Introduction to Mathematics for Life Scientists

Abstract

A few decades ago mathematics played a modest role in life sciences. Today, however, a great variety of mathematical methods is applied in biology and medicine. Practically every mathematical procedure that is useful in physics, chemistry, engineering, and economics has also found an important application in the life sciences.The past and present training of life scientists does by no means reflect this development. However, the impact of the fast growing number of applications of mathematical methods makes it indispensable that students in the life sciences are offered a basic training in mathematics, both on the undergraduate and the graduate level. This book is primarily designed as a textbook for an introductory course. Life scientists may also use it as a reference to find mathematical methods suitable to their research problems. Moreover, the book should be appropriate for self-teaching. It will also be a guide for teachers. Numerous references are included to assist the reader in his search for the pertinent literature.Life scientists are hardly interested in going deeply into mathematics. Therefore, this course differs in many ways from a course offered to mathematicians. Each concept is introduced in an intuitive way. The reader is being kept informed why he is learning a particular method. The relevance of all procedures is proven by examples that have been selected from a wide area of research in the life sciences. It is not intended to distract the student of biology from his main field of activity and to train him as a competent mathematician. The aim is rather to prepare him for an understanding of the basic mathematical operations and to enable him to communicate successfully with a mathematician in case he needs his help.Many illustrations and some historical notes are inserted to encourage the life scientist who is perhaps somewhat reluctant to be involved with the abstract side of mathematics. Most problems were tested in class. Sections and problems marked with an asterisk are not necessarily more difficult, but may be omitted on first reading.The book avoids as much as possible the introduction of cookbook mathematics. This requires a somewhat broad presentation. As a consequence no attempt is made to comprise all mathematical methods that are important for life scientists. For instance, computer techniques and statistics are omitted. These two areas can only be presented in special ContentsChapter

DON content in oat grains in Norway related to weather conditions at different growth stages

“…The proposed models were based on air temperature, soil temperature, precipitation, photoperiodic time and day length, which are easily available variables assumed to be of importance for plant development (Davidson and Campbell 1983;Shaykewich 1995;Saarikko and Carter 1996;Wang and Engel 1998;Sonego et al 2000;McMaster et al 2008;Rajala and Peltonen-Sainio 2011;Olesen et al 2012;Siebert and Ewert 2012). The Gompertz growth function (Batschelet 1976), which is a sigmoid function with asymmetrical growth (Eq. 1), was used as the base function for all proposed model versions.…”

Field Data Based Method for Predicting Long-Term Settlements

“…More recently, it has also been used to predict biological and economic growth (Winsor, 1932;Batschelet, 1977). This shows that Gompertz Model can be used as a reliable and effective prediction tool.…”

Assessing social and environmental links in development strategies for Cameroon: A process approach to sustainability

“…The checklist has been applied to one national development strategy ( In checklist approaches, assessment is done qualitatively (Olsen and Fenhann, 2008) and quality is best measured on an ordinal scale (Batschelet, 1979). Answers to the questions are scored on a three-point ad hoc ordinal scale (Forrest and Bjorn, 1986), where 1 stands for 'issue not mentioned', 2 for 'issue mentioned but not elaborated' and 3 for 'issue elaborated'.…”