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Michael Rosen (mathematician)

Michael Rosen (mathematician) 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 Michael Rosen (mathematician) rather than just read about it. In short: Michael Ira Rosen (born March 7, 1938) is an American mathematician who works on algebraic number theory, arithmetic theory of function fields, and arithmetic algebraic geometry. Biography Rosen earned a bachelor's degree from Brandeis University in 1959 and a PhD from Princeton University in 1963 under John Coleman Moore with thesis Representations of twisted group rings.

Key takeaways

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

Reference excerpt

Michael Ira Rosen (born March 7, 1938) is an American mathematician who works on algebraic number theory, arithmetic theory of function fields, and arithmetic algebraic geometry.

Biography Rosen earned a bachelor's degree from Brandeis University in 1959 and a PhD from Princeton University in 1963 under John Coleman Moore with thesis Representations of twisted group rings. He is a mathematics professor at Brown University. Rosen is known for his textbooks, especially for the book with co-author Kenneth Ireland on number theory, which was inspired by ideas of André Weil; this book, A Classical Introduction to Modern Number Theory, gives an introduction to zeta functions of algebraic curves, the Weil conjectures, and the arithmetic of elliptic curves. For his essay Niels Hendrik Abel and equations of the fifth degree Rosen received the 1999 Chauvenet Prize.

Publications

Books with Kenneth Ireland: A classical introduction to modern number theory, Springer, Graduate Texts in Mathematics, 1982, 2nd edn. 1992, ISBN 038797329X (Rosen and Ireland earlier published Elements of number theory; including an introduction to equations over finite fields, Bogden and Quigley, 1972) Number theory in function fields, Springer, Graduate Texts in Mathematics, 2002, ISBN 0-387-95335-3

Articles Rosen, Michael (1997), "Remarks on the history of Fermat's last theorem 1844 to 1984", in Cornell, Gary; Silverman, Joseph H.; Stevens, Glenn (eds.), Modular forms and Fermat's last theorem: Papers from the Instructional Conference on Number Theory and Arithmetic Geometry held at Boston University, Boston, MA, August 9–18, 1995, New York: Springer, pp. 505–525, MR 1638493 Rosen, Michael (1981), "Abel's theorem on the lemniscate", American Mathematical Monthly, 88 (6): 387–395, doi:10.2307/2321821, JSTOR 2321821, MR 0622954 Rosen, Michael I. (1995), "Niels Hendrik Abel and equations of the fifth degree", American Mathematical Monthly, 102 (6): 495–505, doi:10.2307/2974763, JSTOR 2974763, MR 1336636

References

External links Michael Rosen – Homepage at Brown University Michael Rosen at the Mathematics Genealogy Project "Remarks on the History of Fermat's Last Theorem - Michael Rosen". YouTube. 16 February 2016.

Worked examples

Example 1 — a first encounter with Michael Rosen (mathematician)

Start with the simplest possible case. Write down what Michael Rosen (mathematician) 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 Michael Rosen (mathematician) 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 Michael Rosen (mathematician) 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 Michael Rosen (mathematician)

In research
Michael Rosen (mathematician) 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 Michael Rosen (mathematician) 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
Michael Rosen (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Michael Rosen (mathematician) 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 Michael Rosen (mathematician) in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Michael Rosen (mathematician) means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Michael Rosen (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Michael Rosen (mathematician) in simple terms?

Michael Ira Rosen (born March 7, 1938) is an American mathematician who works on algebraic number theory, arithmetic theory of function fields, and arithmetic algebraic geometry. Biography Rosen earned a bachelor's degree from Brandeis University in 1959 and a PhD from Princeton University in 1963…

Why does Michael Rosen (mathematician) 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 Michael Rosen (mathematician)?

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 Michael Rosen (mathematician).

Tags

  • 1938 births
  • 20th-century American mathematicians
  • 21st-century American mathematicians
  • American mathematician stubs
  • American number theorists
  • Brandeis University alumni
  • Brown University faculty
  • Living people
  • Mathematicians from New York (state)
  • Princeton University alumni

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