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Browse College Algorithms
Stars indicate particularly interesting answers or
good places to begin browsing.
 Decimal To Fraction Conversion [06/25/1998]

I am trying to find a method (one that can be programmed on a PC) to
convert the decimal part of a real number to a fraction represented by
integers for the numerator and denominator.
 Set Terminology [07/07/1997]

What does the terminology inf{...} mean?
 Solving Problems Using Matrices [9/31/1995]

Given a current x,y,z coordinate (i.e. 60,60,60) and an angle (i.e. 90
degrees) and a plane to rotate about (i.e. z), what's the formula to
solve for x,y,z?
 Unsolvable Equations, Feedback Loops, Existence Proofs... [04/14/1997]

How do you solve equations like (9/4)^x = x^(9/4) ?
 Applying Logic to an Interesting Problem on Billiard Balls [03/03/2004]

In front of you is a 100 story building. You must determine which is
the highest floor you can drop a billiard ball from without it
breaking. You have only two billiard balls to use as test objects.
If both of them break and you don't know the answer then you have
failed at your task. What is the least number of drops needed to be
sure you will have determined the breaking point?
 ArbitraryPrecision Arithmetic [08/08/2003]

How could I use QBasic V4.5's math to compute numbers that are greater
than 10^15 in the quickest way, and yet display every single digit in
the product?
 BigO Notation for Measuring Algorithm Efficiency [10/21/2004]

Can you explain the ideas behind the bigO notation?
 BigO Notation in Matrix Multiplication [12/10/2000]

How can I prove that two n x n matrices can be multiplied in O(n^3) time?
Also, is there a faster way to multiply them?
 Calculators  CORDIC Method [05/16/1999]

How can a computer or calculator calculate square roots, cube roots, Xth
root, x^y, logarithm, sine, cosine, ...?
 Complexity of Matrix Inversion [04/25/2001]

What is the computational complexity for the general case of inverting an
NxN matrix?
 Correlation Coefficients of Random Numbers [12/18/2000]

I have to generate random numbers that have a certain correlation
coefficient.
 Creating a List of Permutations with a Computer Program [07/31/2007]

I'm writing a computer program to list all the permutations of a given
set of numbers, but am not sure of the best way to do it. Any ideas?
 Data Compression [08/10/2003]

Is there an algorithm that can reduce any binary number to a much
smaller binary number, then later be reversed to regain the original
number? It has to work for any binary number.
 Elliptic Curves: Algorithms [03/11/1999]

Find the number of points on the curve over F sub p for an elliptic curve
y^2 = x^3 + 1.
 Equation Solving with NewtonRaphson Method [07/23/2004]

Is there a way to solve F = A*(((1+i)^n)  1)/i for i, such that we have
i = ...? I'm thinking I need to use a logarithm, but I'm stuck.
 Erlang B [10/22/2002]

I need to know how to calculate the addition of numbers using
logarithms: 1 + 2 + 3. There is a step that requires adding numbers
that exceed Excel's limits. How can I use logs to add the numbers?
 Euclidean Algorithm [5/13/1996]

How can we prove that Euclid's method for finding the highest common
factor for two numbers will work for all values?
 Euclidean Algorithms [3/13/1996]

What is the Euclidean algorithm? What is a "constructible" number? What
can you tell me about Diophantine equations?
 Euclidean and Division Algorithms [11/26/1997]

Can you show and explain the proofs of the Euclidean Algorithm and the
Division Algorithm?
 Euclidean Modular Inverse Algorithm [08/26/1997]

How to program an algorithm for finding the modular inverse... the number
that when multiplied by the original number produces bar 1?
 Euler's Phi Function Applied to Large Numbers [08/23/2004]

I'm trying to find the phi value of a large (10digit) composite
number. Can it be done in polynomial time, and if so, is there an
algorithm?
 Explaining the Euclidean Algorithm [10/27/1998]

In the Euclidean Algorithm (or the Division Algorithm), why is the last
divisor the greatest common factor?
 Factoring Large Numbers [10/26/1998]

Can you give me an algorithm for factoring large numbers? What about the
Pollard Rho Factoring Algorithm?
 Factoring Polynomials over Real and Complex Numbers [07/17/2006]

I am having difficulties factoring polynomials like x^4  15x^2  75.
It is irreducible over the integers but its graph suggests there are
in fact roots. How can I factor over the real and complex numbers?
 Fast Multiplication Algorithms for Large Integers [08/16/1997]

Are there elementary algorithms for computing the product of 2 ndigit
numbers in less than O(n^1.58) time?
 Ferrari's Method for Quartics [04/16/1999]

Could you explain Ferrari's method for quartics?
 Finding a Series Given the Sum [09/27/1999]

How can I find all series of consecutive integers whose sum is a given
value x?
 A Formula for Iterating [10/11/2002]

Find the value of x if 3 = sqrt(x+sqrt(x_sqrt(x+sqrt(x)))).
 Fraction Algorithm [03/19/2002]

I have been having trouble making an application that can convert a
finite decimal to a fraction without doing 78349/1000000.
 Generating Random Numbers [02/24/2001]

Would you know of any congruential models for the generation of random
numbers?
 Greatest Common Factor [03/28/1997]

How do you find the greatest common factor?
 How a CPU Adds Decimal Numbers [10/22/2000]

How does an 8bit CPU add up two fourdigit decimal numbers, and why does
it take four operations to do so?
 How to Solve Equations with No Analytic Solution Method [10/26/2005]

A discussion of solving equations that can't be solved analytically by
using iterative estimation methods including bisection, false
position, and Newton's method. The equation x(e^x) = 3 is used as an
example.
 The Hungarian Job Assignment [03/10/2011]

A company owner writes in for help costefficiently assigning tasks to different employees when each one commands her own fee for every job. Invoking a little graph theory, Doctor Jacques introduces the Hungarian algorithm and walks through an application to an example assignment.
 An Introduction to Basic Diophantine Equations [08/27/2007]

A birdcage contains both 2legged and 1legged birds, and there are a
total of 11 legs in the cage. Use a Diophantine equation to find all
possible combinations of birds.
 Inverses in the Field GF(2^8) [11/07/2000]

How can I get the multiplicative inverse of a byte in the polynomial
field GF(2^8)?
 An Iterative Method of Calculating Pi [06/09/2004]

I recently saw a method of calculating pi that involves an iterative
function, P(n + 1) = P(n) + sin(P(n)) where P(n) is the approximation
of pi at the nth iteration.
 Julian to Calendar Date Conversion [02/24/2001]

Can you show me an algorithm to convert Julian date values to calendar
date values? For example, Julian date 2451964 = 02/24/2001.
 Karatsuba Multiplication [10/15/2007]

Can you explain the ideas and steps behind the Karatsuba method of
multiplying?
 Matching Invoices with Report Totals [10/31/2000]

I have 14 invoice values and 2 report totals. The sum of the invoices for
each report should be the report total. Is there a fast way of finding
which invoices go with each report, or determining if it is even
possible?
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