B5188 - Mathematics and Elements of Statistics for The Agricultural Sciences

Learning outcomes

Upon successful completion of the course, students will have acquired a solid understanding of the mathematical tools and techniques introduced, together with the main methods and fundamental tools used for the quantitative analysis of collective phenomena. They will be able to formulate and solve problems and to assimilate new concepts by building on prior knowledge and experience. Furthermore, they will be able to independently collect, process, and analyze statistical data, developing the ability to interpret and critically evaluate statistical information.

Course contents

Module 1. Mathematics for Agricultural Sciences (50 hours).

· Course introduction: course content, study materials, tutorials, and assessment.

· Sets; natural, rational, and real numbers; geometric representation of numbers.

· Vectors; vector operations; dot product.

· Review of geometry; linear equations and inequalities.

· Matrices and linear transformations; matrix operations; determinants.

· Review of algebra: linear, quadratic, exponential, polynomial, parabolic, hyperbolic, power, and absolute value functions.

· Graphs of functions: increasing and decreasing functions; maxima and minima of a function; real-valued functions of several variables.

· Linear, polynomial, parabolic, hyperbolic, power, and absolute value functions; exponential functions; logarithmic functions; logarithmic scales; asymptotic behavior.

· Limits and continuity of functions; sequences and recurrence relations; average and instantaneous rates of change; derivatives and integrals.

 

Module 2. Elements of Statistics for Agricultural Sciences (30 hours).

 · Statistical data: concepts of statistical units, populations, quantitative and qualitative variables, absolute, relative, and cumulative frequencies; examples of graphical data representations.

· Descriptive statistics:

1. Measures of central tendency: arithmetic and geometric means, positional measures, median, and loss functions.
2. Measures of variability: range, quartiles and box plots, variance, and standard deviation.
3. Elements of bivariate descriptive statistics: two-way frequency distributions, joint and marginal frequencies, analysis of the association between two variables.

· Elements of probability:

1. Models of uncertainty; theoretical probability distributions: Bernoulli, binomial, uniform, normal, and chi-square distributions;
2. Sampling and the Central Limit Theorem.

· Elements of inferential statistics:

1. Confidence intervals;
2. Parametric and non-parametric statistical tests for comparing means;
3. Chi-square test;
4. Comparison of more than two means: one-way analysis of variance (ANOVA).

· Regression and multiple linear regression; correlation.

Readings/Bibliography

- Matematica per le Scienze, Marco Bramanti, Fulvia Confortola, Sandro Salsa.

- Matematica per le scienze della Vita. Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei. Casa Editrice Ambrosiana.

Teaching methods

Lectures and guided exercises led by the instructor.

Assessment methods

Final Examination:

A written examination (covering both modules), consisting of exercises on the topics presented during the course. The exercises are of the same type as those discussed in class and those included in the exercise sheets available on virtuale.unibo.it.

To pass the examination, students must obtain:

• at least 12 points in the Mathematics module; and
• at least 6 points in the Statistics module.

Midterm Examination:

A midterm examination will be held at the end of the lecture period for Module 1 (Mathematics). The midterm examination is optional. Students who pass it will be eligible to take a reduced final examination covering Module 2 (Statistics) only, provided they sit the first available examination session following the end of the course.

Teaching tools

Lecture slides and lecture notes prepared by the instructor(s).

Exercises completed during class and additional exercises available on virtuale.unibo.it.

Office hours

See the website of Stefano Pagliarani

See the website of Salvatore Federico