|
Thoughts on using Twitter to shrink the size of large classrooms, foster discussion and make class more enjoyable.
|
|
How to Clean Your Dirty Smartphone (Without Breaking Something)
-
justingarrison.com
-
15 years ago
-
eng
|
|
Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.
|
|
Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.
|
|
Problem: Take a chessboard and cut off two opposite corners. Is it possible to completely tile the remaining board with 2-by-1 dominoes? Solution: Notice that every domino covers exactly one white tile and one black tile. Counting up the colors, we have 32 white and 30 black. Hence, any tiling by 2-by-1 dominoes will leave two extra white squares unaccounted for. So no such tiling is possible. Problem: Cut one corner off a chessboard.
|
|
Community Service Mathematics is supposed to be a process of discovery. Definitions, propositions, and methods of proof don’t come from nowhere, although after the fact (when presented in a textbook) they often seem to. As opposed to a textbook, real maths is highly non-linear. It took mathematicians quite a lot of fuss to come up with the quadratic formula, and even simple geometric conjectures were for the longest time the subject of hot ..
|
|
Community Service Mathematics is supposed to be a process of discovery. Definitions, propositions, and methods of proof don’t come from nowhere, although after the fact (when presented in a textbook) they often seem to. As opposed to a textbook, real maths is highly non-linear. It took mathematicians quite a lot of fuss to come up with the quadratic formula, and even simple geometric conjectures were for the longest time the subject of hot ..
|
|
Community Service Mathematics is supposed to be a process of discovery. Definitions, propositions, and methods of proof don’t come from nowhere, although after the fact (when presented in a textbook) they often seem to. As opposed to a textbook, real maths is highly non-linear. It took mathematicians quite a lot of fuss to come up with the quadratic formula, and even simple geometric conjectures were for the longest time the subject of hot ..
|
|
Problem: What is the area of the triangle within the rectangle? Solution: In a moment of inspiration, we draw the following additional line: Now the answer is obvious. Once we split the rectangle into two smaller rectangles, the sides of the triangle become diagonals of their respective rectangles. The diagonals obviously split each of the two smaller rectangles into halves, where one half lies inside our original triangle. Clearly then, th..
|
|
Problem: What is the area of the triangle within the rectangle? Solution: In a moment of inspiration, we draw the following additional line: Now the answer is obvious. Once we split the rectangle into two smaller rectangles, the sides of the triangle become diagonals of their respective rectangles. The diagonals obviously split each of the two smaller rectangles into halves, where one half lies inside our original triangle. Clearly then, th..
|
|
Problem: What is the area of the triangle within the rectangle? Solution: In a moment of inspiration, we draw the following additional line: Now the answer is obvious. Once we split the rectangle into two smaller rectangles, the sides of the triangle become diagonals of their respective rectangles. The diagonals obviously split each of the two smaller rectangles into halves, where one half lies inside our original triangle. Clearly then, th..
|
|
Problem: Find the sum of the first 1000 natural numbers. Solution: Write the numbers twice as follows: $ \begin{matrix} 1 & + & 2 & + & \dots & + & 999 & + & 1000 \\\ 1000 & + & 999 & + & \dots & + & 2 & + & 1 \end{matrix}$ Summing the numbers in each column, we have: $ 2 (1 + 2 + \dots + 1000) = 1001 + 1001 + \dots + 1001$ (1000 times)
|
|
Problem: Find the sum of the first 1000 natural numbers. Solution: Write the numbers twice as follows: $ \begin{matrix} 1 & + & 2 & + & \dots & + & 999 & + & 1000 \\\ 1000 & + & 999 & + & \dots & + & 2 & + & 1 \end{matrix}$ Summing the numbers in each column, we have: $ 2 (1 + 2 + \dots + 1000) = 1001 + 1001 + \dots + 1001$ (1000 times)
|
|
Problem: Find the sum of the first 1000 natural numbers. Solution: Write the numbers twice as follows: $ \begin{matrix} 1 & + & 2 & + & \dots & + & 999 & + & 1000 \\\ 1000 & + & 999 & + & \dots & + & 2 & + & 1 \end{matrix}$ Summing the numbers in each column, we have: $ 2 (1 + 2 + \dots + 1000) = 1001 + 1001 + \dots + 1001$ (1000 times)
|
|
Problem: At any party of 1000 people, must there always exist two people at the party who have the same number of friends at the party? For the sake of this problem, one cannot be friends with oneself, and friendship is bidirectional. Solution: This must always happen. Suppose to the contrary, that every person at the party has a different number of friends at the party. The minimum number of friends one could have is 0, while 999 is the ma..
|
|
Problem: At any party of 1000 people, must there always exist two people at the party who have the same number of friends at the party? For the sake of this problem, one cannot be friends with oneself, and friendship is bidirectional. Solution: This must always happen. Suppose to the contrary, that every person at the party has a different number of friends at the party. The minimum number of friends one could have is 0, while 999 is the ma..
|
|
Problem: At any party of 1000 people, must there always exist two people at the party who have the same number of friends at the party? For the sake of this problem, one cannot be friends with oneself, and friendship is bidirectional. Solution: This must always happen. Suppose to the contrary, that every person at the party has a different number of friends at the party. The minimum number of friends one could have is 0, while 999 is the ma..
|
|
Problem: 1000 players compete in a tournament. In each round, players are matched with opponents, and the winner proceeds to the next round. If there are an odd number of players in a round, one player chosen at random sits out of that round. What is the total number of games are played in the tournament? Solution: 999. Each player loses exactly one game, except for the winner of the tournament.
|
|
Problem: 1000 players compete in a tournament. In each round, players are matched with opponents, and the winner proceeds to the next round. If there are an odd number of players in a round, one player chosen at random sits out of that round. What is the total number of games are played in the tournament? Solution: 999. Each player loses exactly one game, except for the winner of the tournament.
|
|
Problem: 1000 players compete in a tournament. In each round, players are matched with opponents, and the winner proceeds to the next round. If there are an odd number of players in a round, one player chosen at random sits out of that round. What is the total number of games are played in the tournament? Solution: 999. Each player loses exactly one game, except for the winner of the tournament.
|
|
Apologies for the lack of Parkour Ninja updates. I do have fresh info about it somewhere in this post. But first! A list of potentially interesting goings-on of late: School's out for summer! And I'm one year closer to a Computer Science & Engineering undergrad degree from Ohio State. I'll graduate in about a year and a half, right around my 21st birthday actually. I haven't the foggiest idea what to do after that. I'm looking at grad s....
|
|
Last week, I was invited to do a coding dojo for the Java user group in Bergen. I have written a few words about the dojo part of the exercise in a previous blogpost. After “classical” TDD-training, I decided to try something different and gave the group a competition to play with: Extreme startup, a workshop with software created by @rchatley and @mattwynne. The workshop was a huge success and I’m hoping to repeat it soon.
|
|
A Bully By Any Other Name From the New York Times: “Shopping online in late July, Clarabelle Rodriguez typed the name of her favorite eyeglass brand into Google’s search bar. In moments, she found the perfect frames — made by a French company called Lafont — on a Web site that looked snazzy and stood at the top of the search results. Not the tippy-top, where the paid ads are found, but under those, on Google’s version of the gold-medal podi..
|
|
A Bully By Any Other Name From the New York Times: “Shopping online in late July, Clarabelle Rodriguez typed the name of her favorite eyeglass brand into Google’s search bar. In moments, she found the perfect frames — made by a French company called Lafont — on a Web site that looked snazzy and stood at the top of the search results. Not the tippy-top, where the paid ads are found, but under those, on Google’s version of the gold-medal podi..
|
|
A Bully By Any Other Name From the New York Times: “Shopping online in late July, Clarabelle Rodriguez typed the name of her favorite eyeglass brand into Google’s search bar. In moments, she found the perfect frames — made by a French company called Lafont — on a Web site that looked snazzy and stood at the top of the search results. Not the tippy-top, where the paid ads are found, but under those, on Google’s version of the gold-medal podi..
|
|
I write Python and Javascript code. I use Django and jQuery. And I cringe every time I have to run gem install x. I only have a limited understanding of Ruby and hardly any of Ruby on Rails. It seems disorganized to me and hard to process. All this is fine – I don’t have to use any of it if I don’t like it, right? I always knew there was something wrong with the way Ruby works. I don’t mean wrong like murdering children, I just mean wrong....
|
|
I write Python and Javascript code. I use Django and jQuery. And I cringe every time I have to run gem install x. I only have a limited understanding of Ruby and hardly any of Ruby on Rails. It seems disorganized to me and hard to process. All this is fine – I don’t have to use any of it if I don’t like it, right? I always knew there was something wrong with the way Ruby works. I don’t mean wrong like murdering children, I just mean wrong....
|
|
Dangling Nodes and Non-Uniqueness Recall where we left off last time. Given a web $ W$ with no dangling nodes, the link matrix for $ W$ has 1 as an eigenvalue, and if the corresponding eigenspace has dimension 1, then any associated eigenvector gives a ranking of the pages in $ W$ which is consistent with our goals. The first problem is that if there is a dangling node, our link matrix has a column of all zeros, and is no longer column-stoc..
|
|
Dangling Nodes and Non-Uniqueness Recall where we left off last time. Given a web $ W$ with no dangling nodes, the link matrix for $ W$ has 1 as an eigenvalue, and if the corresponding eigenspace has dimension 1, then any associated eigenvector gives a ranking of the pages in $ W$ which is consistent with our goals. The first problem is that if there is a dangling node, our link matrix has a column of all zeros, and is no longer column-stoc..
|
|
Dangling Nodes and Non-Uniqueness Recall where we left off last time. Given a web $ W$ with no dangling nodes, the link matrix for $ W$ has 1 as an eigenvalue, and if the corresponding eigenspace has dimension 1, then any associated eigenvector gives a ranking of the pages in $ W$ which is consistent with our goals. The first problem is that if there is a dangling node, our link matrix has a column of all zeros, and is no longer column-stoc..
|
|
My next book will be Practical Math for Programmers A High-Level Overview of Fully Homomorphic Encryption Searching for Riemann Hypothesis Counterexamples Linear Programming and Healthy Diets Hybrid Images Bezier Curves and Picasso
|
|
My next book will be Practical Math for Programmers A High-Level Overview of Fully Homomorphic Encryption Searching for Riemann Hypothesis Counterexamples Linear Programming and Healthy Diets Hybrid Images Bezier Curves and Picasso
|
|
My next book will be Practical Math for Programmers A High-Level Overview of Fully Homomorphic Encryption Searching for Riemann Hypothesis Counterexamples Linear Programming and Healthy Diets Hybrid Images Bezier Curves and Picasso
|
|
I have tried dozens of code editors, text editors and IDEs. I have carefully weighed the pros and cons of each. I have studied features, extensibility, themes, syntax highlighting options, price, and many other criteria. I have reached my verdict and I’m ready to publish my findings. The best IDE is the one that works for you.
|
|
I have tried dozens of code editors, text editors and IDEs. I have carefully weighed the pros and cons of each. I have studied features, extensibility, themes, syntax highlighting options, price, and many other criteria. I have reached my verdict and I’m ready to publish my findings. The best IDE is the one that works for you.
|
|
I love talking about scalability. Everyone has their own opinion, their own way of performing benchmarks and their own conclusions. And we all know that this is very silly. I recently came across an article by Ted Dziuba that summarizes it very nicely for you: Shut up about scalability, no one is using your app anyway. I love how the author explains the use of the word scalability in this day and age: The most common butth..
|
|
I love talking about scalability. Everyone has their own opinion, their own way of performing benchmarks and their own conclusions. And we all know that this is very silly. I recently came across an article by Ted Dziuba that summarizes it very nicely for you: Shut up about scalability, no one is using your app anyway. I love how the author explains the use of the word scalability in this day and age: The most common butth..
|
|
Story Time Linear algebra was founded around the same time as Calculus (think Leibniz, circa 1700) solely for the purpose of solving general systems of linear equations. The coefficients of a system were written in a grid form, with rows corresponding to equations and columns to the unknown variables. Using a computational tool called the determinant (an awkward, but computable formula involving only the coefficients of the equations in a s..
|
|
Story Time Linear algebra was founded around the same time as Calculus (think Leibniz, circa 1700) solely for the purpose of solving general systems of linear equations. The coefficients of a system were written in a grid form, with rows corresponding to equations and columns to the unknown variables. Using a computational tool called the determinant (an awkward, but computable formula involving only the coefficients of the equations in a s..
|
|
Story Time Linear algebra was founded around the same time as Calculus (think Leibniz, circa 1700) solely for the purpose of solving general systems of linear equations. The coefficients of a system were written in a grid form, with rows corresponding to equations and columns to the unknown variables. Using a computational tool called the determinant (an awkward, but computable formula involving only the coefficients of the equations in a s..
|
|
Last week, I was invited to do a coding dojo for the Java user group in Bergen. I chose a format that let people work more independently rather than the classical style of “lots of people passing the keyboard around and looking on the code on a projector”. The result was an informal, competitive and engaged workshop where people continued playing with the exercise long after the official program was over.
|
|
The Web as a Graph The goal of this post is to assign an “importance score” $ x_i \in [0,1]$ to each of a set of web pages indexed $ v_i$ in a way that consistently captures our idea of which websites are likely to be important. But before we can extract information from the structure of the internet, we need to have a mathematical description of that structure. Enter graph theory.
|
|
The Web as a Graph The goal of this post is to assign an “importance score” $ x_i \in [0,1]$ to each of a set of web pages indexed $ v_i$ in a way that consistently captures our idea of which websites are likely to be important. But before we can extract information from the structure of the internet, we need to have a mathematical description of that structure. Enter graph theory.
|
|
The Web as a Graph The goal of this post is to assign an “importance score” $ x_i \in [0,1]$ to each of a set of web pages indexed $ v_i$ in a way that consistently captures our idea of which websites are likely to be important. But before we can extract information from the structure of the internet, we need to have a mathematical description of that structure. Enter graph theory.
|