mathematics

Roberta Frances Johnson

Roberta Frances Johnson 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 Roberta Frances Johnson rather than just read about it. In short: Roberta Frances Johnson (January 22, 1902–October 12, 1988) was an American mathematician and one of the few women to earn a PhD in that subject in the United States before World War II. She joined the faculty of Wilson College, Colorado State University and University of Colorado.

Key takeaways

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

Reference excerpt

Roberta Frances Johnson (January 22, 1902–October 12, 1988) was an American mathematician and one of the few women to earn a PhD in that subject in the United States before World War II. She joined the faculty of Wilson College, Colorado State University and University of Colorado.

Biography Johnson was born in Philadelphia, Pennsylvania to Mary Wallace (Abdill) and Jesse B. Johnson and attended Philadelphia's Frankford High School. In 1925, she graduated in mathematics (with departmental honors) with a minor in history from Wilson College, in Chambersburg, Pennsylvania. Following her studies, she taught mathematics at Chambersburg High School for three years and then taught both math and history at the high school in Newfoundland, Pennsylvania. Financed by fellowships, including one from Wilson College, she studied at Cornell University and earned her master's degree with her major and minor in mathematics. Her thesis was titled: Certain properties and a classification of nets of conics and was supervised by mathematician Virgil Snyder. In 1933, she received her doctorate from Cornell University with her major subject in geometry, her first minor in analysis and her second minor in philosophy. Her dissertation in algebraic geometry, also directed by Virgil Snyder, was titled Involutions of Order 2 Associated with Surfaces of Genera P(A)=P(G)=0, P(2)=1, P(3)=0, and was published in the American Journal of Mathematics.

Educator Although she had hoped to teach at Cornell, Johnson was asked to return to Wilson College when the head of the mathematics department became ill. Initially, Johnson was to substitute for about one month but that assignment was extended when the department head took a leave of absence. She stayed at Wilson on a temporary assignment for 1933–1934, but then she remained at the College for 25 years, first as an instructor until 1935, then assistant professor until 1944, when she was named associate professor. She was named department head after the former chair retired in 1946. In 1957, she grew unhappy with her role at Wilson and began looking for work elsewhere mentioning in a letter that part of her reasoning was a "refusal to accept the injustice of being passed over when promotions are made." When Wilson administrators learned of her search, they quickly elevated her position to full professor with a tenure contract but the promotion came too late to change her mind. In 1958, Johnson moved to Fort Collins, Colorado, to teach as an associate professor at Colorado State University. There she directed the master's theses of about eight students. She stayed at Colorado State until 1967 when she retired as associate professor emeritus. The following spring the University of Colorado Denver hired her as an associate professor, and she taught there for the next three years. Johnson died October 12, 1988, of bone cancer at her Fort Collins home.

Memberships According to Green, Johnson was active in several organizations.

American Mathematical Society Mathematical Association of America Sigma Delta Epsilon Phi Beta Kappa Phi Kappa Phi Sigma Xi

References

Worked examples

Example 1 — a first encounter with Roberta Frances Johnson

Start with the simplest possible case. Write down what Roberta Frances Johnson 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 Roberta Frances Johnson 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 Roberta Frances Johnson 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 Roberta Frances Johnson

In research: Roberta Frances Johnson 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 Roberta Frances Johnson 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: Roberta Frances Johnson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1902 births, 1988 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Roberta Frances Johnson 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 Roberta Frances Johnson in 20 minutes

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

Frequently asked questions

What is Roberta Frances Johnson in simple terms?

Why does Roberta Frances Johnson 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 Roberta Frances Johnson?

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 Roberta Frances Johnson.