mathematics

Tomek Bartoszyński

Tomek Bartoszyński 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 Tomek Bartoszyński rather than just read about it. In short: Tomasz "Tomek" Bartoszyński (born 16 May 1957) is a Polish-American mathematician who works in set theory. Biography Bartoszyński studied mathematics at the University of Warsaw from 1976 to 1981, and worked there from 1981 to 1987.

Key takeaways

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

Reference excerpt

Tomasz "Tomek" Bartoszyński (born 16 May 1957) is a Polish-American mathematician who works in set theory.

Biography Bartoszyński studied mathematics at the University of Warsaw from 1976 to 1981, and worked there from 1981 to 1987. In 1984, he defended his Ph.D. thesis Combinatorial aspects of measure and category; his advisor was Wojciech Guzicki. In 2004, he received his habilitation from the Polish Academy of Sciences. From 1986 onward, he worked in the United States: he taught at the University of California, Berkeley and University of California, Davis. From 1990 to 2006, he was a professor (full professor from 1998-2006) at Boise State University. In 1990-1991, he visited the Hebrew University of Jerusalem as a fellow of the Lady Davis foundation, and in 1996/97 he visited the Free University of Berlin as a Humboldt fellow. Currently, he is one of the program directors at the National Science Foundation (NSF), responsible for combinatorics, foundations, and probability.

Family His father, Robert Bartoszyński, is a statistician. His wife, Joanna Kania-Bartoszyńska, is the NSF program director for topology and geometric analysis.

Scientific work Bartoszyński's work is mainly concerned with forcing, specifically with applications of forcing to the set theory of the real line. He has written about 50 papers in this field, as well as a monograph:

Tomek Bartoszyński and Haim Judah: Set theory. On the structure of the real line. A K Peters, Ltd., Wellesley, MA, 1995; ISBN 1-56881-044-X

See also Cichoń's diagram Baire property

References

Illustrations

Worked examples

Example 1 — a first encounter with Tomek Bartoszyński

Start with the simplest possible case. Write down what Tomek Bartoszyński 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 Tomek Bartoszyński 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 Tomek Bartoszyński 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 Tomek Bartoszyński

In research: Tomek Bartoszyński 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 Tomek Bartoszyński 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: Tomek Bartoszyński is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1957 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Tomek Bartoszyński 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 Tomek Bartoszyński in 20 minutes

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

Frequently asked questions

What is Tomek Bartoszyński in simple terms?

Tomasz "Tomek" Bartoszyński (born 16 May 1957) is a Polish-American mathematician who works in set theory. Biography Bartoszyński studied mathematics at the University of Warsaw from 1976 to 1981, and worked there from 1981 to 1987.

Why does Tomek Bartoszyński 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 Tomek Bartoszyński?

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 Tomek Bartoszyński.