American Mathematical Monthly

American Mathematical Monthly Problem

Let p be a prime number, and s a positive integer. Let k be an integer, and let n be an integer such that n ≥ k ≥ p s − p s−1 .

American Mathematical Monthly Problem 11415

Definitions. a) A matrix is called a complex matrix if all its entries are complex numbers. (In particular, any vector in C is considered a n× 1 complex matrix.) b) For any complex matrix A, we denote the matrix A T by A∗. c) Let U2 (C) be the group of all unitary 2× 2 complex matrices. In other words, let U2 (C) = { U ∈ GL2 (C) | U∗ = U−1 } . d) A complex matrix A is called Hermitian if it sat...

American Mathematical Monthly Problem 11403

The American Mathematical Monthly - Problem 11173

In this example we have 11 successes and 9 failures. We have to wait until trial 9 to have a …rst run of lenght 2, this isN(1) = 9. If we allow for overlapping, in the example the next runs of size 2 are completed at trial numbers 12; 13 and 16. Here we are interested in N(r) where for each r 1, N(r) denotes the number of trials until we observe the r th run of size 2 for the …rst time and wher...

A Bibliography of Publications in American Mathematical Monthly: 1950–1959

16 [8]. 61 [8]. Amer [8]. approximation [2]. associated [3]. best [2]. connected [6]. cores [7]. curve [3]. double [1]. Fan [8]. functions [2, 7]. G [8]. geometrically [1]. implicants [7]. inequality [4, 8]. integers [6]. integral [4, 8]. Lorentz [8]. Math [8]. Monthly [8]. MR [8]. nonassociative [5]. Note [8]. number [5]. polynomial [2]. prime [7]. series [1]. summed [1]. tetrahedron [3]. Theo...