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Explore the technique known as the Socratic Method, which uses questions to examine a person’s values, principles, and beliefs.
- Keywords:
- Critical thinking Socrates Questioning
- Resource Type:
- Video
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Video
Every day, a sea of decisions stretches before us, and it’s impossible to make a perfect choice every time. But there are many ways to improve our chances — and one particularly effective technique is critical thinking. Samantha Agoos describes a 5-step process that may help you with any number of problems.
- Keywords:
- Problem solving Critical thinking Decision making
- Resource Type:
- Video
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Video
Design Thinking is a 5-step process to come up with meaningful ideas that solve real problems for a particular group of people. The process is taught in top design and business schools around the world. It has brought many businesses lots of happy customers and helped entrepreneurs from all around the world, to solve problems with innovative new solutions
- Keywords:
- Creative thinking Thought thinking Problem solving Creative ability
- Resource Type:
- Video
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Video
Imagine you were asked to invent something new. It could be whatever you want, made from anything you choose, in any shape or size. That kind of creative freedom sounds so liberating, doesn’t it? Or ... does it? if you're like most people you’d probably be paralyzed by this task. Why? Brandon Rodriguez explains how creative constraints actually help drive discovery and innovation.
- Keywords:
- Creative ability Inventions Problem solving
- Resource Type:
- Video
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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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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
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Video
Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics -- Study teaching
- Resource Type:
- Video
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Video
Often people make decisions that are not "rational" from a purely economical point of view — meaning that they don't necessarily lead to the best result. Why is that? Are we just bad at dealing with numbers and odds? Or is there a psychological mechanism behind it? Sara Garofalo explains heuristics, problem-solving approaches based on previous experience and intuition rather than analysis.
- Subjects:
- Psychology
- Keywords:
- Decision making
- Resource Type:
- Video