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2008
Abstract As an appetizer, here is a typical problem of the kind you should be able to solve when you have worked through this Toolchest. You are invited to try it as soon as you wish. You will probably find it hard for now, but by the end of Section 3, where its solution is given, it should not look difficult to you.
Alexander Zawaira, Gavin Hitchcock
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Abstract As an appetizer, here is a typical problem of the kind you should be able to solve when you have worked through this Toolchest. You are invited to try it as soon as you wish. You will probably find it hard for now, but by the end of Section 3, where its solution is given, it should not look difficult to you.
Alexander Zawaira, Gavin Hitchcock
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The Mathematics Teacher, 1960
An example shows how a teacher may enrich the students’ learning of the binomial theorem.
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An example shows how a teacher may enrich the students’ learning of the binomial theorem.
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2019
You may have wondered why the numbers \(\left( {\begin{array}{c}n\\ k\end{array}}\right) \) are called binomial coefficients, and not the “choice numbers” or “combination numbers” or something related to subsets. Why “binomial”? We’ll see why in this chapter, which begins a theme for us: encoding combinatorial results algebraically.
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You may have wondered why the numbers \(\left( {\begin{array}{c}n\\ k\end{array}}\right) \) are called binomial coefficients, and not the “choice numbers” or “combination numbers” or something related to subsets. Why “binomial”? We’ll see why in this chapter, which begins a theme for us: encoding combinatorial results algebraically.
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Henry Briggs. The Binomial Theorem Anticipated
The Mathematical Gazette, 1961One of the pleasant aspects of research into mathematical history is the way in which existing material, passed over in the conventional account, may allow us not only to establish the bare, if unexpected, fact of a priority but, more importantly, to assess the significance of major currents in mathematical thought with greater precision.
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Induction; the Binomial Theorem
1979The first part of the course deals with the integers ℤ and the natural numbers ℕ. You know how to add and subtract, multiply and divide integers, and you know when one integer is bigger than another; we shall not review these things. One property of the integers which does need review is the principle of induction.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Nature Machine Intelligence, 2021Lu Lu, Pengzhan Jin, Guofei Pang
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Experimental quantum key distribution certified by Bell's theorem
Nature, 2022David Nadlinger +2 more
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