Mathematics: from algebra to computer algebra

Prof. Dr. Wilfried Lex
Sets, magmas, monoids: encouragement for algebra at school

School mathematics offers a wealth of opportunities for algebraic considerations at all levels - algebra, understood as the study of algebraic structures, which occur in abundance throughout the curriculum: For example, monoids, groups, rings, solids and lattices; almost inevitably in the treatment of number fields, but also in set theory, number theory, combinatorics, geometry and analysis, as well as in the foundations of theoretical computer science, for example in formal languages, in automata theory, cryptology and coding theory, but also in the widely applicable formal concept analysis.

The lecture will use many examples to remind the audience how elementary algebra can be practised, largely independently of age, in order to gain a better overview and understanding of interrelationships and to systematize the wealth of possibilities and real phenomena, but also to awaken the joy of discovery and aesthetics. It is helpful that informative examples and counterexamples - which also demonstrate the need for proof of various lemmas - are plentiful or can be easily constructed, for example using Cayley tables. - Much could then also be expanded and deepened in working groups.

StD Thomas Sperlich
Computer algebra calculators in mathematics lessons - opportunities and problems

For years, more and more schools in Lower Saxony have been introducing computer algebra-capable calculators and working with them right through to the central Abitur. The tools for schools are also becoming more and more powerful, so that various questions arise for mathematics lessons:

For example, what opportunities are opening up in terms of teaching and task culture, such as problem solving, exploration and discovery in mathematics?

What problems arise, for example, from the fact that more and more simple operations such as calculus are no longer necessary for pupils and may be replaced by more complex questions, or from the fact that this results in accelerated learning and other skills (have to) be developed in some cases?

Dr. Henning Behnke
Never learn math again?

The lecture will provide a brief introduction to the computer algebra systemMathematicawill be given.

Is it possible for a student to pass an engineering math exam using only Mathematica? This question will be investigated using a typical exam from the first semester of Mathematics for Engineers.

Program