mathematics

Mark Tomforde

Mark Tomforde 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 Mark Tomforde rather than just read about it. In short: Mark Louis Tomforde is an American mathematician who works on operator algebras and C*-algebras, topics in the broader area of functional analysis. He held academic positions at the University of Houston and at the University of Colorado Colorado Springs.

Key takeaways

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

Reference excerpt

Mark Louis Tomforde is an American mathematician who works on operator algebras and C*-algebras, topics in the broader area of functional analysis. He held academic positions at the University of Houston and at the University of Colorado Colorado Springs.

Biography Tomforde earned his Ph.D. in mathematics at Dartmouth College in 2002. He was an invited speaker at the 2015 Abel Symposium, and he is a founding member of the Algebras and Rings in Colorado Springs (ARCS) center. Tomforde has researched the related areas of graph C*-algebras and Leavitt path algebras. With Doug Drinen, he is co-creator of the Drinen–Tomforde desingularization, often simply called desingularization. With Gene Abrams, Tomforde has formulated the Abrams–Tomforde conjectures, and Abrams and Tomforde have verified certain special cases of the conjectures. Tomforde studied ultragraph C*-algebras. Tomforde has also been active in organizing several conferences on graph C*-algebras and their generalizations, with the goal of bringing together analysts and algebraists to share ideas and collaborate. Tomforde created and directed the Cougars and Houston Area Mathematics Program (CHAMP), which was last active in Spring 2019. CHAMP had previously received an award from Phi Beta Kappa and the Award for Mathematics Programs that Make a Difference from the American Mathematical Society. In 2019 Tomforde was recognized with the MAA Texas Section's Distinguished College and University Teaching of Mathematics Award. In 2020 he was a recipient of a Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics from the Mathematical Association of America.

References

Illustrations

Worked examples

Example 1 — a first encounter with Mark Tomforde

Start with the simplest possible case. Write down what Mark Tomforde 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 Mark Tomforde 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 Mark Tomforde 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 Mark Tomforde

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

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

Frequently asked questions

What is Mark Tomforde in simple terms?

Why does Mark Tomforde 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 Mark Tomforde?

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 Mark Tomforde.