mathematics

Samuel Karlin

Samuel Karlin 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 Samuel Karlin rather than just read about it. In short: Samuel Karlin (June 8, 1924 – December 18, 2007) was an American mathematician at Stanford University in the late 20th century. Education and career Karlin was born in Janów, Poland and immigrated to Chicago as a child.

Key takeaways

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

Reference excerpt

Samuel Karlin (June 8, 1924 – December 18, 2007) was an American mathematician at Stanford University in the late 20th century.

Education and career Karlin was born in Janów, Poland and immigrated to Chicago as a child. Raised in an Orthodox Jewish household, Karlin became an atheist in his teenage years and remained an atheist for the rest of his life. Later in life he told his three children, who all became scientists, that walking down the street without a yarmulke on his head for the first time was a milestone in his life. Karlin earned his undergraduate degree from Illinois Institute of Technology; and then his doctorate in mathematics from Princeton University in 1947 (at the age of 22) under the supervision of Salomon Bochner. He was on the faculty of Caltech from 1948 to 1956, before becoming a professor of mathematics and statistics at Stanford. Throughout his career, Karlin made fundamental contributions to the fields of mathematical economics, bioinformatics, game theory, evolutionary theory, biomolecular sequence analysis, and total positivity. Karlin authored ten books and more than 450 articles. He did extensive work in mathematical population genetics. In the early 1990s, Karlin and Stephen Altschul developed the Karlin-Altschul statistics, a basis for the highly used sequence similarity software program BLAST.

Honors and awards Karlin was a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the American Philosophical Society. He won a Lester R. Ford Award in 1973. In 1989, President George H. W. Bush bestowed Karlin the National Medal of Science "for his broad and remarkable research in mathematical analysis, probability theory and mathematical statistics, and in the application of these ideas to mathematical economics, mechanics, and population genetics." He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences.

Personal life One of Karlin's sons, Kenneth D. Karlin, is a professor of chemistry at Johns Hopkins University and the 2009 winner of the American Chemical Society's F. Albert Cotton Award for Synthetic Chemistry. His other son, Manuel, is a physician in Portland, Oregon. His daughter, Anna R. Karlin, is a theoretical computer scientist, the Microsoft Professor of Computer Science & Engineering at the University of Washington.

Selected publications Karlin, Samuel; Arrow, Kenneth J.; Suppes, Patrick (1960). Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium. Stanford, California: Stanford University Press. ISBN 978-0-8047-0021-4. {{cite book}}: ISBN / Date incompatibility (help) Karlin, Samuel; Fabens, Augustus J. (1960), "A stationary inventory model with Markovian demand", in Arrow, Kenneth J.; Karlin, Samuel; Suppes, Patrick (eds.), Mathematical models in the social sciences, 1959: Proceedings of the first Stanford symposium, Stanford mathematical studies in the social sciences, IV, Stanford, California: Stanford University Press, pp. 159–175, ISBN 978-0-8047-0021-4. {{citation}}: ISBN / Date incompatibility (help) S. Karlin and H. M. Taylor. A First Course in Stochastic Processes. Academic Press, 1975 (second edition). S. Karlin and H. M. Taylor. A Second Course in Stochastic Processes. Academic Press, 1981. S. Karlin and H. M. Taylor. An Introduction to Stochastic Modeling, Third Edition. Academic Press, 1998. ISBN 0-12-684887-4 S. Karlin, D. Eisenberg, and R. Altman. Bioinformatics: Unsolved Problems and Challenges. National Academic Press Inc., 2005. ISBN 978-0-309-10029-8. S. Karlin (Ed.). Econometrics, Time Series, and Multivariate Statistics. Academic Press, 1983. ISBN 978-0-12-398750-1. S. Karlin (Author) and E. Nevo (Editor). Evolutionary Processes and Theory. Academic Press, 1986. ISBN 978-0-12-398760-0. S. Karlin. Mathematical Methods and Theory in Games, Programming, and Economics. Dover Publications, 1992. ISBN 978-0-486-67020-1. S. Karlin and E. Nevo (Eds.). Population Genetics and Ecology. Academic Press, 1976. ISBN 978-0-12-398560-6. S. Karlin and W. J. Studden. Tchebycheff systems: With applications in analysis and statistics (pure and applied mathematics). Interscience Publishers, 1966 (1st edition). ASIN B0006BNV2C. S Karlin and S. Lessard. Theoretical Studies on Sex Ratio Evolution. Princeton University Press, 1986. ISBN 978-0-691-08412-1 S. Karlin. Theory of Infinite Games. Addison Wesley Longman Ltd. Inc., 1959. ASIN B000SNID12. S. Karlin. Total Positivity, Vol. 1. Stanford, 1968. ASIN B000LZG0Xu. Karlin Samuel, Altschul Stephen F. (1990). "Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes". Proc Natl Acad Sci USA. 87 (6): 2264–8. Bibcode:1990PNAS...87.2264K. doi:10.1073/pnas.87.6.2264. PMC 53667. PMID 2315319. Karlin S, Altschul SF. (1993). "Applications and statistics for multiple high-scoring segments in molecular sequences". Proc Natl Acad Sci USA. 90 (12): 5873–7. Bibcode:1993PNAS...90.5873K. doi:10.1073/pnas.90.12.5873. PMC 46825. PMID 8390686.

Worked examples

Example 1 — a first encounter with Samuel Karlin

Start with the simplest possible case. Write down what Samuel Karlin 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 Samuel Karlin 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 Samuel Karlin 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 Samuel Karlin

In research: Samuel Karlin 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 Samuel Karlin 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: Samuel Karlin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1924 births, 2007 deaths, 20th-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Samuel Karlin 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 Samuel Karlin in 20 minutes

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

Frequently asked questions

What is Samuel Karlin in simple terms?

Samuel Karlin (June 8, 1924 – December 18, 2007) was an American mathematician at Stanford University in the late 20th century. Education and career Karlin was born in Janów, Poland and immigrated to Chicago as a child.

Why does Samuel Karlin 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 Samuel Karlin?

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 Samuel Karlin.