MATH4992 Capstone Project in Applied Mathematics

Instructor: Shingyu Leung
Email: masyleung @ ust.hk
This is a project-based course that provides students an opportunity to integrate and apply their mathematical knowledge. Students will be assigned to a section according to their program or track. Upon completion of projects, students are required to submit written reports following standard professional formats. For MATH Year 4 students in the AM track only.

Lectures: Monday 130pm-250pm and Friday 9am-1020am, Room 3209A
Textbook: Lecture notes
Classblog: http://math4992-2017f.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 (25%): both hand-written and computational.
Project 1 (25%)
Project 2 (30%)
Project Presentation (20%)

SCHEDULE

Software for Applied/Computational Mathematics: MATLAB, LaTex
Introduction to Mathematical Modeling
Dynamical Systems: Nondimensionalization - Phase Space - Stability of Fixed Points - Basin of Attraction
Chaos and Fractals: Poincare Section - Bifurcation - Fractal Dimensions and Correlation Dimension
Computational Maths: Overview - Accuracy - Stability - Convergence - Computational Efficiency
Designing Mathematical Graphics
Writing an Academic Paper
Doing an Academic Presentation

Actual Schedule of Lectures

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