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Бакалаврская программа «Программа двух дипломов НИУ ВШЭ и Лондонского университета "Прикладной анализ данных"»

Linear Algebra and Geometry

2019/2020
Учебный год
ENG
Обучение ведется на английском языке
8
Кредиты
Статус:
Курс обязательный
Когда читается:
1-й курс, 1-4 модуль

Преподаватели

Course Syllabus

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

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

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

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

Assessment Elements

  • non-blocking 1st module In-class Written Test
    Written work up to 90 minutes.
  • non-blocking 3rd module In-class Written Test
    Written work up to 90 minutes.
  • non-blocking 2nd module In-class Oral Test
  • non-blocking 4th module In-class Oral Test
  • non-blocking 2nd module Written Exam
    Written work up to 160 minutes.
  • non-blocking 4th module Written Exam
    Written work up to 160 minutes.
  • non-blocking 1st semester Quizzes
    The average grade of all the quizzes in the 1st semester.
  • non-blocking 2nd semester Quizzes
    The average grade of all the quizzes in the 2nd semester.
  • non-blocking 1st semester Homework assignments
    The average grade of all the homework assignments in the 1st semester.
  • non-blocking 2nd semester Homework assignments
    The average grade of all the homework assignments in the 2nd semester.
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.2 * 1st module In-class Written Test + 0.125 * 1st semester Homework assignments + 0.175 * 1st semester Quizzes + 0.2 * 2nd module In-class Oral Test + 0.3 * 2nd module Written Exam
  • Interim assessment (4 module)
    0.125 * 2nd semester Homework assignments + 0.175 * 2nd semester Quizzes + 0.2 * 3rd module In-class Written Test + 0.2 * 4th module In-class Oral Test + 0.3 * 4th module Written Exam
Bibliography

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