Convergence of Infinite Series in General and Taylor Series in Particular E. L. Lady (October 31, 1998)

Source URL: www.math.hawaii.edu

• Harmonic series
• Taylor series
• Binomial series
• Geometric series
• Pi
• Summation
• Divergent series
• Laurent series
• Mathematical analysis
• Mathematical series
• Series

UIUC UNDERGRADUATE MATH CONTEST April 8, 2006 Solutions 1. Determine, without numerical calculations, which of the two numbers

Source URL: www.math.illinois.edu

• Combinatorics
• Integer sequences
• Number theory
• Real analysis
• Taylor series
• Factorial
• Summation
• Exponentiation
• Characterizations of the exponential function
• Mathematics
• Mathematical analysis
• Exponentials

U OF I UNDERGRADUATE MATH CONTEST April 14, [removed]Let f (n) = (12 + 1)1! + (22 + 1)2! + · · · + (n2 + 1)n!. Find a simple general formula for f (n). 2. Prove that for every odd integer n the sum 1n + 2n + · · · +

Source URL: www.math.illinois.edu

• Number theory
• Combinatorics
• Factorial
• Pi
• Summation
• Mathematics
• Mathematical analysis
• Integer sequences

2014 UI UNDERGRADUATE MATH CONTEST Solutions 1. (a) Does there exist a multiple of 2013 whose decimal representation ends in the digits 2014? Explain! (b) Does there exist a power of 2 whose decimal representation ends i

Source URL: www.math.illinois.edu

• Integer sequences
• Number theory
• Exponentials
• Binomial coefficient
• Factorial
• Summation
• Exponential function
• Proof that π is irrational
• Basel problem
• Mathematics
• Mathematical analysis
• Combinatorics

2013 UI UNDERGRADUATE MATH CONTEST Solutions 1. Let a1 = 2 and an+1 = a2n − an + 1 for n = 1, 2, . . . . (i) Prove that the integers a1 , a2 , . . . are pairwise coprime (i.e., do not have a common prime factor). P 1

Source URL: www.math.illinois.edu

• Series
• Summability methods
• Fourier analysis
• Cesàro summation
• Fourier series
• Mathematical analysis
• Mathematics
• Calculus

U OF I UNDERGRADUATE MATH CONTEST April 14, 2007 Solutions 1. Let f (n) = (12 + 1)1! + (22 + 1)2! + · · · + (n2 + 1)n!. Find a simple general formula for f (n).

Source URL: www.math.illinois.edu

• Number theory
• Exponentials
• Factorial
• Summation
• Exponentiation
• Mathematics
• Combinatorics
• Integer sequences

U OF I UNDERGRADUATE MATH CONTEST MARCH 7, 2009 − denote the integer obtained by reversing the 1. Given a nonnegative integer n, let ← n ←−

Source URL: www.math.illinois.edu

• Arithmetic
• Mathematical notation
• Summation
• Combinatorics
• Binomial coefficient
• Fermat number
• Mathematics
• Number theory
• Integer sequences

Automatic online tuning for fast Gaussian summation (Poster W61) Vlad I. Morariu, Balaji V. Srinivasan, Vikas C. Raykar, Ramani Duraiswami, Larry S. Davis • Cost is quadratic

Source URL: www.umiacs.umd.edu

Scalable machine learning for massive datasets: Fast summation algorithms Getting good enough solutions as fast as possible

Source URL: www.umiacs.umd.edu

• Non-parametric statistics
• Learning
• Supervised learning
• Kernel density estimation
• Statistical classification
• Machine learning
• Statistics
• Artificial intelligence

An Introduction to the Theory of Numbers by Leo Moser

Source URL: www.trillia.com

• Analytic number theory
• Integer sequences
• Modular arithmetic
• Quadratic residue
• Summation
• Riemann zeta function
• Prime number
• Mathematics
• Mathematical analysis
• Number theory