**First course in mathematics and statistics for students of biology, biotechnology, and environmental protection (30 hours)**

The whole lecture deals with following themes:

Lecture 1: Some basic mathematics (numbers, mathematical thinking, models, logarithms, exponents, Euler number)

Lecture 2: Basic operations and functions, fractal geometry (power, exponential, logarithmic, and hyperbolic functions)

Lecture 3: Matrix algebra I

Lecture 4: Matrix algebra II

Lecture 5: Handling a changing world (differential calculus)

Lecture 6: The sum of infinities (integral calculus, error functions)

Lecture 7: Probabilities and distributions

Lecture 8: First steps in statistics

Lecture 9: Moments and descriptive statistics

Lecture 10: Important statistical distributions (Bernoulli, hypergeometric, Poisson, normal)

Lecture 11: Parametric hypothesis testing (t-test, F-test, Chi2 test, G-test)

Lecture 12: Correlation and linear regression (model I and model II regression)

Lecture 13: Analysis of variance (ANOVA, ANCOVA, Kruskal Wallis test)

Lecture 14: Non-parametric testing (U-test, Wilcoxon test, sign test, randomization, bootstrap)

Lecture 15: Cluster analysis

Exercises (2 hours weekly in groups up to 16 students) are designed to deepen the material dealt with in the lecture. Students will especially be trained to use spreadsheet programs and the internet to solve mathematical problems.

Literature: A list of literature and internet pages is given during lecture 1

Older scripts that do not completely cover the present material:

Math1, Math2, Math3

Stat1, Stat2, Stat3

Examine: written test after the end of the term.

You pass the Exercises after solving some own work prepared for each lesson.

**First course in mathematics and statistics for students of biology, biotechnology, and environmental protection (15 hours)**

The whole lecture deals with following themes:

Lecture 1: Introduction

Lecture 2: Important functions in the biological sciences

Lecture 3: Matrix algebra

Lecture 4: Calculus

Lecture 5: Descriptive statistics

Lecture 6: Moments and distributions

Lecture 7: Parametric hypothesis testing

Lecture 8: Correlation and regression

Exercises (2 hours weekly in groups up to 16 students) are designed to deepen the material dealt with in the lecture. Students will especially be trained to use spreadsheet programs and the internet to solve mathematical problems.

Literature: A list of literature and internet pages is given during the lecture.

Examine: written test after the end of the term. Download an example of this test here.

You pass the Exercises after solving some own work prepared for each lesson.

**Matrix algebra for students of biotechnology**

**(for students of the first year of master studies)**

The lecture deals with basic matrix algebra and applications:

Lecture 1: Introductions to vectors

Lecture 2: Basic matrix operations

Lecture 3: Linear systems

Lecture 4: Linear and multiple regression

Lecture 5: Eigenvalues, eigenvectors, and Markov chains

Literature: A list of literature and internet pages is given during the lecture.

Examine: written test after the end of the excercises.

**Basic mathematics for students of agrobiotechnology(for students of the first year)**

The lecture deals with basic school mathematics:

Lecture 1: History and foundations

Lecture 2: Logic

Lecture 3: Numbers and counting

Lecture 4: Elementary geometry

Lecture 5: Trigonometry

Lecture 6: Vectors

Lecture 7: Simple equations

Literature: A list of literature and internet pages is given during the lecture.

Examine: written test after the end of the excercises.

**Second course in statistics for students of biology and biotechnology**

** (for students of the first year of master studies)**

The lecture deals with basic matrix algebra and applications:

Lecture 1: Short recapitulation of matrix algebra

Lecture 2: On the philosophy of statistical testing

Lecture 3: Analysis of variance

Lecture 4: General linear models

Lecture 5: Ordination

Lecture 6: Randomization techniques

Exercises (2 hours weekly in groups up to 16 students) are designed to deepen the material dealt with in the lecture. Students will especially be trained to use spreadsheet programs and the internet to solve mathematical problems.

Literature: A list of literature and internet pages is given during the lecture.

Examine: written test after the end of the term. Download an example of this test here.

You pass the Exercises after solving some own work prepared for each lesson.