Linear Algebra (MATH 201)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Canan Kaşıkcı canankasikci@sabanciuniv.edu,
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English
Undergraduate
--
Formal lecture,Recitation
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CONTENT

Systems of linear equations; Gaussian elimination. Vector spaces, subspaces, linear, independence, dimension, change of basic. Linear transformations. Inner product, orthogonality. Eigenvalues. Diagonalization and canonical forms. Cayley-Hamilton theorem.

OBJECTIVE

This course aims to introduce basic concepts of linear algebra such as vector spaces, bases, linear transformations, eigenvalues and eigenspaces. The course gives students training to develop their mathematical skills, analytical and critical thinking abilities, their ability to apply these capabilities to practical problems, and to communicate their knowledge of these areas.

LEARNING OUTCOME

Understand the notion of mathematical thinking, mathematical proofs, and able to apply them in problem solving.
Present simple proofs in a precise and formally correct way.
Solve a system of linear equations using matrix reduction
Do basic arithmetical operations with matrices.
Understand the notions of linear independence, basis and dimension of a vector space.
Find a basis and dimension of Euclidean or abstract vector spaces.
Geometrically interpret the above concepts.
Represent linear transformations as matrices and, conversely, interpret matrices as linear maps.
Compute determinant of square matrices and understand the properties of determinant.
Compute eigenvalues and eigenspaces of matrices.
Identify whether a matrix is diagonalizable or not.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 35
Midterm 35
Assignment 20
Participation 10

RECOMENDED or REQUIRED READINGS

Textbook

G. Strang, Introduction to Linear Algebra. Fifth edition (2016) Wellesley-Cambridge Press and SIAM

Readings

Anton H., Rorres C., ?Elementary Linear Algebra with supplemental applications?, Wiley International Student Version, 11th edition, 2015.

Bretscher O., ?Linear Algebra with Applications?, 2nd Edition, Prentice-Hall, 2001.

Poole D., ?Linear Algebra: A Modern Introduction? 3rd Edition, Brooks Cole, 2011.

Leon, S. J., Linear Algebra with Applications, 9th Edition, Prentice Hall, 2014.

Kolman B., Hill D., ?Elementary Linear Algebra witg Applications?, 9th edition, Prentice-Hall, 2008.

Takahashi S, Inoue I, ?The Manga Guide to Linear Algebra?, 2012.

Gilbert Strang lectures on linear algebra, Lectures 1-34, Spring 2005,
{https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D}