Round_i(3/10*E_1 + 7/10*C_1), where O_1 is the grade for the first in-class oral test; W_1 is the grade for the first in-class written test; Q_1 is the average grade of all the quizzes in the first semester; H_1 is the average grade of all the homework assignments in the first semester; E_1 is the grade for the first exam.
Interim assessment (4 module)
The cumulative course grade for the second semester, C_2, is obtained without rounding by the following formula: C_2 = 5/16*O_2 + 4/16*W_2 + 4/16*Q_2 + 3/16*H_2. The intermediate course grade for the second semester, I_2, is obtained by the following formula: I_2 = Round_2(3/10*E_2 + 7/10*C_2), where O_2 is the grade for the second in-class oral test; W_2 is the grade for the second in-class written test; Q_2 is the average grade of all the quizzes in the second semester; H_2 is the average grade of all the homework assignments in the second semester; E_2 is the grade for the second exam.

Bibliography

Recommended Core Bibliography

Anthony, M., & Harvey, M. (2012). Linear Algebra : Concepts and Methods. Cambridge, UK: Cambridge eText. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=443759

Recommended Additional Bibliography

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

Course Syllabus