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2022
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Video
EDC presents a series of showcases that share project deliverables and innovations in TEL, promoting sustainable and impactful practices that resonate across PolyU and beyond. Showcase One proudly presents two departmental interventions funded by PolyU’s Quality Incentive Scheme Stage 1, which promotes eLearning, Teaching and Assessment (eLTA) by grooming and rewarding outstanding performance:
APSS on the Move: Incubation of L&T Strategies before, during and beyond the Pandemic Era.
AAE: Using an online platform, Github, to shape and build the students' problem-solving and learning-to-learn abilities through a flip-class project teaching approach.
Event Date: 13/10/2022
Presenter(s): Chui, Eric; Chu, Rodney; Hsu, Li Ta
Facilitator: Harbutt, Darren
- Subjects:
- Lesson Design, Student Engagement, and Good Practices
- Keywords:
- Internet in education Educational technology Web-based instruction
- Resource Type:
- Video
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Video
Before the advent of computers around 1950, optimization centered either on small-dimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinite-dimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving large-scale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Convex sets Mathematical optimization Computer science -- Mathematics
- Resource Type:
- Video
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Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Sampling (Statistics) Differential equations Partial -- Numerical solutions Mathematical models Adaptive computing systems
- Resource Type:
- Video
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MOOC
Design thinking has become very popular recently. It is because many people believe that design thinking can help generate innovative solutions. Many business and non-business organizations are adopting it to resolving their problems. Even business schools and other disciplines include design thinking in their curriculum. Then, what is design thinking, really? And how can it benefit us?
Design thinking is commonly recognized as a problem-solving process that includes five stages - Empathize, Define, Ideate, Prototype and Test. However, when we compare the design thinking process with the conventional problem-solving process, there are no major differences, except the implementation part. Design thinking looks at problems with a holistic and human-centric perspective. It also tackles complex problems by using a non-linear approach. However, some people claim that considering design thinking as a problem-solving process is too simplistic.
Actually, design thinking should be considered as behaviors and attitudes when dealing with problems. Design thinkers use different thinking styles and attitudes when approaching problems. Design thinkers possess certain personal traits like human-centeredness, having a flexible and creative thinking style, being comfortable with subjective and intuitive judgement, and high self-efficacy. These thinking styles and attitudes help not only in problem-solving but also in finding opportunities. In order to be proficient in design thinking, we should not only understand the design Thinking process, but also have to make ourselves become a design thinker.
This MOOC provides you with core knowledge about design thinking and demystifies design thinking as a process for solving complex and wicked problems.
- Keywords:
- Creative ability Product design Critical thinking
- Resource Type:
- MOOC
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MOOC
Operations management deals with operational planning and control issues, and is needed in all sectors of the society. One of the challenges to operations manager is how to make use of the available resources in the best way for meeting a certain objective. Quantitative approaches are inevitably needed in tackling many of such problems. Operations Research (OR) deals with problem formulation and application of analytical methods to assist in decision-making of operational problems in planning and control. The techniques of OR are useful quantitative tools to assist operations managers, and has a wide applicability in engineering, manufacturing, construction, financial and various service sectors. Operations Research is an applied mathematics subject and is also a course in many engineering and management programmes. This course is designed for both students learning OR and learners who are practitioners in their respective professionals. The mathematical procedures for the OR techniques are introduced in details in the examples provided in the course. This helps learners to master the methodology and the techniques and apply them to achieve their goals through active learning. This course introduces two prominent OR techniques and their extended topics. The Simplex Method for Linear Programming (LP) has been considered one of the top 10 algorithms of the 20th century. LP is an optimization technique for solving problems such as finding the optimal product mix, production plan, and shipment allocation, in order to maximize the profir or minimize the cost. The Critical Path Method (CPM) is a popular technique employed by project managers in scheduling project activities. Some extended topics of CPM are also introduced to deal with certain special situations in project management. In reality, many systems operate under stochastic environment and the operational problems cannot be solved by the known analytical methods. To this end, the simulation approach is introduced in the last chapter of this course. Simulation is a powerful technique for tackling OR problems under such situations.
- Subjects:
- Statistics and Research Methods
- Keywords:
- Operations research
- Resource Type:
- MOOC
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MOOC
This award-winning course aims to sharpen your competitive edge in work and life. It empowers you with positive values and practical problem-solving skills, including creative strategies for addressing challenges from COVID-19. Enriched with interesting animations, a new success story and breakthrough pedagogies, this updated version (2.5) effectively helps you master knowledge and skills requisite for a successful life.
- Keywords:
- Creative thinking Learning ability Critical thinking
- Resource Type:
- MOOC
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Video
Convex Matrix Optimization (MOP) arises in a wide variety of applications. The last three decades have seen dramatic advances in the theory and practice of matrix optimization because of its extremely powerful modeling capability. In particular, semidefinite programming (SP) and its generalizations have been widely used to model problems in applications such as combinatorial and polynomial optimization, covariance matrix estimation, matrix completion and sensor network localization. The first part of the talk will describe the primal-dual interior-point methods (IPMs) implemented in SDPT3 for solving medium scale SP, followed by inexact IPMs (with linear systems solved by iterative solvers) for large scale SDP and discussions on their inherent limitations. The second part will present algorithmic advances for solving large scale SDP based on the proximal-point or augmented Lagrangian framework In particular, we describe the design and implementation of an augmented Lagrangian based method (called SDPNAL+) for solving SDP problems with large number of linear constraints. The last part of the talk will focus on recent advances on using a combination of local search methods and convex lifting to solve low-rank factorization models of SP problems.
Event date: 11/10/2022
Speaker: Prof. Kim-Chuan Toh (National University of Singapore)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex programming Semidefinite programming
- Resource Type:
- Video