mathematics

Samuel S. Wagstaff Jr.

Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr. rather than just read about it. In short: Samuel Standfield Wagstaff Jr. (born 21 February 1945) is an American mathematician and computer scientist, whose research interests are in the areas of cryptography, parallel computation, and analysis of algorithms, especially number theoretic algorithms.

Key takeaways

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

Reference excerpt

Samuel Standfield Wagstaff Jr. (born 21 February 1945) is an American mathematician and computer scientist, whose research interests are in the areas of cryptography, parallel computation, and analysis of algorithms, especially number theoretic algorithms. He is currently a professor of computer science and mathematics at Purdue University who coordinates the Cunningham project, a project to factor numbers of the form bn ± 1, since 1983. He has authored/coauthored over 50 research papers and four books. He has an Erdős number of 1. Wagstaff received his Bachelor of Science in 1966 from Massachusetts Institute of Technology. His doctoral dissertation was titled, On Infinite Matroids, PhD in 1970 from Cornell University. Wagstaff was one of the founding faculty of Center for Education and Research in Information Assurance and Security (CERIAS) at Purdue, and its precursor, the Computer Operations, Audit, and Security Technology (COAST) Laboratory.

Selected publications with John Brillhart, D. H. Lehmer, John L. Selfridge, Bryant Tuckerman: Factorization of bn ± 1, b = 2,3,5,6,7,10,11,12 up to high powers, American Mathematical Society, 1983, 3rd edition 2002 as electronic book, Online text Archived 2005-02-15 at the Wayback Machine Samuel S. Wagstaff Jr. (2002). Mikhail J. Atallah (ed.). Cryptanalysis of Number Theoretic Ciphers. Computational Mathematics Series. CRC Press. ISBN 1-58488-153-4. Carlos J. Moreno; Samuel S. Wagstaff, Jr. (2005). Sums of Squares of Integers. CRC Press. ISBN 1-58488-456-8. Samuel S. Wagstaff Jr. (2013). The Joy of Factoring. Student Mathematical Library. American Mathematical Society. ISBN 978-1-4704-1048-3. Wagstaff The Cunningham Project, Fields Institute, pdf file Carl Pomerance; John L. Selfridge; Samuel S. Wagstaff, Jr. (July 1980). "The pseudoprimes to 25·109" (PDF). Mathematics of Computation. 35 (151): 1003–1026. doi:10.1090/S0025-5718-1980-0572872-7. JSTOR 2006210. Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. JSTOR 2006406. MR 0583518. Robert Baillie; Andrew Fiori; Samuel S. Wagstaff, Jr. (July 2021). "Strengthening the Baillie-PSW Primality Test" (PDF). Mathematics of Computation. 90 (330): 1931–1955. arXiv:2006.14425. doi:10.1090/mcom/3616. S2CID 220055722.

References

External links Cunningham project website CERIAS WWW site Archival COAST WWW site

Worked examples

Example 1 — a first encounter with Samuel S. Wagstaff Jr.

Start with the simplest possible case. Write down what Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr.

In research: Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr. 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: Samuel S. Wagstaff Jr. is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr. in 20 minutes

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

Frequently asked questions

What is Samuel S. Wagstaff Jr. in simple terms?

Why does Samuel S. Wagstaff Jr. 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 Samuel S. Wagstaff Jr.?

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 Samuel S. Wagstaff Jr..