mathematics

Julius L. Shaneson

Julius L. Shaneson 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 Julius L. Shaneson rather than just read about it. In short: Julius L. Shaneson (born July 24, 1944, Richmond, Virginia) is an American mathematician.

Key takeaways

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

Reference excerpt

Julius L. Shaneson (born July 24, 1944, Richmond, Virginia) is an American mathematician. He works at the University of Pennsylvania, where he was department chair from 2002 to 2006 and is currently the Class of 1939 Professor of Mathematics.

Education and career Shaneson earned his Ph.D. in 1968 from the University of Chicago, under the supervision of Melvin Rothenberg. He taught at Rutgers University before joining the University of Pennsylvania; his students at Rutgers included Abigail Thompson.

Recognition Shaneson was a Guggenheim Fellow in 1981. He was an invited speaker at the International Congress of Mathematicians in 1982 and 1996. In March 2005, a conference was held at the Courant Institute of Mathematical Sciences of New York University, in honor of his 60th birthday. He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to topology".

Selected publications Shaneson, Julius L. (1969), "Wall's surgery obstruction groups for G × Z", Annals of Mathematics, Second Series, 90 (2): 296–334, doi:10.2307/1970726, JSTOR 1970726, MR 0246310. Cappell, Sylvain E.; Shaneson, Julius L. (1974), "The codimension two placement problem and homology equivalent manifolds", Annals of Mathematics, Second Series, 99 (2): 277–348, doi:10.2307/1970901, JSTOR 1970901, MR 0339216. Cappell, Sylvain E.; Shaneson, Julius L. (1976), "Some new four-manifolds", Annals of Mathematics, Second Series, 104 (1): 61–72, doi:10.2307/1971056, JSTOR 1971056, MR 0418125.

References

Worked examples

Example 1 — a first encounter with Julius L. Shaneson

Start with the simplest possible case. Write down what Julius L. Shaneson 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 Julius L. Shaneson 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 Julius L. Shaneson 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 Julius L. Shaneson

In research: Julius L. Shaneson 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 Julius L. Shaneson 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: Julius L. Shaneson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Julius L. Shaneson 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 Julius L. Shaneson in 20 minutes

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

Frequently asked questions

What is Julius L. Shaneson in simple terms?

Julius L. Shaneson (born July 24, 1944, Richmond, Virginia) is an American mathematician.

Why does Julius L. Shaneson 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 Julius L. Shaneson?

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 Julius L. Shaneson.