Hasil Pencarian  ::  Simpan CSV :: Kembali

Abstrak :
This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics, and Euclidean geometry, enabling a broad familiarity. The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit.

Abstrak :
A proof theory for description logics introduces sequent calculi and natural deduction for some DLs (ALC, ALCQ). Cut-elimination and normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.

Abstrak :
This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as : (1) the potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice, (2) the developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades, and (3) the development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving.