New answers tagged mathematics
3
votes
Original description of point sources and point spread functions
Partial answer to get things started.
Point sources were a natural concept for mathematicians pondering waves, and the Huygens construction for a spherical wavefront generated by a point source is an ...
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7
votes
Accepted
Is there a theorem proof whose accuracy is doubted because it is short?
There's something like this in Volume II of Feller's Introduction to Probability Theory and Its Applications, Section I.5. Suppose $X_0, X_1, X_2, \ldots$ is an infinite sequence of i.i.d. real-...
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6
votes
Accepted
Jacobi's product for the discriminant
I found an answer to my own question from Ranjan Roy's book "Elliptic and Modular Functions from Gauss to Dedekind to Hecke".
On page 293, Roy says the $q$-product of the $\Delta$-function ...
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4
votes
Origin of Riemann-Stieltjes Integral
An important use of the Stieltjes integral, after its creation by Stieltjes, was its use by Riesz in $1909$ to describe the continuous dual space of $C([0,1])$, the space of real-valued continuous ...
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6
votes
Origin of Riemann-Stieltjes Integral
The Riemann-Stieljes was introduced by Thomas Stieltjes in his long paper (or book) on continued fractions,
Recherches sur les fractions continues,
Mém. Sav. étr. 32, Nr. 2, 197 S. (1904).
The purpose ...
- 45.4k
3
votes
New mathematics theory vs new mathematical theorem
The distinction is not formal. A new theory usually involves
some new set of definitions, new methods and several theorems.
Examples are abundant. Theory of groups, theory of distributions (...
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4
votes
Accepted
New mathematics theory vs new mathematical theorem
The Riemann integral is very useful for most of the basic needs of integration. However, it became clear around the end of the XIXth century that it wasn't general enough. That's why Lebesgue ...
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1
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When was the first time/s that sheaves entered algebra and algebraic geometry?
Jean Pierre Serre was awarded the Field medal in 1954. I recommend you his talk for the occasion.
Cohomologie et géométrie algébrique. Congrès int. d’Amsterdam, 1954, vol. III, pp. 515-520
He starts ...
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2
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Use of the verb "induct" in proofs by mathematical induction
If we search 19th century Google books, "induct on" does not exist with "mathematical induction". Perhaps, the term "induct on N" means to "form an induction on N&...
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