MATHEMATICS AND STATISTICS APPLIED TO FOOD SCIENCE

Learning Objectives

The course aims to provide a foundational understanding of infinitesimal, differential, and integral calculus for functions of a single variable and its applications.

Knowledge and Understanding

This course in mathematics, tailored for food science and technology, aims to provide a solid foundation in the essential mathematical concepts of real numbers, continuous functions, derivatives, integrals, and statistics. It enables students to apply these tools effectively to everyday problem-solving. Through rigorous study and practical applications, students will develop a sound understanding of these mathematical principles and acquire the analytical skills necessary for success in their academic path.

Applying Knowledge and Understanding

Students are encouraged to leverage their knowledge of mathematical tools to solve practical problems. Through hands-on exercises and real-world applications, they will develop the ability to use these mathematical concepts as powerful tools for analysis and modeling.

Autonomy of Judgment

Students will be challenged to express informed judgments by evaluating the appropriateness and accuracy of mathematical techniques applied to practical problems. They will develop the ability to critically assess and select the most suitable mathematical methods, enhancing their problem-solving and decision-making skills.

Communication Skills

The course places strong emphasis on developing effective communication skills, enabling students to clearly and concisely articulate mathematical concepts and problem-solving approaches. Through exercises and collaborative discussions, students will learn to convey complex mathematical ideas to both technical and non-technical audiences—an essential skill for success in their careers.

Learning Skills

Core learning skills will be cultivated, including self-directed study, problem-solving strategies, and adaptability in facing mathematical challenges. Through a variety of exercises and self-assessment activities, students will develop the ability to independently explore and apply mathematical concepts, fostering a lasting capacity for lifelong learning.

The teaching (6 CFU) includes 21 hours of lectures and 42 hours of other activities, mainly guided numerical exercises for solving problems of practical interest for the profession of food technologist. 

Information for students with disabilities and/or DSA

As a guarantee of equal opportunities and in compliance with current laws, interested students can ask for a personal interview in order to plan any compensatory and/or dispensatory measures, based on their specific needs and on teaching objectives of the discipline. It is also possible to ask the departmental contacts of CInAP (Center for Active and Participatory Integration - Services for Disabilities and/or DSAs), in the persons of professor Anna De Angelis.

Ability to argue and communicate, both orally and in written form. Knowing how to identify, describe, and work with sets. Recognizing hypotheses and theses of a theorem. Identifying whether a condition is necessary or sufficient. Knowing how to negate a proposition and understand a proof by contradiction. Understanding the difference between examples and counterexamples. Knowing numerical sets, particularly the algebraic and ordering properties of real numbers.

Knowing the definition, graph, and main properties of functions.

Being able to apply algebraic and monotonic properties of fundamental functions to solve simple equations and inequalities involving irrational, exponential, logarithmic, and trigonometric functions. Knowing the equations or inequalities of simple geometric figures (line, half-plane, circle, ellipse, hyperbola, parabola). Knowing the main trigonometric formulas.

Basic Mathematics
Fundamental concepts such as sets, functions, equations, inequalities, plane geometry, and trigonometry will be explored through examples drawn from the food science context. Students will learn how to model the nutrient content of food products or calculate acidity curves in solutions. Limits, derivatives, and integrals will be introduced not in an abstract way, but as tools for analyzing rates of change and areas under concentration curves, helping interpret the evolution of physicochemical phenomena.

Numerical and Statistical Techniques
The course will present numerical methods such as interpolation and approximation to forecast market trends or estimate the physical properties of food products. Numerical integration techniques will be applied, for instance, to estimate the thermal energy required in pasteurization processes. The statistical part will introduce tools such as probability distributions and regression models, useful for analyzing experimental data and optimizing production processes.

Applied Modeling
Students will learn how to build and use evolution models to describe typical phenomena in the food sector, such as fermentation, raw material deterioration, or microbial growth. Particular attention will be paid to practical problems, such as optimizing time and temperature in preservation processes, using both mathematical tools and supporting numerical software. The goal is to foster a critical and quantitative approach to solving real-world problems in the agri-food domain.

The final exam consists of a written test, an oral examination, and a project. The exam is considered passed if the overall score—calculated as a weighted average—is at least 18 out of 30.

• Written test: 25%

• Oral exam: 25%

• Project: 50%

Registration for the exam is mandatory and must be completed exclusively online through the university student portal within the specified deadlines.

General Evaluation Criteria
Assessment will take into account:

• clarity of exposition,

• completeness and accuracy of knowledge,

• ability to connect and elaborate on course concepts.

Students are expected to demonstrate a sufficient understanding of the main topics and the ability to solve at least the simpler assigned exercises.

Grading Scale

• Not eligible

  • Knowledge and understanding: major gaps and significant inaccuracies.

  • Analytical and synthesis skills: lacking or irrelevant, with frequent overgeneralizations.

  • Use of references: completely inappropriate.

• 18–20/30

  • Knowledge and understanding: barely sufficient, with evident flaws.

  • Analytical and synthesis skills: minimal and barely adequate.

  • Use of references: marginally appropriate.

• 21–23/30

  • Knowledge and understanding: routine level.

  • Analytical and synthesis skills: adequate, with coherent and logical reasoning.

  • Use of references: standard.

• 24–26/30

  • Knowledge and understanding: good.

  • Analytical and synthesis skills: good, with clearly expressed arguments.

  • Use of references: appropriate.

• 27–29/30

  • Knowledge and understanding: very good.

  • Analytical and synthesis skills: strong.

  • Use of references: in-depth.

• 30–30 cum laude

  • Knowledge and understanding: excellent.

  • Analytical and synthesis skills: outstanding, with critical re-elaboration.

  • Use of references: excellent, with significant insights.