USyd - Introduction to Linear Algebra
- Offered byCoursera
Introduction to Linear Algebra at Coursera Overview
Duration | 36 hours |
Total fee | Free |
Mode of learning | Online |
Official Website | Explore Free Course  |
Credential | Certificate |
Introduction to Linear Algebra at Coursera Highlights
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Introduction to Linear Algebra at Coursera Course details
- Linear algebra and calculus are the two most important foundational pillars on which modern mathematics is built. They are studied by almost all mathematics students at university, though typically labelled as different subjects and taught in parallel. Over time, students discover that linear algebra and calculus are inseparable (but not identical) twins that interlock to form the backbone of almost all applications of mathematics to physical and biological sciences, engineering and computer science. It is recommended that participants in the MOOC Introduction to Linear Algebra have already taken, or take in parallel, the MOOC Introduction to Calculus.
- All of our modern technical and electronic systems, such as the internet and search engines, on which we rely and tend to take for granted in our daily lives, work because of methods and techniques adapted from classical linear algebra. The key ideas involve vector and matrix arithmetic as well as clever methods for working around or overcoming difficulties, a form of obstacle avoidance, articulated in this course as the Conjugation Principle. This course emphasises geometric intuition, gradually introducing abstraction and algebraic and symbolic manipulation, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. Students taking Introduction to Linear Algebra will: Gain familiarity with the arithmetic of geometric vectors, which may be thought of as directed line segments that can move about freely in space, and can be combined in different ways, using vector addition, scalar multiplication and two types of multiplication, the dot and cross product, related to projections and orthogonality (first week),
- Develop fluency with lines and planes in space, represented by vector and Cartesian equations, and learn how to solve systems of equations, using the method of Gaussian elimination and introduction of parameters, using fields of real numbers and modular arithmetic with respect to a prime number (second week),
- Be introduced to and gain familiarity with matrix arithmetic, matrix inverses, the role of elementary matrices and their relationships with matrix inversion and systems of equations, calculations and theory involving determinants (third week),
- Be introduced to the theory of eigenvalues and eigenvectors, how they are found or approximated, and their role in diagonalisation of matrices (fourth week),
- See applications to simple Markov processes and stochastic matrices, and an introduction to linear transformations, illustrated using dilation, rotation and reflection matrices (fourth week),
- See a brief introduction to the arithmetic of complex numbers and discussion of the Fundamental Theorem of Algebra (fourth week).
Introduction to Linear Algebra at Coursera Curriculum
Week 1 - Geometric Vectors in the Plane and in Space
Welcome and introduction to Week 1
Geometric vectors - part 1
Geometric vectors - part 2
Hat notation and parallel vectors
Position vectors and components
Linear independence for two vectors
Dot product of two vectors
Projections and orthogonal components
Cross products of two vectors - part 1
Cross products of two vectors - part 2
How to navigate this MOOC
Overview of assessments and activities
Geometric vectors - part 1
Geometric vectors - part 2
Hat notation and parallel vectors
Position vectors and components
Linear independence for two vectors
Dot product of two vectors
Projections and orthogonal components
Cross products of two vectors - part 1
Cross products of two vectors - part 2
Geometric vectors - part 1
Geometric vectors - part 2
Hat notation and parallel vectors
Position vectors and components
Linear independence for two vectors
Dot product of two vectors
Projections and orthogonal components
Cross products of two vectors - part 1
Cross products of two vectors - part 2
Week 1 - Geometric vectors in the plane and in space
Week 2 - Lines and Planes in Space and Systems of Linear Equations
Introduction to Week 2
Lines in space - part 1
Lines in space - part 2
Planes in space
Systems of linear equations (a)
Systems of linear equations (b)
Modular arithmetic
Mixing arithmetics
Lines in space - part 1
Lines in space - part 2
Planes in space
Systems of linear equations
Modular arithmetic
Mixing arithmetics
Lines in space - part 1
Lines in space - part 2
Planes in space
Systems of linear equations
Modular arithmetic
Mixing arithmetics
Week 2 - Lines and planes in space and systems of linear equations
Week 3 - Matrix Arithmetic and the Theory of Determinants
Introduction to Week 3
Matrix addition and scalar multiplication
Matrix multiplication (a)
Matrix multiplication (b)
Matrix operations continued (a)
Matrix operations continued (b)
Matrix inverses (a)
Matrix inverses (b)
Determinants (a)
Determinants (b)
Determinants (c)
Matrix addition and scalar multiplication
Matrix multiplication
Matrix operations continued
Matrix inverses
Determinants
Matrix addition and scalar multiplication
Matrix multiplication
Matrix inverses
Determinants
Week 3 - Matric arithmetic and the theory of determinants
Week 4 - Eigentheory and Diagonalisation
Introduction to Week 4
Eigenvalues and eigenvectors (a)
Eigenvalues and eigenvectors (b)
Finding eigenvectors (a)
Finding eigenvectors (b)
Diagonalisation (a)
Diagonalisation (b)
Introduction to stochastic matrices (a)
Introduction to stochastic matrices (b)
Introduction to linear transformations (a)
Introduction to linear transformations (b)
Introduction to linear transformations (c)
The fundamental theorem of algebra
Eigenvalues and eigenvectors
Finding eigenvectors
Diagonalisation
Introduction to stochastic matrices
Introduction to linear transformations
The fundamental theorem of algebra
Eigenvalues and eigenvectors
Finding eigenvectors
Diagonalisation
Introduction to stochastic matrices
Introduction to linear transformations
Week 4 - Eigentheory and diagonalisation
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