mathematics

Richard S. Varga

Richard S. Varga 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 Richard S. Varga rather than just read about it. In short: Richard Steven Varga (October 9, 1928 - February 25, 2022) was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University.

Key takeaways

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

Reference excerpt

Richard Steven Varga (October 9, 1928 - February 25, 2022) was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University. Varga was known for his contributions to many areas of mathematics, including matrix analysis, complex analysis, approximation theory, and scientific computation. He was the author of the classic textbook Matrix Iterative Analysis. Varga served as the Editor-in-Chief of the journal Electronic Transactions on Numerical Analysis (ETNA).

Birth and education Richard Varga was born in Cleveland, Ohio of Hungarian-born parents in 1928. He obtained a bachelor's degree in mathematics from Case Institute of Technology (present Case Western Reserve University) in 1950. Varga was a member of the collegiate wrestling team of Case. Following the advice of Professor Max Morris at Case, Varga joined Harvard University for the master's degree and obtained an A.M. in mathematics. Continuing his doctoral work at Harvard under the supervision of Joseph L. Walsh, Varga worked on the theory of rational approximation of complex analytic functions. Varga received his Ph.D. degree in 1954 with a dissertation Properties of a Special Set of Entire Functions and their Respective Partial Sums. While at Harvard, Varga also studied with Garrett Birkhoff, who later came to collaborate with Varga in research both on iterative methods for differential equations and on positive matrices (and positive operators on partially ordered vector spaces).

Career From 1954 until 1960, Varga worked for Bettis Atomic Power Laboratory in Pittsburgh. In 1960 he returned to Case Institute of Technology as a professor of mathematics and remained there for the next nine years. He then moved to Kent State University as University Professor of mathematics. At Kent Varga has held numerous academic positions, including director (1980–1988) and research director (1988–2006) of the Institute for Computational Mathematics. His work includes numerical analysis—particularly iterative methods in numerical linear algebra, matrix theory, and differential equations—complex approximation theory, particularly Padé approximation (often with Edward B. Saff, Jr.)—and analytic number theory, including high-precision calculations related to the Riemann hypothesis. He is also known for advocating experimentation in mathematics, and for writing a monograph surveying his contributions on scientific computing to resolve open problems and conjectures.

Awards and honors In 2012 he became a fellow of the American Mathematical Society.

Illustrations

Worked examples

Example 1 — a first encounter with Richard S. Varga

Start with the simplest possible case. Write down what Richard S. Varga 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 Richard S. Varga 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 Richard S. Varga 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 Richard S. Varga

In research: Richard S. Varga 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 Richard S. Varga 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: Richard S. Varga is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1928 births, 2022 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard S. Varga 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 Richard S. Varga in 20 minutes

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

Frequently asked questions

What is Richard S. Varga in simple terms?

Why does Richard S. Varga 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 Richard S. Varga?

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 Richard S. Varga.