Lorraine Foster

Key takeaways

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

Reference excerpt

Lorraine Lois Foster (December 25, 1938, Culver City, California) is an American mathematician. In 1964 she became the first woman to receive a Ph.D. in mathematics from California Institute of Technology. Her thesis advisor at Caltech was Olga Taussky-Todd. Foster's Erdos number is 2. Born Lorraine Lois Turnbull, she attended Occidental College where she majored in physics. She was admitted to Caltech after receiving a Woodrow Wilson Foundation fellowship. In 1964 she joined the faculty of California State University, Northridge. She works in number theory and the theory of mathematical symmetry.

Selected bibliography Foster, L. (1966). On the characteristic roots of the product of certain rational integral matrices of order two. Pacific Journal of Mathematics, 18(1), 97–110. http://doi.org/10.2140/pjm.1966.18.97 Brenner, J. L., & Foster, L. L. (1982). Exponential diophantine equations. Pacific Journal of Mathematics, 101(2), 263–301. Alex, L. J., & Foster, L. L. (1983). On diophantine equations of the form 1 + 2 a = p b q c + 2 d p e q f {\displaystyle 1+2^{a}=p^{b}q^{c}+2^{d}p^{e}q^{f}} . Rocky Mountain Journal of Mathematics, 13(2), 321–332. http://doi.org/10.1216/RMJ-1983-13-2-321 Alex, L. J., & Foster, L. L. (1985). On the Diophantine equation 1 + p a = 2 + 2 b + 2 c p d {\displaystyle 1+p^{a}=2+2^{b}+2^{c}p^{d}} . Rocky Mountain Journal of Mathematics, 15(3), 739–762. http://doi.org/10.1216/RMJ-1985-15-3-739 L. Foster (1989). Finite Symmetry Groups in Three Dimensions, CSUN Instructional Media Center, Jan. 1989 (video, 27 minutes). L. Foster (1990). Archimedean and Archimedean Dual Polyhedra, CSUN Instructional Media Center, Feb. 1990 (video, 47 minutes). https://www.worldcat.org/title/archimedean-and-archimedean-dual-polyhedra/oclc/63936926&referer=brief_results Foster, L. L. (1990). On the symmetry group of the dodecahedron. Mathematics Magazine, 63, 106–107. Foster, L. L. (1991). Convex Polyhedral Models for the Finite Three-Dimensional Isometry Groups. The Mathematical Heritage of CF Gauss, pp 267–281. L. Foster (1991). The Alhambra Past and Present—a Geometer’s Odyssey Part 1, CSUN Instructional Media Center, December 1991 (video, 40 minutes). L. Foster (1991). The Alhambra Past and Present—a Geometer’s Odyssey Part 2, CSUN Instructional Media Center, December 1991 (video, 40 minutes). https://www.worldcat.org/title/alhambra-past-and-present-a-geometers-odyssey-parts-1-and-2/oclc/28680624?loc=94043&tab=holdings&start_holding=7 Foster, L. L. (1991). Convex polyhedral models for the finite three-dimensional isometry groups. In G. M. Rassias (Ed.), The Mathematical Heritage of C F Gauss (pp. 267–281). Singapore: World Scientific. L. Foster (1992). Regular-Faced Polyhedra—an Introduction, CSUN Instructional Media Center, Dec. 1992 (video, 47 minutes) Alex, L. J., & Foster, L. L. (1992). On the Diophantine equation 1 + x + y = z {\displaystyle {\bf {1+x+y=z}}} . Rocky Mountain Journal of Mathematics, 22(1), 11–62. http://doi.org/10.1216/rmjm/1181072793 Alex, L. J., & Foster, L. L. (1995). On the Diophantine equation w + x + y = z {\displaystyle w+x+y=z} , with w x y z = 2 r 3 s 5 t {\displaystyle wxyz=2^{r}3^{s}5^{t}} . Rev. Mat. Univ. Complut. Madrid, 8(1), 13–48.

References

Illustrations

Worked examples

Example 1 — a first encounter with Lorraine Foster

Start with the simplest possible case. Write down what Lorraine Foster 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 Lorraine Foster 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 Lorraine Foster 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 Lorraine Foster

In research: Lorraine Foster 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 Lorraine Foster 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: Lorraine Foster is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lorraine Foster 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.

How to study Lorraine Foster in 20 minutes

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

Frequently asked questions

What is Lorraine Foster in simple terms?

Lorraine Lois Foster (December 25, 1938, Culver City, California) is an American mathematician. In 1964 she became the first woman to receive a Ph.D. in mathematics from California Institute of Technology.

Why does Lorraine Foster 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 Lorraine Foster?

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 Lorraine Foster.