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How Many Ways are there to Juggle?
How Many Ways are there to Juggle?

Some Mathematical Preliminaries
Some Mathematical Preliminaries

Lecture 11
Lecture 11

1 - Computer Science Department
1 - Computer Science Department

EVERY POSITIVE K-BONACCI-LIKE SEQUENCE EVENTUALLY
EVERY POSITIVE K-BONACCI-LIKE SEQUENCE EVENTUALLY

... If we are dealing with the Fibonacci numbers (k = 2), the support of d is [0, 1], and Z(d) = d(1) and Z(Sd) = d(0) + d(1). Appropriate choices of d(0) and d(1) can give any desired values for Z(d) and Z(Sd). If we are dealing with the tribonacci numbers (k = 3), the support of d is [−1, 0, 1], and Z ...
Fractuals and Music by Sarah Fraker
Fractuals and Music by Sarah Fraker

CHAP09 Logs and Exponentials
CHAP09 Logs and Exponentials

Topic 2c (foundation) – Homework on Pictograms
Topic 2c (foundation) – Homework on Pictograms

Full text
Full text

... is, without a hypothesis on N(x), and it is those I am concerned with here* Those needing a hypothesis on N(x) , I assume included in §2. However, the fact that the g.i, can be ordered and so a counting function N(x) exists, is important. Since there will now be a slight change in notation, I will r ...
A Combinatorial Miscellany
A Combinatorial Miscellany

... the Notes section points to some more general accounts that can help remedy this shortcoming. With some simplification, combinatorics can be said to be the mathematics of the finite. One of the most basic properties of a finite collection of objects is its number of elements. For instance, take word ...
36(4)
36(4)

Densities and derivatives - Department of Statistics, Yale
Densities and derivatives - Department of Statistics, Yale

... For example, if µ is Lebesgue measure on B(R), the probability measure defined by the density (x) = (2π )−1/2 exp(−x 2 /2) with respect to µ is called the standard normal distribution, usually denoted by N (0, 1). If µ is counting measure on N0 (that is, mass 1 at each nonnegative integer), the pro ...
Precalculus
Precalculus

Mathematical Investigation: Paper Size
Mathematical Investigation: Paper Size

RISES, LEVELS, DROPS AND - California State University, Los
RISES, LEVELS, DROPS AND - California State University, Los

... [7], meets between subsets of a lattice [3], and alternating sign matrices [4], to name just a few. Alladi and Hoggatt also derived results about the number of times a ...
Section 3.4 - GEOCITIES.ws
Section 3.4 - GEOCITIES.ws

Real Induction - Department of Mathematics
Real Induction - Department of Mathematics

CS1231 - Lecture 09
CS1231 - Lecture 09

Sequences
Sequences

... the Secret Service assigns a code name to the president of the United States and the first family. Some classic code names for former U.S. presidents were “Tumbler” for President George Walker Bush, “Timberwolf” for President George Herbert Walker Bush, “Deacon” for President Jimmy Carter, and “Lanc ...
Using Mapping Diagrams to Understand Functions
Using Mapping Diagrams to Understand Functions

Sequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006
Sequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006

Mathematical writing - QMplus - Queen Mary University of London
Mathematical writing - QMplus - Queen Mary University of London

MAT 1015 Calculus I 2010/2011 John F. Rayman
MAT 1015 Calculus I 2010/2011 John F. Rayman

Total recursive functions that are not primitive recursive
Total recursive functions that are not primitive recursive

... recursive. Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function ϕ. Ackermann’s three-argument function, ϕ(m, n, p), is defined such that for p = 0, 1, 2, it reproduces the basic operations of addition, multiplication, a ...
Sheffer sequences, probability distributions and approximation
Sheffer sequences, probability distributions and approximation

... Taylor expansion of polynomials is a special case of (5) where sk (x) = xk /k! and thus Q = D and S = I. Moreover, (6) with the same choice yields that each shift-invariant operator can be expanded into a power series in D. Note that there are no convergence problems, since all infinite sums reduce ...
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Series (mathematics)

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