Syllabus
Ten modules are offered to the students during the basic course of mathematics for biology. Not all of these modules are expected to run each term. As declared in the annotation, the lecturers prefer robust understanding over the quantity of information, and therefore they could skip some of the modules if the progress of the students were slow. The lecturers are, however, rather the moderators of the student’s discussion, than speakers, and so the students can ask them not to skip a module if they were interested.
Notation: lesson - how to turn biology into math equations; "grammar" and "syntax" of mathematical "formulas" ; types of queries and information that one can impose and receive, respectively when solving mathematical equations or inequalities; unit invariance. practice - basic skills in mathematical notation; how to solve and simplify equations and inequations with respect to the question in focus.
Function 0: lesson - function as a modell of biological datasets; functions that fitt and bound datasets; graph and equation of a linear, polynomic, logarithmic, exponencial and hyperbolic function. practice - link between formal notation and graphical pattern for selected functions.
Recurrence relations and differential equations: lesson - recurrence relations and their use in population ecology; differentiation of a recurrence relations and the most frequent mistakes; derivative of a function, meaning and definition; case studies. practice - training in function derivatives and its graphical representation.
Integration: lesson - we introduce the idea of integral using a case study from biology; definite and indefinite integral; link between integral and addition and patch area; integral and probability; basic in statistical testing; units of an integral. practice - training in function integration and graphical representation of integrals.
Functional equations: lesson - functional equations; differential equations; integral equations - graphic visualisation; case studies from biology. practice - training in functional and differential equations.
Logarithm: lesson - we show that a logarithmic function is a solution of a functional equation; maening and usage of a logarithmic function; logarithmic data transformation for statistical analyses; case studies. practice - training in logarithms; practice in the reading of the biological texts with logarithms in it.
Invariances: lesson - mathamatization using invariances; unit invariance, principle of superpozition, taxon and area invariance, scale invariance, self-similarity and fraktals; case studies. practice - practice in the reading of the biological texts with invariance in it.
Functions 1: lesson - functions of multiple arguments; derivative of a function of multiple arguments along a curve and in a focal direction - we show all the problemes in a visual way; case studies. practice - training in the function of multiple variables; simple calculations.
Statistical methods: lesson - probability distribution functions; we show usage of mean, median, modus and maximum likelihood in case studies from biology; basic in multivariable statistical methods (GLM) and a link between these methods and linear function of multiple arguments. practice - practice in usage of mean, median, modus, maximum likelihood and multivariable statistical methods.
Transformations: lesson - transformation of variables; how to prepare data for statistical analyses; link between a function and data transformation; changes in functions, frequency distributions and units while we apply a transformation. practice - transformation of a dataset, graphic representation of a function and frequency distribution; case studies.
Matrices: lesson - how to design Leslie matrix and a vector of the population in population ecology; determinant and eigenvalues of a matrix; the meaning of the determinants and eigenvalues for biology. practice - practice in matrices calculus; determinant and eigenvalues of a matrix; how to use matrices when one solves a system of linear equations.
Annotation
The lessons are running once a week during the winter term 2015/16. The students will be shown (i) how to see the links between formal descriptions and graphs; (ii) how to draw schemes and calculate particular examples when reading a new, biological text with mathematical equations; (iii) to see differences between discrete and continuous world; (iv) to see that the mathematical formalism is only a part of our language, which can help with understanding to our problems in biology. Please note that the lessons are given in the Czech language only; we can, however, switch to English on request.
During the forthcoming term, we will also run a class of practical computational skills that will support the lessons. The class is not mandatory, but only recommended. However, the class will be closed for those who will not attend the lessons.