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We introduce a newly designed undergraduate-level interdisciplinary course in scientific computing that aims to prepare students as the next generation of research-oriented computational scientists and engineers. The course offers students…

Humans can leverage hierarchical structures to split a task into sub-tasks and solve problems efficiently. Both imitation and reinforcement learning or a combination of them with hierarchical structures have been proven to be an efficient…

In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them. Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood. Here we…

These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…

Computing has a huge memory problem. The memory system, consisting of multiple technologies at different levels, is responsible for most of the energy consumption, performance bottlenecks, robustness problems, monetary cost, and hardware…

Reinforcement learning (RL) can elicit strong reasoning in large language models (LLMs), yet most open efforts focus on math and code. We propose Reasoning Curriculum, a simple two-stage curriculum that first elicits reasoning skills in…

As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…

Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to perform complex reasoning tasks, transitioning from fast and intuitive thinking (System 1) to slow and deep reasoning (System 2). While System…

The aim of this study is to construct and compose an instructional design in combinatorial learning, particularly in the concept of counting. A composed design is expected to optimize students' combinatorial-thinking skill. This research…

A technique used to accelerate an adaptive optics simulation platform using reconfigurable logic is described. The performance of parts of this simulation have been improved by up to 600 times (reducing computation times by this factor) by…

Curriculum design is a fundamental component of education. For example, when we learn mathematics at school, we build upon our knowledge of addition to learn multiplication. These and other concepts must be mastered before our first algebra…

To effectively prepare engineering students requires of formation of a system of fundamental physical knowledge together with the ability to apply them in specific productive activities, both on fundamental and on the profiled-oriented…

Past research has defined a general process for the data-driven redesign of educational technologies and has shown that in carefully-selected instances, this process can help make systems more effective. In the current work, we test the…

Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks,…

Deep neural networks have shown superior performance in many regimes to remember familiar patterns with large amounts of data. However, the standard supervised deep learning paradigm is still limited when facing the need to learn new…

Probabilistic graphical models (PGMs) serve as a powerful framework for modeling complex systems with uncertainty and extracting valuable insights from data. However, users face challenges when applying PGMs to their problems in terms of…

The development of IT and WWW provides different teaching strategies, which are chosen by teachers. Students can acquire knowledge through different learning models. The problem based learning is a popular teaching strategy for teachers.…

Recently, introducing computer science and educational robots in compulsory education has received increasing attention. However, the use of screens in classrooms is often met with resistance, especially in primary school. To address this…