Related papers: Refining Calculus Pedagogy
We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
ZX-calculus has proved to be a useful tool for quantum technology with a wide range of successful applications. Most of these applications are of an algebraic nature. However, other tasks that involve differentiation and integration remain…
This article discusses the process of creating, implementing and experiencing Flipped Learning in a Multivariable Calculus course for second year engineering students. We describe the construction of the teaching material, consisting of…
This article is a part of the report for the research project ``Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)'' in 1995, supported by the National Ministry of Education. There are…
The integration of AI tools into programming education has become increasingly prevalent in recent years, transforming the way programming is taught and learned. This paper provides a review of the state-of-the-art AI tools available for…
Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in…
The ability to persist in the spacial environment is, not only in the robotic context, an essential feature. Positional knowledge is one of the most important aspects of space and a number of methods to represent these information have been…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
The $q$-calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling. The proposed technique is applied to a different…
Curriculum learning is often employed in deep reinforcement learning to let the agent progress more quickly towards better behaviors. Numerical methods for curriculum learning in the literature provides only initial heuristic solutions,…
Quantum computing presents a transformative potential for the world of computing. However, integrating this technology into the curriculum for computer science students who lack prior exposure to quantum mechanics and advanced mathematics…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates into the students a loss of interest with a consequent removal of motivation in the…