mathematics

Philip M. Whitman

Philip M. Whitman 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 Philip M. Whitman rather than just read about it. In short: Philip Martin Whitman (December 23, 1916 – April 11, 1997) was an American mathematician who contributed to lattice theory, particularly the theory of free lattices. Living in Pittsburgh, he attended Haverford College, where he earned a corporation scholarship for 1936–37, and a Clementine Cope fellowship for 1937–38, and was awarded highest honors in mathematical astronomy in 1937.

Key takeaways

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

Reference excerpt

Philip Martin Whitman (December 23, 1916 – April 11, 1997) was an American mathematician who contributed to lattice theory, particularly the theory of free lattices. Living in Pittsburgh, he attended Haverford College, where he earned a corporation scholarship for 1936–37, and a Clementine Cope fellowship for 1937–38, and was awarded highest honors in mathematical astronomy in 1937. He was elected to the college's chapter of Phi Beta Kappa society. In June 1937, he was conferred the Bachelor of Science degree from Haverford. According to Garrett Birkhoff, Whitman was an undergraduate Harvard student in 1937, and an outstanding graduate student not later than 1940, one of the first who taught elementary courses to freshmen in the mathematics department. In 1938 he earned his AM, and in June 1941 he obtained his Ph.D. degree from Harvard University. He was a member of the AMS not later than 1947, and was awarded an AMS honorary membership not later than 1995. Whitman died on April 11, 1997 in Lexington, Massachusetts, at the age of 80.

Selected publications Whitman, Philip Martin (Jun 1940). Schrödinger Wave Mechanics of the Hydrogen Atom (Manuscript minor thesis in mathematics). Harvard students' essays. Harvard University. Whitman, Philip Martin (1941). Free lattices (Ph.D. thesis). Harvard University. Philip Whitman (1941). "Free Lattices". Annals of Mathematics. 42 (1): 325–329. doi:10.2307/1969001. JSTOR 1969001. Philip Whitman (1942). "Free Lattices II". Annals of Mathematics. 43 (1): 104–115. doi:10.2307/1968883. JSTOR 1968883. Phillip M. Whitman (1943). "Splittings of a lattice". American Journal of Mathematics. 65 (1): 179–196. doi:10.2307/2371781. JSTOR 2371781. Philip Whitman (1946). "Lattices, equivalence relations, and subgroups". Bulletin of the American Mathematical Society. 52 (6): 507–522. doi:10.1090/s0002-9904-1946-08602-4. Philip M. Whitman (Apr 1948). "Groups with a cyclic group as lattice-homomorph". Annals of Mathematics. 49 (2): 347–351. doi:10.2307/1969283. JSTOR 1969283. Garrett Birkhoff; Philip M. Whitman (1949). "Representation of Jordan and Lie Algebras" (PDF). Transactions of the American Mathematical Society. 65 (1): 116–136. doi:10.2307/1990517. JSTOR 1990517. Philip M. Whitman (1961). "Status of word problems for lattices". In R. P. Dilworth (ed.). Lattice Theory. Proceedings of Symposia in Pure Mathematics. Vol. 2. Providence/RI: American Mathematical Society. pp. 17–21. ISBN 978-0-8218-1402-4. {{cite book}}: ISBN / Date incompatibility (help)

References Garrett Birkhoff (1988). "Mathematics at Harvard, 1836–1944". In Peter Duren; Richard A. Askey; Uta C. Merzbach (eds.). A Century of Mathematics in America — Part II (PDF). History of Mathematics. Vol. 2. Providence, RI: American Mathematical Society. pp. 3–58. ISBN 0-8218-0130-9. Haverford College Bulletin, Vol. 35–36, 1936–1938

External links Philip M. Whitman at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Philip M. Whitman

Start with the simplest possible case. Write down what Philip M. Whitman 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 Philip M. Whitman 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 Philip M. Whitman 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 Philip M. Whitman

In research: Philip M. Whitman 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 Philip M. Whitman 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: Philip M. Whitman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1916 births, 1997 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Philip M. Whitman 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 Philip M. Whitman in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Philip M. Whitman means in your own words.
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Frequently asked questions

What is Philip M. Whitman in simple terms?

Why does Philip M. Whitman 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 Philip M. Whitman?

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 Philip M. Whitman.