mathematics

Lexing Ying

Lexing Ying 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 Lexing Ying rather than just read about it. In short: Lexing Ying is a professor of mathematics at Stanford University, where he is also a member of the Institute for Computational and Mathematical Engineering. He specializes in scientific computing and numerical analysis.

Key takeaways

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

Reference excerpt

Lexing Ying is a professor of mathematics at Stanford University, where he is also a member of the Institute for Computational and Mathematical Engineering. He specializes in scientific computing and numerical analysis. In particular, his research concerns the design of numerical algorithms for problems in scientific computing. Ying received his bachelor's degree in computer science and applied mathematics from Shanghai Jiaotong University in 1998. He received his Ph.D. from the Courant Institute at New York University in 2004, under the guidance of Denis Zorin. Before joining Stanford in 2012, he was a post-doc at California Institute of Technology and a professor at University of Texas, Austin. The awards Ying has received include a Sloan Fellowship in 2007, an NSF Career Award in 2009, the James H. Wilkinson Prize in Numerical Analysis and Scientific Computing in 2013 (for "his outstanding contributions in many areas, including the rapid evaluation of oscillatory integral transforms, high frequency wave propagation and the computation of electron structure in metallic systems"), and a silver Morningside Medal in 2016. He is an invited speaker of International Congress of Mathematicians 2022.

References

Worked examples

Example 1 — a first encounter with Lexing Ying

Start with the simplest possible case. Write down what Lexing Ying 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 Lexing Ying 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 Lexing Ying 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 Lexing Ying

In research: Lexing Ying 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 Lexing Ying 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: Lexing Ying is common in secondary-school and first-year university syllabi. It links to neighbouring topics American mathematician stubs, Chinese mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Lexing Ying 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 Lexing Ying in 20 minutes

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

Frequently asked questions

What is Lexing Ying in simple terms?

Why does Lexing Ying 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 Lexing Ying?

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 Lexing Ying.