mathematics

Jo Ellis-Monaghan

Jo Ellis-Monaghan 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 Jo Ellis-Monaghan rather than just read about it. In short: Joanna Anthony Ellis-Monaghan is an American mathematician and mathematics educator whose research interests include graph polynomials and topological graph theory. She is a professor of mathematics at the Korteweg-de Vries Institute for Mathematics of the University of Amsterdam.

Key takeaways

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

Reference excerpt

Joanna Anthony Ellis-Monaghan is an American mathematician and mathematics educator whose research interests include graph polynomials and topological graph theory. She is a professor of mathematics at the Korteweg-de Vries Institute for Mathematics of the University of Amsterdam.

Education and career Ellis-Monaghan grew up in Alaska. She graduated from Bennington College in 1984 with a double major in mathematics and studio art, and earned a master's degree in mathematics from the University of Vermont in 1986. After beginning a doctoral program at Dartmouth College, she transferred to the University of North Carolina at Chapel Hill, where she completed her Ph.D. in 1995. Her dissertation, supervised by Jim Stasheff, was A unique, universal graph polynomial and its Hopf algebraic properties, with applications to the Martin polynomial. She joined the Saint Michael's College faculty in 1992, chaired the department there, and has also held positions at the University of Vermont. In 2020, she became professor of Discrete Mathematics at the University of Amsterdam. From 2010 to 2020, she served as a subject editor of PRIMUS, a journal on the teaching of undergraduate mathematics.

Bibliography With Iain Moffat, Ellis-Monaghan is the author of the book Graphs on Surfaces.

References

External links Home page

Worked examples

Example 1 — a first encounter with Jo Ellis-Monaghan

Start with the simplest possible case. Write down what Jo Ellis-Monaghan 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 Jo Ellis-Monaghan 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 Jo Ellis-Monaghan 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 Jo Ellis-Monaghan

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

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

Frequently asked questions

What is Jo Ellis-Monaghan in simple terms?

Why does Jo Ellis-Monaghan 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 Jo Ellis-Monaghan?

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 Jo Ellis-Monaghan.