MAED5851 Scientific Computation

Instructor: Shingyu Leung
Email: masyleung @ ust.hk
This course introduces various case studies drawn from different areas of science to illustrate the use of computers as a problem-solving tool. Each integrates physical principles and mathematical models, as well as numerical techniques and computer implementations, into a coherent perspective.

Lectures: Saturday 10am-1250pm, Room 3209A
Textbook: Lecture notes
Classblog: http://maed5851-2017f.blogspot.hk/

Intended Learning Outcomes

Upon sucessful completion of this course, students should
Explain advanced mathematical theories, concepts and principles using precise mathematical language.
Apply independent judgment to investigative mathematical work.
Apply a rigorous logical and analytic approach to execute tasks and solve mathematical problems.
Work independently and collaborate effectively in a team.
Communicate mathematical concepts and methods effectively to a range of audiences, both orally and in writing.
Evaluate individual performance to identify and work towards targets for personal, academic and career development.
Apply the fundamental principles and conventions of ethical scientific practice and academic integrity.
Analyze the influence of mathematical sciences and their impact on human activity.
Draw on a global perspective and sound scientific evidence to evaluate the role of mathematical sciences in the international science community.

Announcement

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Assessment Scheme

HW assignment (30%): both hand-written and computational.
Project (70%)

SCHEDULE

Software for Applied/Computational Mathematics: MATLAB, LaTex
Introduction to Mathematical Modeling
Image as Matrix
Tools: Linear Algebra. Singular value decomposition.
Applications: Histogram processing for image enhancement. Filtering for image enhancement and restoration. Linear signal/image compression. Image segmentation. (*) Compressed Sensing.
Topics: Image sampling and quantization
Dynamical Systems: Nondimensionalization - Phase Space - Stability of Fixed Points - Basin of Attraction
Chaos and Fractals: Poincare Section - Bifurcation - Fractal Dimensions and Correlation Dimension
Designing Mathematical Graphics
Writing an Academic Paper

Actual Schedule of Lectures

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