The objective of the course is not to teach mathematics as an abstract body of knowledge, nor to reproduce an economics course through mathematical language. Rather, students learn to use mathematical concepts and techniques to understand, formulate and solve problems arising in business contexts.
What distinguishes this version of the subject is that the learning is organised around a team challenge that runs for the whole semester. Students work in teams of five on a single firm — a campus cafeteria — and apply each mathematical technique, in the same fortnight it is taught, to a real decision the management has to make. The challenge is not an assignment added at the end of the course: it is the thread that carries the whole content.
Titular Professors
Professors
This subject is designed as a review of the main mathematical methods needed by Business, Economics and Management students. It only requires basic knowledge of mathematical analysis and will be developed progressively, starting from elementary concepts to an introduction to calculus and the more complex methods used in more advanced studies.
This course seeks to help you in:
· Reviewing basic mathematical concepts.
· Practicing operations and estimations of quantities.
· Understanding how mathematics plays an important role in Business
Concepts covered:
1.Basic concept review
2.Linear equations — systems of linear equations — supply and demand — linear programming
3.Quadratic functions — cost, revenue and profit functions
4.Differentiation — marginal functions and elasticity
5.Optimisation of economic functions and partial derivatives
6.Integration — consumer’s and producer’s surplus
7.Indices and logarithms
8.Mathematics of finance
9.Matrices
Detailed content break-down
Week | Content | Team challenge |
Week 1 | Mathematical language and algebra. Diagnostic activity, algebra review, fractions, formula transposition, guided practice and reflection. Level test. | Sprint 0 — teams formed and roles assigned. |
Week 2 | Linear functions and graphical thinking. Slope, intercept, graph construction, interpretation and modelling. | Sprint 1 begins. |
Week 3 | Systems of linear equations. Substitution and elimination, graphical interpretation and applications. Supply and demand. | Sprint 1 checkpoint (second session). |
Week 4 | Quadratic functions. Graphs, symmetry, vertex, completing the square and interpretation. Revenue, cost and profit. | Sprint 2 begins. |
Week 5 | Understanding change. Average and instantaneous rates of change, slope and graphical reasoning. Applications of derivatives and sign diagrams. | |
Week 6 | Differentiation techniques. Power rule, sums and differences, marginal functions and elasticity. | Sprint 2 checkpoint (second session). |
Week 7 | Integrated workshop and revision. Midterm examination. | |
Week 8 | Optimisation foundations. Stationary points, first-order condition and the second-derivative test. | Sprint 3 begins. |
Week 9 | Partial derivatives. Functions of two variables and two-product optimisation. | |
Week 10 | Linear programming and optimisation. Feasible regions, constraints, objective functions and decision making. | Sprint 3 checkpoint (second session). |
Week 11 | Integration. Consumer’s and producer’s surplus; accumulation over time. | Sprint 4 begins. |
Week 12 | Indices and logarithms; mathematics of finance. Compound interest, present value, NPV and IRR. | Sprint 4 checkpoint (second session). |
Week 13 | Matrices. Operations, inverse, Cramer’s rule and Markov chains. | Sprint 5 — integrated report and board pitch. |
Weeks 14–15 | Revision and final examination. |
Weekly teaching consists of two 100-minute sessions. Throughout the course different types of session are combined.
The central principle of the course is:
The purpose of teaching is not simply to transmit knowledge, but to create the conditions in which students develop the ability to use that knowledge.
Students have access to an increasing amount of information through textbooks, digital resources and AI-based tools. The distinctive value of the classroom is therefore not the delivery of information. It is the opportunity to practise, receive feedback, make decisions, solve problems and develop professional skills.
Students are consequently expected to come prepared to work; participate actively in problem-solving activities; practise regularly; explain their reasoning rather than only provide an answer; assess their own work honestly; use feedback to improve; and take responsibility for their learning.
The team challenge
The FreshStart Cafeteria Team Challenge is organised in five sprints aligned with the teaching weeks. Teams have five members; each member owns an analytical role and leads one sprint. The first four sprints close with a short checkpoint; the fifth closes with an integrated report and a board pitch.
Sprint | Weeks | Mathematical content |
0 — Kick-off | W1 | Algebra and transposition of formulae |
1 — The cost model | W2–W3 | Linear equations, systems, supply and demand |
2 — The pricing decision | W4–W6 | Quadratic functions, differentiation, elasticity |
3 — Capacity | W8–W10 | Optimisation, partial derivatives, linear programming |
4 — Money over time | W11–W12 | Integration, logarithms, mathematics of finance |
5 — System and pitch | W13 | Matrices, Cramer’s rule, Markov chains |
Materials for each topic
Element | Methodology |
Maths review | Lecture |
Example problems | Lecture |
Individual practice problems | Problem solving — individual learning |
Exam rehearsals (without solutions) | Problem solving — self-evaluation |
In-class quizzes | Problem solving |
Team challenge sprints | Project-based learning — teamwork |
A typical class may include a short introduction or review of the relevant concept; examples illustrating how it works; individual or collaborative problem-solving; discussion and explanation of solutions; identification of common errors; and reflection on the techniques used and their application.
Continuous assessment has the following evaluation structure:
Evaluation type | Weight | Content | AI Use Level | Activity type |
Midterm Exam | 25% | First part of subjects | 1 | Highly important |
Final Exam | 25% | Second part of subjects | 1 | Highly important |
Installment I — Diagnose (group part + Individual Playbook) | 10% | Topics 1–3 | 3 for the group part, 1 for the individual playbook | Highly important |
Installment II — Decide (group + Individual Playbook) | 10% | Topics 4–6 | 3 for the group part, 1 for the individual playbook | Highly important |
Installment III — Optimize (group + Individual Playbook) | 10% | Topics 7–10 | 3 for the group part, 1 for the individual playbook | Highly important |
Individual homeworks (5) | 20% | All topics, drawn from the Cup dataset | 1 | Moderately important |
TOTAL | 100% |
Level of AI use: This following table describes the 5 levels with a synthesis of the guidelines
for the use of AI and the requirements it entails for the student.
Level | Meaning | Use of AI | Student Requirements |
1 | No AI | The use of AI is not allowed in any phase of the task. The work must be carried out entirely without artificial assistance. | The activity must be completed independently, demonstrating the student’s own knowledge and skills, without the use of AI tools. |
2 | AI for Idea Generation and Structure | AI may be used for brainstorming, outlining, initial guidance, or organizational suggestions, but not for producing the final content. | AI may be used only as preliminary support. The final submission must be entirely human-authored and must not include AI-generated content. |
3 | AI for editing | AI is allowed to improve writing, clarity, grammar, punctuation, or phrasing, but not to generate new content. | Students must submit original work and include the initial (pre-AI) version as evidence of the editing process. |
4 | AI to perform tasks, with human evaluation | The use of AI is authorized to complete specific parts of the task. The focus is on critical analysis and human evaluation of the generated content. | Students must use AI for the indicated parts, critically analyse and evaluate the outputs, and clearly reference any AI-generated content. |
5 | Full use of AI | AI may be used extensively throughout the process as a support tool or "co-pilot" to develop the work. | Students may freely integrate AI to support their work according to the task objectives. In this version of the scale, specifying which parts were generated with AI is not mandatory. |
Team challenge
The challenge is scored out of 100 project points: 20 points for the four checkpoints (5 each), 40 points for the integrated report, 25 points for the board pitch and 15 points for each member’s evidenced contribution, which is applied individually. The full rubric is given in the challenge document.
Midterm and final exams
A 2-hour exam is organised during the designated weeks, according to a schedule provided by the administration. Calculators are not allowed. A formula sheet prepared by the teachers is provided; no other material is allowed. Students with justified absences due to illness must provide official documentation and are invited to an additional session one week later. A revision session is held before each exam. No minimum grade is required.
The evaluation criteria apply to all the students; retakers must attend class and submit all the deliverables requested. Any exceptional situation should be communicated previously to the professors and validated by the tutor.
It is mandatory to have submitted the 3 project installments to sit in the final exam.
Late deliveries of individual assignments will have a rating of zero
Pass threshold. The subject is passed if the overall score is ≥ 5.0, and the if the final exam score is ≥ 5.0.
There is no retake exam scheduled for Mathematics. This means that students who do not achieve a passing grade will need to re-enroll in the course and start studying the subject from the beginning. The policy is designed to ensure that students actively participate during class sessions, as consistent engagement is essential for developing a strong understanding of the material. Mathematics is a cumulative subject, and missing key concepts can make it difficult to progress. By requiring full participation throughout the course rather than offering a retake, the program helps students build a solid foundation for future learning.
Ian Jacques, Mathematics for Economics and Business. Pearson Education, 10th edition, 2023.
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