Description:
This course starts from solving linear systems and covers standard topics in linear algebra including
vector space, matrices and system of linear equations, linear mappings and matrix forms, inner product, orthogonality, eigenvalues and
eigenvectors, symmetric matrix.
Prerequisites: A passing grade in AL Pure Mathematics / AL Applied Mathematics; OR MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024.
Exclusions: MATH 2111, MATH 2131, MATH 2350
Instructor: Shingyu Leung
Email: masyleung @ ust.hk
Office: 3491
Office hours:
Class webpage: http://www.math.ust.hk/~masyleung/2121.18s.html
Class blog: http://math2121-2018s.blogspot.com/
TA:
Email:
Lectures: Room XXXX, Monday 4-520pm and Friday 12-130pm
References: (1) Linear Algebra and its Applications, by D. Lay;
(2) Linear algebra with Applications, Steven J. Leon.
Midterm: TBA in class
Final: TBA
Intended Learning Outcomes
Upon sucessful completion of this course, students should
1. Develop an understanding of the core ideas and concepts of numerical methods.
2. Be able to recognize the power of abstraction and generalization, and to carry out investigative mathematical work with independent judgment.
3. Be able to apply rigorous, analytic, highly numerate approach to analyze and solve problems using numerical methods.
4. Be able to communicate problem solutions using correct mathematical terminology and good English.
Announcement
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Notes
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Grading Scheme
Scheme A: HW 15% + MT 30 % + Final 55 %
Scheme B: HW 15% + Final 85 %
Total Marks = max(Scheme A, Scheme B)
More information will be given in the lecture prior to the exams.
No make-up exams.
Homeworks and Solutions
Bi-weekly homework: one lowest homework score will be dropped.
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Topics
(*) if time permits
Linear Equations and Matrix Algebra
Systems of Linear Equations (1.1)
Row Reduction and Echelon Forms (1.2)
Vector Equations (1.3)
The Matrix Equation Ax=b (1.4)
Solution Sets of Linear Systems (1.5)
Matrix Operations (2.1)
The Inverse of a Matrix (2.2)
Introduction to Determinants (3.1)
Properties of Determinants (3.2)
Vector Spaces
Vector Spaces and Subspaces (4.1)
Linearly Independence (4.3)
Bases and Dimensions (4.3, 4.5)
Change of Basis (4.7)
Coordinate Systems (4.4)
Null Spaces, Column Spaces (4.2)
Rank-Nullity Theorem (4.6)
Linear Transformation
Introduction to Linear Transformations (1.8, 1.9)
Matrix Representation of a Linear Transformation (5.4)
Eigenvectors and Eigenvalues (5.1)
The Characteristic Equation (5.2)
Diagonalization (5.3)
Complex Eigenvalues (5.5)
Orthogonality and Least-Squares
Inner Product, Length, and Orthogonality (6.1)
Inner Product Space (6.7)
Orthogonal Projections (6.3)
Orthogonal Sets (6.2)
Least-Squares Problems (6.5)
The Gram-Schmidt Process (6.4)
(*) Symmetric Matrices and Quadratic Forms
Diagonalization of Symmetric Matrices (7.1)
Quadratic Forms (7.2)
The Singular Value Decomposition (7.4)
Actual Schedule of Lectures
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MATH2121 Linear Algebra (4 credits)