Applied Math

What does it mean to build a 'model' of a real-world system using math? Why is it necessary to leave out some details when creating a useful mathematical model? Can you think of a time when a simple model helped you or others make a better decision? How can we test whether a model is good enough for the question we care about? What dangers arise when people forget that a model is a simplification rather than reality itself?

What kinds of problems in everyday life and business can be framed as optimization problems? How can mathematics help clarify trade-offs between cost, quality, safety, and time? What is the difference between finding a perfect solution and a 'good enough' solution in practice? When might optimizing one part of a system cause harm in another part that the model ignored? Can you think of a decision you made recently that could be described as optimizing something?

How do basic mathematical ideas like percentages and compounding shape people’s financial futures? Why is understanding interest rates and growth so important for borrowing, saving, and investing? What assumptions do common financial formulas make about human behavior and markets? How can simple models of supply and demand help explain prices, but also fail to capture real complexity? In what ways can math give people power in financial decisions, and in what ways can it be used to obscure risks?

How do engineers rely on mathematics when designing structures, machines, or electronic systems? What are examples where mathematical predictions prevented real-world failures or disasters? How does applied math bridge the gap between idealized theories and messy measurements? Why is it important for applied mathematicians to collaborate closely with domain experts like doctors or engineers? How might advances in computing change what kinds of real-world problems we can model mathematically?

How can mathematical ideas help us reason more clearly about uncertain outcomes? What is the difference between risk we can reasonably estimate and uncertainty we barely understand? How do people’s emotions and biases interfere with rational, mathematically grounded decisions? What are some tools—like expected value or scenario planning—that help people make better choices under uncertainty? Can you think of a public policy decision where misunderstanding risk had serious consequences?

When a mathematical model guides public policy or business decisions, who is responsible for its impact? How can the choice of what to include or ignore in a model reflect hidden values or priorities? What are some examples of models that unintentionally harmed certain groups of people? How can transparency and open discussion improve trust in mathematical models used in society? What questions should citizens ask when a leader justifies decisions by saying 'the model says so'?