mathematics

Philip Franklin

Philip Franklin 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 Franklin rather than just read about it. In short: Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr.

Key takeaways

Philip Franklin 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 Franklin to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Philip Franklin from memory before moving on to harder problems.

Reference excerpt

Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr. Franklin received a B.S. in 1918 from City College of New York (who later awarded him its Townsend Harris Medal for the alumnus who achieved notable postgraduate distinction). He received his M.A. in 1920 and Ph.D. in 1921 both from Princeton University. His dissertation, The Four Color Problem, was supervised by Oswald Veblen. After teaching for one year at Princeton and two years at Harvard University (as the Benjamin Peirce Instructor), Franklin joined the Massachusetts Institute of Technology Department of Mathematics, where he stayed until his 1964 retirement. In 1922, Franklin gave the first proof that all planar graphs with at most 25 vertices can be four-colored. In 1928, Franklin gave the first description of an orthonormal basis for L²([0,1]) consisting of continuous functions (now known as "Franklin's system"). In 1934, Franklin disproved the Heawood conjecture for the Klein bottle by showing that any map drawn on the Klein bottle can be coloured with at most six colours. An example which shows that six colours may be needed is the 12-vertex cubic graph now known as the Franklin graph. Franklin also worked with Jay W. Forrester on Project Whirlwind at the Office of Naval Research (ONR). Franklin was editor of the MIT Journal of Mathematics and Physics from 1929. In 1940, his comprehensive textbook A Treatise on Advanced Calculus was first published. Franklin was married to Norbert Wiener's sister Constance. Their son-in-law is Václav E. Beneš.

Books 1933: Differential equations for Electrical Engineers. New York: John Wiley & Sons. Differential equations for Engineers. Dover Publications. 1960. ASIN B000859ANA. 1940: A Treatise on Advanced Calculus. John Wiley & Sons. 5th printing edition. 1955. ASIN B00JCV5MYW. Franklin, Philip (2016). Dover reprint. Courier Dover Publications. ISBN 978-0486807072. 1941: The Four Color Problem. OCLC 03049925. 1944: Methods of Advanced Calculus. 1949: Fourier Methods. McGraw-Hill. ASIN B001U3912Y. An Introduction to Fourier Methods and the Laplace Transform. Dover Publications. 1958. ASIN B004QPEH18. 1953: Differential and Integral Calculus. McGraw-Hill. ASIN B0000CIJ2B. 1958: Functions of Complex Variables. Englewood Cliffs, New Jersey: Prentice Hall. 2021 edition. Hassell Street Press. 9 September 2021. ISBN 978-1014075574. 1963: Compact Calculus. McGraw-Hill. ASIN B0000CLVV1. 2021 edition. Hassell Street Press. 9 September 2021. ISBN 978-1014263575.

References

External links O'Connor, John J.; Robertson, Edmund F., "Philip Franklin", MacTutor History of Mathematics Archive, University of St Andrews Philip Franklin at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Philip Franklin

Start with the simplest possible case. Write down what Philip Franklin 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 Franklin 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 Franklin 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 Franklin

In research: Philip Franklin 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 Franklin 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 Franklin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1898 births, 1965 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Philip Franklin 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 Franklin in 20 minutes

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

Frequently asked questions

What is Philip Franklin in simple terms?

Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr.

Why does Philip Franklin 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 Franklin?

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 Franklin.