mathematics

Patrick Brosnan

Patrick Brosnan is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Patrick Brosnan rather than just read about it. In short: Patrick Brosnan is an American mathematician, known for his work on motives, Hodge theory, and algebraic groups. He received his Ph.D. from the University of Chicago in 1998 under the direction of Spencer Bloch.

Key takeaways

Patrick Brosnan belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Patrick Brosnan to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Patrick Brosnan from memory before moving on to harder problems.

Reference excerpt

Patrick Brosnan is an American mathematician, known for his work on motives, Hodge theory, and algebraic groups. He received his Ph.D. from the University of Chicago in 1998 under the direction of Spencer Bloch. Brosnan is the 2009 recipient of the Coxeter–James Prize of the Canadian Mathematical Society. In 2003, Brosnan (in joint work with Prakash Belkale) disproved the Spanning Tree Conjecture of Maxim Kontsevich.

Notes

External links "Home page". Patrick Brosnan at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Patrick Brosnan

Start with the simplest possible case. Write down what Patrick Brosnan claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Patrick Brosnan before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Patrick Brosnan ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Patrick Brosnan

In research: Patrick Brosnan appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Patrick Brosnan in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Patrick Brosnan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1968 births, 20th-century American mathematicians, 20th-century Canadian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Patrick Brosnan outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Patrick Brosnan in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Patrick Brosnan means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Patrick Brosnan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Patrick Brosnan in simple terms?

Why does Patrick Brosnan matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Patrick Brosnan?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Patrick Brosnan.