Mike Spivey

25,880 reputation

256129

bio	website	math.pugetsound.edu/~mspivey
	location	Tacoma, WA
	age	40
visits	member for	2 years, 7 months
	seen	yesterday
stats	profile views	3,188

I am a math professor at the University of Puget Sound. My background is in operations research, and I teach typical OR courses such as optimization, modeling, and probability, as well as calculus, statistics, and differential equations.

My math blog, A Narrow Margin, includes (among other things) discussion of some of my favorite posts - of mine and of others - from math.SE.

	25,880 reputation	bio	website	math.pugetsound.edu/~mspivey	visits	member for	2 years, 7 months
256129 badges		location	Tacoma, WA		seen	yesterday

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66 Favorites

added views newest activity votes

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145

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Wanted: Insight into formula involving binomial coefficients

combinatorics binomial-coefficients

mar 3 at 5:51 Marc van Leeuwen 23.9k

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answer

127

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Closed-form expression for $\sum_{n=1}^{k} (-1)^{n+1}n^2(n^2-1)\binom{2k}{k-n}$?

feb 22 at 23:46 David Moews 10.2k

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answer

182

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Summation of an Infinite Series: $\sum_{n=1}^\infty \frac{4^{2n}}{n^3 \binom{2n}{n}^2} = 8\pi G-14\zeta(3)$

calculus real-analysis sequences-and-series binomial-coefficients summation

feb 21 at 7:40 Integral 486

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answers

119

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Combinatorial Proofs of Real Analysis Identity

combinatorics

dec 29 at 4:38 combcereal 31

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208

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Binomial sum of $n$ terms in closed form

sequences-and-series binomial-coefficients summation

may 7 at 22:49 cyclochaotic 406

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198

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Problem of limit with binomial coefficients

limit proof-strategy binomial-coefficients random-walk

jan 23 at 16:48 marty cohen 6,869

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150

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How to understand this combinatorially: $\sum^{2k}_{i=0} \binom{4k}{2i} (-1)^{i}=2^{2k}(-1)^{k}$

combinatorics binomial-coefficients

jan 22 at 14:28 Mike Spivey 25.9k

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answer

340

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proof that $1 = \sum\limits_{k=0}^n (-1)^k { 2n \choose n,k,n-k } \frac{n}{n+k}$

combinatorics binomial-coefficients

may 9 '12 at 8:40 J. M. 38.9k

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answers

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Characterization of Sequences with Integral Binomial Coefficients

combinatorics binomial-coefficients

jan 20 at 14:03 Ofir 2,194

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571

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Is it true that any matrix can be decomposed into product of rotation,reflection,shear,scaling and projection matrices?

linear-algebra matrices transformation

jan 19 at 0:26 David Moews 10.2k

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answers

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Can that two double series representations of the $\eta$/$\zeta$ function be converted into each other?

sequences-and-series zeta-functions dirichlet-series

jan 19 at 2:19 Gottfried Helms 7,217

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answers

292

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What is the transformation representation/interpretation of symmetric matrices?

linear-algebra matrices

jan 27 '12 at 19:21 yoyo 4,850

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answer

146

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If $\lambda_n \sim \mu_n$, is it true that $\sum \exp(-\lambda_n x) \sim \sum \exp(-\mu_n x)$ as $x \to 0$?

real-analysis sequences-and-series analysis asymptotics

jan 13 at 23:11 Community♦ 1

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answer

103

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Are these numbers $h_{r,s}$ irrational?

probability combinatorics number-theory special-functions irrational-numbers

jan 14 at 4:01 Mike Spivey 25.9k

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536

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Symmetry of function defined by integral

calculus

jan 4 at 19:20 Sasha 41.4k

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260

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A relationship between matrices, bernoulli polynomials, and binomial coefficients

linear-algebra number-theory binomial-coefficients bernoulli-numbers

dec 26 at 21:19 oen 7,477

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kviews

Mathematics problems for very young children?

education

may 8 at 7:51 MvG 2,597

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914

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Eigenvalue problem: Prove that all of the eigenvalues of $A$ are 1.

linear-algebra eigenvalues

may 2 at 13:59 Community♦ 1

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276

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Sum of binomial coefficients

combinatorics binomial-coefficients

jan 8 at 6:46 Mike Spivey 25.9k

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222

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The horizontal pivot line of $\sin^2 x$ here is exactly $\frac{3}{8}$. Why?

calculus integral physics

feb 11 '12 at 18:55 Christian Blatter 32.6k

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answers

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Binomial transform of a scaled version of the catalan numbers.

binomial-coefficients catalan-numbers

jun 4 '12 at 15:21 Mike Spivey 25.9k

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202

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Prove that $x_1^2+x_2^2+x_3^2=1$ yields $ \sum_{i=1}^{3}\frac{x_i}{1+x_i^2} \le \frac{3\sqrt{3}}{4} $

inequality

feb 7 '12 at 11:19 Christian Blatter 32.6k

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answer

368

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Bell numbers, recursions, bijections

combinatorics recursion

may 29 '12 at 2:01 Michael Hardy 48.2k

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answer

120

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Solution for Logistic Growth Equation with Linearly Growing Carrying Capacity

differential-equations

oct 11 '11 at 2:04 Hans Engler 2,799

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answer

490

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Combinatorial proof of arithmetic geometric mean inequality

combinatorics inequality

feb 20 '12 at 17:47 Dejan Govc 5,549

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177

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Why does $S(n,k)=\sum 1^{a_1-1}2^{a_2-1}\cdots k^{a_k-1}$?

combinatorics partitions stirling-numbers

jan 31 '12 at 2:23 robjohn♦ 60k

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answers

191

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Particle moving at constant speed with Poisson setbacks

puzzle probability

dec 1 '10 at 6:14 Mike Spivey 25.9k

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answer

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Is there a simple expression of this sum related to the coefficients of a generating function of $e^{x+x^2/2}$?

combinatorics generating-functions

jan 25 '12 at 2:46 Sasha 41.4k

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answers

kviews

Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even

combinatorics binomial-coefficients

dec 21 at 22:52 Mike Spivey 25.9k

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answers

677

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Odds of guessing suit from a deck of cards, with perfect memory

probability statistics

jan 11 '12 at 22:08 alex.jordan 8,844