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Latin Squares are so Beautiful
Figure 1: Image of a 5 by 5 Latin Square with colors mapped to numbers. I was recently reading another math blog on Latin Squares and it brought the concept back to the forefront of my mind. For years...
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Puzzle Generation Idea (Its Working)
A lot of my friends ask me what I do with my spare time. There are a number of ways I could answer that question, but the answer is basically this site. Its full of the thoughts that go through my mind...
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The Beauty of Euler’s phi function
The recent conversation I had about number theory has brought it back into my awareness. In particular, the concept of beauty in numbers. I’m definitely not any kind of graphical designer or fashion...
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Pascal’s Triangle
I had a recent conversation with a friend who asked me “what makes number theory interesting?”. I loved the question, mainly because it gave me an opportunity to talk about math in a positive manner....
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Set Partition Problems
This is my first post of 2019 and my first post in a while. There was one posted a few months ago, but not really geared towards the algorithms and learning focus of the site. I have been doing a lot...
View ArticleBinary Puzzles
As you can probably tell, I’m a big fan of puzzles. On one hand you can say that a good puzzle is nothing but particular instance of a complex problem that we’re being asked to solve. What exactly...
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Range Puzzles
Range Puzzles I have always liked puzzles. I really enjoy discovering a new puzzle. Sometimes when I have discovered a new puzzle, I enjoy it so much that I can’t seem to do enough of them. In such...
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Floyd-Warshall Shortest Paths
The Floyd Warshall algorithm is an all pairs shortest paths algorithm. This can be contrasted with algorithms like Dijkstra’s which give the shortest paths from a single node to all other nodes in the...
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Degree Centrality of a Graph
I wanted to spend some time on centrality measures of a graph. These are measurements of how important each node (or edge) is to the overall graph. But how do we define, or determine, importance?...
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Tarjan’s Strongly Connected Components Algorithm
I just added a program that finds the strongly connected components of a graph using Tarjan’s Algorithm. A strongly connected component of a graph is a subgraph S of G where every pair of nodes, u and...
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Longest Common Subsequence at LEARNINGLOVER.COM
Suppose you and I each had an ordered list of items and we were interested in comparing how similar those lists are. One calculation we can perform on these two strings is the Longest Common...
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Independent Set Puzzles
In this post, I want to return to the idea of NP-Complete problems. There is a more technical, more formal definition that I can refer you to, but I like to refer to the images from Garey and Johnson’s...
View ArticleLets Learn About XOR Encryption
One of the more common things about this generation is the constant desire to write up (type) their thoughts. So many of the conversations from my high school days were long lasting, but quickly...
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Discrete-time Markov Chains
Much of how we interact with life could be described as transitions between states. These states could be weather conditions (whether we are in a state of “sunny” or “rainy”), the places we may visit...
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Topological Sort
One of the things I generally say about myself is that I love learning. I can spend hours upon hours reading papers and algorithms to better understand a topic. Some of these topics are stand alone...
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The RSA Algorithm
I can remember back when I was in school, still deciding whether I wanted to study pure or applied mathematics. One of the common questions I would receive from those in applied mathematical realms...
View ArticleHow To Take Notes in Math Class
I was recently asked by someone how they should be taking notes in math class. I could immediately relate because I once asked this very same question. In both undergrad and grad, I had to ask myself...
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The Depth-First-Search Algorithm
I remember when I was younger I used to play the game of hide-and-seek a lot. This is a game where a group of people (at least two) separate into a group of hiders and a group of seekers. The most...
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The Breadth-First-Search Algorithm
I remember when I was younger I used to play the game of hide-and-seek a lot. This is a game where a group of people (at least two) separate into a group of hiders and a group of seekers. The most...
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ID3 Algorithm Decision Trees
As I grow LEARNINGlover.com, I’m always thinking of different ways to expose my own personality through the site. This is partially because it is easier for me to talk about subjects where I am...
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