Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
How to test without making mistakes
Statistical tests are invaluable for assessing a hypothesis about a population from observations of a random sample. But they are also the source of many errors. Let's learn how to avoid them—in both methodology and the interpretation of results!
Build your first magic square | Tangente
can numbers be arranged so perfectly that they produce equal sums in every direction? The challenge is certainly difficult, but construction methods do exist! The magic of arithmetic...
When errors propagate...
Error is inseparable from scientific computation. Calculations of this kind inevitably involve errors. However, it is essential to know where they may come from, to keep them under control, and to estimate their order of magnitude so as to determine whether a result is reliable.
Optimizing renewable energy use | Tangente
Fossil fuels result from a decomposition process lasting several million years, which concentrates them into a form that can be transported, stored and released when needed. By contrast, the energy carried by sunlight, blowing wind or flowing water must be captured directly where it occurs.
Scheduling: Mathematical planning | Tangente
Deciding when to carry out the tasks needed to achieve a goal sometimes calls for imagination—or abstraction. Yet all such situations can draw on scheduling theory, a field of operations research that has been highly active for over a century.
Metaheuristics: approximate optimization | Tangente
NP-hard problems, combinatorial explosion, models with millions of variables and exponentially many inequalities… What can we do when no optimization method works? Which method should we use when we want to solve a problem quickly?
Operations research to preserve biodiversity
Biodiversity, a blend of "biological" and "diversity," refers to the variety of living organisms and their habitats. Its increasingly rapid erosion has made preserving it a major priority for some countries.
Is P equal to NP?
The question has kept the scientific community on tenterhooks for more than forty years. It is one of the "Millennium Prize Problems," a list of seven major mathematical puzzles posed by the Clay Mathematics Institute in 2000. Here is a closer look.
Integer linear programming | Tangente
Solving optimization problems may require formulating them as mathematical models. Integer linear programming does this using only linear polynomials whose variables must take integer values.
Animal welfare
Respect for animal welfare has become a major public concern. Anticipating the emergence of certification labels, a group of researchers came together in the 2000s to propose that the European Commission develop animal-welfare assessment protocols: the Welfare Quality® project.
Operations research in healthcare: medical assignment problems | Tangente
Hospitals face many optimization problems that can be solved optimally within a reasonable time using so-called polynomial-time algorithms. Among them, the Hungarian algorithm is used to assign resources, while the Gale–Shapley algorithm is used for matching (or pairing).
Surgical scheduling using operations research | Tangente
Healthcare is a broad field of application for operations research, which provides tools for optimizing the use of limited resources—budgets, beds, healthcare staff, and so on—to meet demand. The hospital network employs thousands of people to treat tens of thousands of patients, using tonnes of medicines and equipment. Managing such a large and varied demand for care has become a scientific challenge.
Electoral redistricting: the mathematics of voting | Tangente
The bill to renew democratic life, as presented to the Council of Ministers in August 2019, includes a major reform of parliamentary elections. How, and to what extent, can the principle of "one person, one vote"—the foundation of the republican ideal that all citizens should have an equal say at the ballot box—be achieved with this new electoral map?
Fair optimization
Decisions made within organizations often affect several individuals, whose interests must be considered fairly. Fair optimization finds efficient solutions while maintaining a balance among the individuals’ levels of satisfaction.
Coming to grips with randomness
Stochastic optimization problems are specifically characterized by uncertainty in the data. The modeler has only imperfect knowledge of the data relating to the system under consideration or how it will evolve. Their values can, however, be characterized by probability distributions.
Network flows, transport and cuts | Tangente
Many transport problems can be modelled using "flows". One example is the transmission of electricity discussed in this article. Other classic applications involve transporting fluids (gas, water, oil, etc.) as well as people or goods (by truck, train, ship, etc.).
Tree search
Optimizing how a telescope is used—and deciding which part of the sky to observe—is crucial. This challenge can be reduced to a coloring problem, but finding a solution requires more trials than even a modern computer has time to test exhaustively.
Combinatorial paths: shortest paths | Tangente
When we choose our route as we go, we must decide between several paths, just as in a maze. The same question arises at every new junction, creating a combinatorial explosion in the number of possible routes. How can we circumvent this explosion?
RO in quarantine: optimizing lockdown life | Tangente
Confined to our homes because of Covid-19, we all suffered from having to restrict our living space, share the household computer, continue our schooling in chaotic conditions and help with chores we had previously managed to avoid.
Great names in operations research: Edmonds and Dantzig | Tangente
A few portraits of mathematicians whose work had a major impact on operational research