mathematics

Thomas M. Cover

Thomas M. Cover 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 Thomas M. Cover rather than just read about it. In short: Thomas M. Cover (; August 7, 1938 – March 26, 2012) was an American information theorist and professor jointly in the Departments of Electrical Engineering and Statistics at Stanford University.

Key takeaways

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

Reference excerpt

Thomas M. Cover (; August 7, 1938 – March 26, 2012) was an American information theorist and professor jointly in the Departments of Electrical Engineering and Statistics at Stanford University. He devoted almost his entire career to developing the relationship between information theory and statistics.

Early life and education He received his B.S. in Physics from MIT in 1960 and Ph.D. in electrical engineering from Stanford University in 1964. His doctoral studies were supervised by Norman Abramson.

Career Cover was President of the IEEE Information Theory Society and was a Fellow of the Institute of Mathematical Statistics and of the Institute of Electrical and Electronics Engineers. He received the Outstanding Paper Award in Information Theory for his 1972 paper "Broadcast Channels"; he was selected in 1990 as the Shannon Lecturer, regarded as the highest honor in information theory; in 1997 he received the IEEE Richard W. Hamming Medal; and in 2003 he was elected to the American Academy of Arts and Sciences. During his 48-year career as a professor of Electrical Engineering and Statistics at Stanford University, he graduated 64 PhD students, authored over 120 journal papers in learning, information theory, statistical complexity, pattern recognition, and portfolio theory; and he partnered with Joy A. Thomas to coauthor the book Elements of Information Theory, which has become the most widely used textbook as an introduction to the topic since the publication of its first edition in 1991. He was also coeditor of the book Open Problems in Communication and Computation.

Selected works Cover, T. M.; Thomas, J. A. (2006). "Chapter 12, Maximum Entropy". Elements of Information Theory (2 ed.). Wiley. ISBN 0471241954. T. Cover, J. Thomas (1991). Elements of Information Theory. Wiley. ISBN 0-471-06259-6. Van Campenhout, Jan. and Cover, T. (1981). Maximum entropy and conditional probability. Information Theory, IEEE Transactions on Cover, T. (1974). The Best Two Independent Measurements Are Not the Two Best. Systems, Man and Cybernetics, IEEE Transactions on Cover, T. and Hart, P. (1967). "Nearest neighbor pattern classification". IEEE Transactions on Information Theory. Cover, T. (1965). Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition. Electronic Computers, IEEE Transactions on

See also k-nearest neighbors algorithm Cover's theorem

References

External links Thomas M. Cover Stanford University homepage Thomas M. Cover at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Thomas M. Cover

Start with the simplest possible case. Write down what Thomas M. Cover 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 Thomas M. Cover 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 Thomas M. Cover 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 Thomas M. Cover

In research: Thomas M. Cover 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 Thomas M. Cover 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: Thomas M. Cover is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 2012 deaths, 20th-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Thomas M. Cover 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 Thomas M. Cover in 20 minutes

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

Frequently asked questions

What is Thomas M. Cover in simple terms?

Thomas M. Cover (; August 7, 1938 – March 26, 2012) was an American information theorist and professor jointly in the Departments of Electrical Engineering and Statistics at Stanford University.

Why does Thomas M. Cover 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 Thomas M. Cover?

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 Thomas M. Cover.