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international theoretical physics throughout the period.The biography is to a large extent based on archival and other unpublished material.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.

This book will have distinct chapters with each section providing key messages in the form of a slide set that readers can use in order to share the ideas and lessons discussed with others.

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.

Document from the year 2013 in the subject Mathematics - Geometry, grade: 3.00, , language: English, abstract: Ever since the creation of math, mathematicians have attempted to extend, or challenge the work of another mathematician with the intent to try and disprove their discoveries. The applications of math we now use to solve the problems of life, are due to discoveries of these great minds. Mathematics is no longer a system to count objects, as this examination will attempt to: Propose a Hypothetical Method of Attempting to Break the Current Sailing Record Around the World using Spherical Trigonometry.The scope in which this examination will take into account is that of spherical trigonometry at its sole. Situations will be adjusted to make spherical trigonometry the tool to attempt to challenge the current record of sailing around the world. It will not include the vector components entirely. Needless to say, the majority of the trigonometry used in this examination will be explained just enough to be understandable for the common math enthusiast. The record breaking component, is only a form in which this sub-branch of spherical geometry can be applied in the real world. The result of this examination ended with a success. The method taken resulted in breaking the current record held by Loïck Peyron within an astonishing 45 days 13 hours 42 minutes and 53 seconds. But from this examination it was derived that, with respect to the given points, that you could go around the world in 20 days 17 hours 5 minutes and 17 seconds when going at a speed of 40 knots. However, this result was attained by not taking into consideration certain external factors that Loïck Peyron may have encountered when he broke the record. Therefore, if the condition were just right, and a constant speed of 40 knots was kept consistent throughout, the results from this examination would be valid.

We are proud to introduce the proceedings of the Seventh International C- ference on Parallel Problem Solving from Nature, PPSN VII, held in Granada, Spain, on 7-11 September 2002. PPSN VII was organized back-to-back with the Foundations of Genetic Algorithms (FOGA) conference, which took place in Torremolinos, Malaga, Spain, in the preceding week. ThePPSNseriesofconferencesstartedinDortmund,Germany[1].Fromthat pioneering meeting, the event has been held biennially, in Brussels, Belgium [2], Jerusalem, Israel [3], Berlin, Germany [4], Amsterdam, The Netherlands [5], and Paris, France [6]. During the Paris conference, several bids to host PPSN 2002 were put forward; it was decided that the conference would be held in Granada with Juan J. Merelo Guerv¿ os as General Chairman. The scienti?c content of the PPSN conference focuses on problem-solving paradigms gleaned from natural models, with an obvious emphasis on those that display an innate parallelism, such as evolutionary algorithms and ant-colony optimization algorithms. The majority of the papers, however, concentrate on evolutionary and hybrid algorithms, as is shown in the contents of this book and itspredecessors.Thiseditionoftheconferenceproceedingshasalargesectionon applications,betheytoclassicalproblemsortoreal-worldengineeringproblems, which shows how bioinspired algorithms are extending their use in the realms of business and enterprise.

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 thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in many applications in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. The overall presentation covers not only modeling aspects and qualitative analysis of mathematical problems, but also inverse problems, which lead to a detailed assessment of models in connection with their applications, and to computational problems, which lead to an effective link of models to the analysis of real-world systems. The book is divided into three parts: Part I presents fundamental aspects of the Boltzmann equation; Part II deals with the modeling of semiconductor devices as well as related applications and computational topics; Part III covers a variety of applications in physics and the natural sciences, offering a range of very different conceivable developments of mathematical kinetic theory.  Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.

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.

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.

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.