mathematics

Keith Stroyan

Keith Stroyan 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 Keith Stroyan rather than just read about it. In short: Keith D. Stroyan is Professor of Mathematics at the University of Iowa.

Key takeaways

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

Reference excerpt

Keith D. Stroyan is Professor of Mathematics at the University of Iowa. His main research interests are in analysis and visual depth perception. In 2006 he received a Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics.

Publications Stroyan, K. D.; Luxemburg, W. A. J. Introduction to the theory of infinitesimals. Pure and Applied Mathematics, No. 72. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Reviewer Frank Wattenberg for Math Reviews wrote that "mathematicians whose principal interest is in functional analysis, complex analysis, or topology will find here some very valuable contributions to our understanding of these subjects" here. The book was cited over 365 times at Google Scholar in 2011. Stroyan, K. D.; Bayod, José Manuel: Foundations of infinitesimal stochastic analysis. Studies in Logic and the Foundations of Mathematics, 119. North-Holland Publishing Co., Amsterdam, 1986. Reviewer Tom L. Lindström for Math Reviews wrote that "the authors have written a very comprehensive and readable monograph which will be a great help to experts and beginners alike" here. Stroyan, K. D. Uniform continuity and rates of growth of meromorphic functions. Contributions to non-standard analysis (Sympos., Oberwolfach, 1970), pp. 47–64. Studies in Logic and Foundations of Math., Vol. 69, North-Holland, Amsterdam, 1972.

See also Influence of non-standard analysis

References

Web page at the University of Iowa

Worked examples

Example 1 — a first encounter with Keith Stroyan

Start with the simplest possible case. Write down what Keith Stroyan 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 Keith Stroyan 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 Keith Stroyan 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 Keith Stroyan

In research: Keith Stroyan 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 Keith Stroyan 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: Keith Stroyan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, 21st-century American mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Keith Stroyan 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 Keith Stroyan in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Keith Stroyan 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 Keith Stroyan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Keith Stroyan in simple terms?

Keith D. Stroyan is Professor of Mathematics at the University of Iowa.

Why does Keith Stroyan 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 Keith Stroyan?

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 Keith Stroyan.