mathematics

John E. Dennis

John E. Dennis 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 John E. Dennis rather than just read about it. In short: John Emory Dennis, Jr. (born 1939) is an American mathematician who has made major contributions in mathematical optimization.

Key takeaways

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

Reference excerpt

John Emory Dennis, Jr. (born 1939) is an American mathematician who has made major contributions in mathematical optimization. Dennis is currently a Noah Harding professor emeritus and research professor in the department of computational and applied mathematics at Rice University in Houston, Texas. His research interests include optimization in engineering design. He is the founder and editor-in-chief of the SIAM Journal on Optimization. In 2010, he was elected a Fellow of the Society for Industrial and Applied Mathematics.

Education Dennis earned a Bachelor of Science in Industrial Engineering (BSIE), in 1962 and a Master of Science in mathematics in 1964 at the University of Miami. He earned a Ph.D. in mathematics at the University of Utah in 1966.

Academic career University of Utah, Department of Mathematics, Assistant Professor, 1966–1967 Cornell University, Department of Computer Science, full professor, 1969–1974 Rice University, Department of Computational and Applied Mathematics, full professor (retired), 1979–2007 At Rice, Dennis served as department chairman in both the Department of Computational and Applied Mathematics (CAAM) and Department of Computer Science (CS). He was also the chair of the Center for Research in Parallel Computing (CRPC) Optimization Project. He was the thesis director for 32 PhD students at Rice.

Publications

Books & monographs On the matrix polynomial, lambda-matrix and block eigenvalue problems (1971). Pittsburgh, PA: Carnegie-Mellon University. (co-authors J. F. Traub and Robert Philip Weber) Algorithms for solvents of matrix polynomials (1975). Pittsburgh, PA: Carnegie-Mellon University. (co-authors J. F. Traub and R. P. Weber) An Adaptive Nonlinear Least-Squares Algorithm (1977), Cambridge, MA: National Bureau of Economic Research. (co-authors Roy E. Welsch and David M. Gay) Numerical methods for unconstrained optimization and nonlinear equations (1983). Englewood Cliffs, NJ: Prentice-Hall, Inc. (co-author Robert B. Schnabel)

References

Worked examples

Example 1 — a first encounter with John E. Dennis

Start with the simplest possible case. Write down what John E. Dennis 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 John E. Dennis 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 John E. Dennis 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 John E. Dennis

In research: John E. Dennis 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 John E. Dennis 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: John E. Dennis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1939 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for John E. Dennis 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 John E. Dennis in 20 minutes

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

Frequently asked questions

What is John E. Dennis in simple terms?

John Emory Dennis, Jr. (born 1939) is an American mathematician who has made major contributions in mathematical optimization.

Why does John E. Dennis 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 John E. Dennis?

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 John E. Dennis.