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In this matching game, learners are required to match the different phases of a research project.
- Subjects:
- Statistics and Research Methods
- Keywords:
- Research -- Methodology Research
- Resource Type:
- Others
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Video
In this video, a group of students came to a professor’s office and enquired how to cite sources in their research proposal.
- Subjects:
- Statistics and Research Methods
- Keywords:
- Bibliographical citations Scientific literature -- Evaluation Technical writing Research -- Methodology
- Resource Type:
- Video
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Video
In this video, a team of students found one article about the candy-soda geyser from the Journal of Chemical Education and would like to add this into the General Chemistry Laboratory. However, the journal article was published in 2007, so it is a bit out of date. Prof Cheong encourages you to search for any recent updates to this experiment.
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Video
In this video, Prof. Cheong will introduce the general procedure to carry out a literature search and the necessary resources that the students should consult.
- Subjects:
- Statistics and Research Methods
- Keywords:
- Proposal writing in research Chemistry -- Research Research -- Methodology Research
- Resource Type:
- Video
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Video
In this video, a group of students comes to a librarian’s office to enquire about how to manage their references.They scheduled an appointment with Ms. Janet Lee, a Research Support Librarian to learn about citation management.
- Subjects:
- Statistics and Research Methods
- Keywords:
- Report writing Citation of electronic information resources Bibliographical citations -- Computer programs Technical writing
- Resource Type:
- Video
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Others
In this matching game, learners are required to match various scientific content types, for example, books, literature review articles, encyclopedia entry, conference proceedings, scholarly journal articles, government documents, reference books, technical reports, with their intended purpose.
- Subjects:
- Statistics and Research Methods
- Keywords:
- Research Information literacy Information resources
- Resource Type:
- Others
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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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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
We introduce a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only Hessian-vector products in two directions. Moreover; the computational overhead remains comparable to the first-order such as the gradient descent method. We show that the method has a local super-linear convergence and a global convergence rate of 0(∈-3/2) to satisfy the first-order and second-order conditions under a commonly used approximated Hessian assumption. We further show that this assumption can be removed if we perform one step of the Krylov subspace method at the end of the algorithm, which makes DRSOM the first first-order-type algorithm to achieve this complexity bound. The applicability and performance of DRSOM are exhibited by various computational experiments in logistic regression, L2-Lp minimization, sensor network localization, neural network training, and policy optimization in reinforcement learning. For neural networks, our preliminary implementation seems to gain computational advantages in terms of training accuracy and iteration complexity over state-of-the-art first-order methods including SGD and ADAM. For policy optimization, our experiments show that DRSOM compares favorably with popular policy gradient methods in terms of the effectiveness and robustness.
Event date: 19/09/2022
Speaker: Prof. Yinyu Ye (Stanford University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex programming Nonconvex programming Mathematical optimization
- 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