Matematik for forskere

»Matematik? Det kan jeg ikke finde ud af!«, lyder standardudtalelsen ofte fra folk, der har svært ved eller ligefrem er angst for matematik.Mange tror nemlig, at matematiske evner er noget, man er født med – eller uden. Der findes dem, der kan finde ud af det, og dem, der ikke kan. Og hører man til de sidste, kan man lige så godt give op på forhånd – ikke?Matematikangst er en ond spiral: Hvis vi har dårlige oplevelser med matematik, får vi lave forventninger til os selv. Og har vi lave forventninger, præsterer vi også dårligere. Ikke mindst piger går til faget med en tro på, at det mest er noget for drenge.Men hvorfor er angsten for matematik så udbredt? Hvad bunder den i? Og hvad skal der til for at overkomme den?Matematikangst giver indsigt i, hvordan ubevidste fordomme om matematik påvirker os, og hvordan de kan modvirkes. Gennem teori, interviews og analyser klæder den matematiklæreren på til at vise eleverne, at matematik er noget, alle kan lære. Og som vi alle sammen bruger hver dag uden at tænke over det.Maria Kirstine Østergaard er cand.pæd. i matematikkens didaktik og underviser i matematik på læreruddannelsen.

From Quanta to Gravitation is a full biography of the danish physicist Christian Møller (1904-1980) and his important contributions to quantum mechanics, particle physics, and general relativity theory. Because of his life-long association with the Niels Bohr Institute the book is also, more generally, a history of this institute and physics in Copenhagen from about 1930 to 1980. Moreover, Møller interacted with an extensive network og physicists including luminaries such as Niels Bohr, Werner Heisenberg, and Paul Dirac, and for this reason his life and career reflect major developments in international theoretical physics throughout the period.The biography is to a large extent based on archival and other unpublished material. It covers not only Møller’s scientific contributions, but also his involvement in the political and organisational aspects of physics.

Over the past decade or so, we have seen a multitude of improvement programmes and projects to improve the safety of patient care in healthcare. However, the full potential of these efforts and especially those that seek to address an entire system has not yet been reached. The current pandemic has made this more evident than ever.We have tended to focus on problems in isolation, one harm at a time, and our efforts have been simplistic and myopic. If we are to save more lives and significantly reduce patient harm, we need to adopt a holistic, systematic approach that extends across cultural, technological, and procedural boundaries. Patient Safety Now is about the fact that it is time to care for everyone impacted by patient safety, how we need to take the time to care for everyone in a meaningful way and how hospitals need to enable staff time to care safely.This book builds on the author's two previous books on patient safety. Rethinking Patient Safety talked about ways in which we need to rethink patient safety in healthcare and describes what we've learned over the last two decades. Implementing Patient Safety talked about what we can do differently and how we can use those lessons learned to improve the way we implement patient safety initiatives and encourage a culture of safety across a healthcare system. Patient Safety Now unites the concepts, theories and ideas of the previous two books with updated material and examples, including what has been learned by patient safety specialists during a pandemic.Patient Safety Now provides the reader with a unique view of patient safety that looks beyond the traditional negative and retrospective approach to one that is proactive and recognizes the impact of conditions, behaviours and cultures that exist in healthcare on everyone. It is written not only for healthcare professionals and patient safety personnel, but for patients and their families who all want the same thing. Too often when things go wrong, relationships quickly become adversarial when in fact this can be avoided by recognizing that, rather than being in separate camps, there are shared needs and goals in relations to patient safety.

Aimed at graduate students, this textbook examines the importance of data analysis to understanding biological, physical, and chemical systems, and outlines its practical applications at the intersection of probability theory, statistics, optimisation, statistical physics, inference, and machine learning.

Dieses Lehrbuch stellt eine umfassende und leicht verstandliche Einfuhrung in die Tensoranalysis dar, die hier als Oberbegriff von klassischer Tensoranalysis und Tensoralgebra zu verstehen ist und die in vielen Anwendungen der Physik und der Ingenieurwissenschaften benotigt wird. Es vermittelt die notigen algebraischen Hilfsmittel und enthalt zahlreiche Ubungsaufgaben mit Losungen, so dass es sich auch fur ein Selbststudium eignet.

Die Lehre und das Lernen der Hochschulmathematik kosten viel Zeit. Lässt sich der Aufwand reduzieren, ohne die Qualität der Lehre zu beeinträchtigen?Mit einem klaren "Ja" beantwortet das vorliegende Buch diese Frage und stellt hierfür einen vom Autorenteam entwickelten und erprobten Lösungsansatz vor: die Open Source Software MATeX. Durch eine programmiertechnische Kopplung eines Computeralgebrasystems mit einem Textverarbeitungsprogramm ist MATeX in der Lage, in Sekunden mathematische Übungsaufgaben zu lösen und die Lösungswege in LaTeX und PDF auszugeben. So können über eine intuitive webbasierte Schnittstelle vom Benutzer individuell gestaltete oder zufällig generierte Aufgabentypen zu über 30 Themen der Höheren Mathematik gestellt, gelöst und die Lösungen zur Verfügung gestellt werden.Inhaltlich spannt sich der Bogen von elementaren Grundlagen über die Analysis einer Veränderlichen, die lineare Algebra, Wahrscheinlichkeitsrechnung, die Analysis mehrerer Veränderlicher bis hin zu fortgeschrittenen Themen der Analysis, wie z. B. die Fourier-Reihe, die Laplace-Transformation und Optimierungsprobleme mit Nebenbedingungen.Informationen zum programmiertechnischen und konzeptionellen Hintergrund sowie Vorschläge für einen wirkungsvollen Einsatz der Software in der Lehre runden das Buch ab.Herausragende Merkmale sind:Dank der ca. 130 klickbaren QR-Codes stellt dieses Werk als PDF aber auch in gedruckter Form selbst eine Schnittstelle zur mathematischen Software MATeX dar.Insgesamt ca. 300 Links auf die MATeX-Webschnittstelle erleichtern den Einstieg und das Bedienen der Software.Über 140 Beispielaufgaben spiegeln das breite Leistungsspektrum der Software.Aufträge zum Erstellen von zufälligen Aufgaben können direkt aus dem Buch via klickbaren QR-Codes erteilt werden.Mit diesem Buch und der Software MATeX lassen sich Aufgaben und Lösungen in PDF-Form um zwei Größenordnungen schneller erzeugen.

This book constitutes the thoroughly refereed post-proceedings of the 7th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics, CIBB 2010, held in Palermo, Italy, in September 2010. The 19 papers, presented together with 2 keynote speeches and 1 tutorial, were carefully reviewed and selected from 24 submissions. The papers are organized in topical sections on sequence analysis, promoter analysis and identification of transcription factor binding sites; methods for the unsupervised analysis, validation and visualization of structures discovered in bio-molecular data -- prediction of secondary and tertiary protein structures; gene expression data analysis; bio-medical text mining and imaging -- methods for diagnosis and prognosis; mathematical modelling and simulation of biological systems; and intelligent clinical decision support systems (i-CDSS).

This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields like civil engineering, car design, aeronautics, metal forming, or biomechanics.Boundary value problems involving contact are of great importance in industrial applications in engineering such as bearings, metal forming processes, rubber seals, drilling problems, crash analysis of cars, rolling contact between car tires and the road, cooling of electronic devices... Other applications are related to biomechanical engineering design where human joints, implants or teeth are of consideration. Due to this variety, contact problems are today combined either with large elastic or inelastic deformations including time dependent responses. Thermal coupling also might have to be considered. Even stability behaviour has to be linked to contact.The topic of computational contact is described in depth providing an up-to-date treatment of different formulations, algorithms and discretisation techniques for contact problems which are established in the geometrically linear and nonlinear range. This book provides the necessary continuum mechanics background which includes the derivation of the contact constraints. Constitutive equations stemming from tribology which are valid at the contact interface are discussed in detail. Discretization schemes for small and finite deformations are discussed in depth. Solid and beam contact is considered as well as contact of unstable systems and thermomechanical contact. The algorithmic side covers a broad range of solution methods. Additionally adaptive discretisation techniques for contact analysis are presented as a modern tool for engineering design simulations. The present text book is written for graduate, Masters and PhD students, but also for engineers in industry, who have to simulate contact problems in practical application and wish to understand the theoretical and algorithmic background of contact treatment in modern finite element systems.For this second edition, illustrative simplified examples and new discretisation schemes as well as adaptive procedures for coupled problems are added.

Hvad gør man, når man møder elever med læringsvanskeligheder i matematik? Seks cases fra virkelighedens matematiktimer fortæller, hvordan du som lærer kan motivere og hjælpe de elever, der har vanskeligt ved faget.Bogen giver et dybtgående indblik i de læringsvanskeligheder, forskellige elever kæmper med. For at vise bredden af problemfeltet rækker bogens kapitler fra cases, hvor læringsvanskelighederne på trods af en omfattende indsats gav flere udfordringer end forudset, til cases, som må betragtes som solstrålehistorier.Det er en vigtig problemstilling at tage hånd om, fordi læringsvanskeligheder i matematikfaget kan afstedkomme personlige nederlag og barrierer for videre uddannelse og fremtidige jobmuligheder for den enkelte elev.Læringsvanskeligheder i matematik er andet bind af to med cases og erfaringer fra Efteruddannelsen til matematikvejleder (RUC) samt fra vejledernes efterfølgende praksis ude på landets ungdomsuddannelser. Første bind, Fra snublesten til byggesten, udkom i 2016.Med de to bøger får matematiklærere landet over nu konkrete redskaber til at hjælpe de elever, der ønsker at gøre en indsats i faget, men som har svært ved at få fod på matematikken.Mogens Niss er cand.scient., professor og dr.h.c. ved Roskilde Universitet. Han er leder på matematikvejlederprogrammet ved RUC. Uffe Thomas Jankvist er cand.scient og professor MSO ved DPU, Aarhus Universitet. Han er leder på matematikvejlederprogrammet ved RUC.

This is the first comprehensive study about the non-mathematical writings and activities of the Russian algebraic geometer and number theorist Igor Shafarevich (b. 1923). In the 1970s Shafarevich was a prominent member of the dissidents' human rights movement and a noted author of clandestine anti-communist literature in the Soviet Union. Shafarevich's public image suffered a terrible blow around 1989 when he was decried as a dangerous ideologue of anti-Semitism due to his newly-surfaced old manuscript Russophobia. The scandal culminated when the President of the National Academy of Sciences of the United States suggested that Shafarevich, an honorary member, resign. The present study establishes that the allegations about anti-Semitism in Shafarevich's texts were unfounded and that Shafarevich's terrible reputation was cemented on a false basis.