doc. Mgr. Petr Habala, Ph.D.

The recent transfer to distance education caused by the pandemic forced higher education to reshape courses and adopt new educational tools. Many teachers became aware of and acquired valuable first-hand experience with alternative techniques of teaching. In this contribution we look at advantages and disadvantages of some popular approaches, assessing them not only from the point of view of distance education (which could still be useful), but also regarding their potential for improving on-site education. This is based on the authors' personal observations and student surveys at our institution (a kind of case study in our department and university), influenced by discussions with colleagues in formal and informal networks across Europe and supplemented with published results when possible.

When mastering new topics, the importance of timely and topical feedback is hard to overestimate. Distance education forced recently on educational community by COVID brought obstacles to one-on-one interaction, making direct feedback difficult. However, it also inspired educators to consider new tools and ideas. A possible approach allowing for quality feedback is outlined, supported by a comparison of pre-COVID and COVID results.

We introduce a new numerical methods library for Maple. We compare its commands with their standard Maple counterparts, based on features that could be found desirable when we want our students to experiment and explore.

An overview is given of the use of the theory behind the derivative and examples are given of its applications in mathematics, physics, and engineering.

There are many quantities that cannot be determined precisely using finite calculations, for instance 2 and π, or solutions of transcendental equations like cos⁡(x)=x. Many of the methods devised to find approximate answers to such untractable problems use the notions of sequences and series. Here we explore several such situations, in particular situations that relate to real-world computing, which is a topic that every engineer should be aware of. This chapter can thus also serve as a gentle introduction to the world of numerical analysis.

Differential equations and numerical mathematics are arguably the two mathematical tools that engineers cannot do without in their professional careers. We survey common approaches to incorporating these crucial subjects in bachelor engineering programs. Then we look in detail at a particular implementation that connects these two fields.

Arguably the largest obstacle freshmen face in their mathematics courses is their unfamiliarity with the language of mathematics. Addressing this problem right at the start seems like a sensible strategy, as comprehension of mathematical communication helps students in all mathematics courses they will take. In this paper we discuss general strategies that can be used when addressing the competency in understanding and speaking the language of mathematics. In particular we focus on benefits of teaching students to prove statements and difficulties related to such endeavour. We introduce discrete mathematics as a particularly suitable course for such activity. Then we look closer at practical experiences we had when teaching comprehension of mathematical language and proofs in discrete mathematics courses.

Banach spaces provide a framework for many branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory.