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Category Archives: Examples
Permutation Problems
I love to play with puzzles. When I was in grade school I would spend hours at a time figuring out ways to solve from things like Tetris, Mindsweeper, Solitare, and Freecell. Later I was introduced to puzzles involving numbers … Continue reading
Posted in Blog, Examples
Tagged algorithm, algorithms, computer science, enumeration, games, javasctipt, list, math, next, permutation, previous, programming, random, script, search, sudoku
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Approximating the Set Cover Problem
I just finished my weekly task of shopping for groceries. This can be a somewhat daunting task because I generally have a list of things that I’ll need which cannot all be purchased at a single location. What often happens … Continue reading
Posted in Blog, Examples
Tagged algorithm, algorithms, animation, approximation, computer science, greedy, integer programming, JavaScript, learning, linear programming, math, mathematics, operations research, probability, programming, randomized, research, rounding, script, search, set cover, set theory, sort
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What is a “Hard” Problem?
Throughout our lives, we are introduced to a wide variety of problems. Naturally we tend to think of some problems as more difficult than others. If you were doing the exercises at the end of a chapter in a book, … Continue reading
Posted in Examples
Tagged algorithm, cook, deterministic, hard, karp, knapsack, np, np-complete, np-hard, polynomial, problem, quick, reduce, reduction, sat, satisfiability
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Knapsack Problems
I have added a script to help users understand the knapsack problem as well as some attempts at solving it. To help understand this problem, I want you to think about a common situation in many people’s lives. You have … Continue reading
Triangle Trigonometry
I haven’t forgotten about my pledge to focus more content here towards some of the areas I’ve been asked to tutor on recently. This latest one is designed to help users understand the properties of triangles. It is based on … Continue reading
Posted in Blog, Examples
Tagged angle, cos, cosine, JavaScript, law, law of cosines, law of sines, learn, learning, math, mathematics, programming, script, sin, sine, triangle
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Sudoku Program Updates
Here in DC, we recently had an unexpected snow day. By the word unexpected, I don’t mean that the snow wasn’t forecast – it was definitely forecast. It just never came. However due to the forecast I decided to avoid … Continue reading
Posted in Examples
Tagged algorithm, backtracking, column, generation, how to solve sudoku, JavaScript, learn about math, learning, learning about math, make your own sudoku, math, mathematics, play sudoku online free, programming, puzzle, row, script, solutions puzzle, solve, solve sudoku online, solving sudoku, solving sudoku puzzles, sudoku, sudoku answer generator, sudoku games, sudoku maker, sudoku puzzles, sudoku solver, sudoku solver online, sudoku solvers
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The PageRank Algorithm
I think one of the best recent examples of the importance of mathematics is the rise of the search engine Google. I remember the world of search engines before Google and it was dominated by names like AltaVista, Yahoo, WebCrawler, … Continue reading
Nonogram Puzzles
A friend introduced me to a type of puzzles called Nonograms and I enjoyed them so much that I wrote a script that automatically generates these puzzles. Nonograms are grid puzzles based on discovering the hidden pattern based on the … Continue reading
Geometric Sequences
I’ve added a script which helps to understand geometric sequences. Suppose you were to draw an equilateral triangle on a sheet of paper. It might look something like this: Now suppose that you draw lines connecting the midpoints of each … Continue reading
Posted in Blog, Examples
Tagged difference, first, geometric, geometric sequence, JavaScript, math, script, sequence, series, term
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Arithmetic Sequences
I’ve added a script which helps to understand arithmetic sequences. At a previous job of mine, there was a policy of holding a dinner party for the company each time we hired a new employee. At these dinners, each employee … Continue reading
Posted in Blog, Examples
Tagged arithmetic, common difference, data, difference, first, JavaScript, learning, list, math, mathematics, script, sequence, sum
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