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A Pragmatic Introduction to Signal Processing
A retirement project created and maintained by Tom O'Haver , Professor Emeritus , Department of Chemistry and Biochemistry
New
The latest blog posts to take off on Hacker News. 213 posts.
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The scrypt parameters
The recommended scrypt parameters in the Go docs were recently brought up for discussion given they haven’t changed since 2009.
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Learning from Scratch by Thinking Fast and Slow
Reinforcement Learning
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Colorized Math Equations
Years ago, while working on an explanation of the Fourier Transform, I found this diagram: Most ideas aren't inherently confusing, but their technical…
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Algorithmic Solution to My Insomnia
I’ve struggled with insomnia for all of my adult life. It began in college and has waxed and waned in severity ever since, correlating with stress levels…
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The strange story of “Extended Random”
Yesterday, David Benjamin posted a pretty esoteric note on the IETF’s TLS mailing list. At a superficial level, the post describes some seizure-inducingly boring flaws in older Canon printers…
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A Zero-Math Introduction to Markov Chain Monte Carlo Methods
For many of us, Bayesian statistics is voodoo magic at best, or completely subjective nonsense at worst. Among the trademarks of the…
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Simulating Chutes and Ladders in Python
Edit 12/19/2017: added a new subsection on analyzing Chutes & Ladders as an Absorbing Markov Chain.
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The ABC conjecture has still not been proved
Five years ago, Cathy O’Neil laid out a perfectly cogent case for why the (at that point recent) claims by Shinichi Mochizuki should not (yet) be regarded as constituting a proof of the ABC conjecture. I have nothing further to add on the sociological aspects of mathematics discussed in that post, but I just wanted to…
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Stats without Tears (2016)
Printer Friendly: The whole text in one file , all 164,000 words, convenient for printing. (The printed length will vary, depending to your browser settings. For me it’s 401 pages.)
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Gerrymandering with geographically compact districts
The following tweet has been making the rounds on social media: Notice that since the Democrats won overall, it would be impossible for Republicans to win all seven districts, no matter how the map…
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What are the complex numbers, really?
Where did complex numbers come from? You might think that people invented \(i\) just so that they had a solution to the quadratic equat...
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Modes, Medians and Means: A Unifying Perspective
Introduction / Warning Link to heading Any traditional introductory statistics course will teach students the definitions of modes, medians and means. But, because introductory courses can’t assume that students have much mathematical maturity, the close relationship between these three summary statistics can’t be…
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Matrices from a geometric perspective
Graphics is all about geometry. In particular, there are points that have a certain color, and the pattern of colors gives you a certain picture. You can change the way the points are distributed by applying certain transformations like translation (movement), rotation and scaling. While most people familiar with the…
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Understanding LSTM Networks (2015)
Humans don’t start their thinking from scratch every second. As you read this essay, you understand each word based on your understanding of previous words. You don’t throw everything away and start thinking from scratch again. Your thoughts have persistence.
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Statistics, we have a problem
Recently, while browsing Twitter, I saw a few machine learning researchers post about an incident at one of their big conferences (NIPS) in…
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Three-Valued Logic
Making decision despite missing SQL data (NULL): How to avoid OR…IS NULL in the WHERE clause.
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Using loaded dice to cheat at Settlers of Catan, and p-values to avoid suspicion
My copy of Settlers of Catan came with two normal wooden dice. To load these dice, I placed them in a small plate of water overnight, leaving the 6 side exposed.
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Communicating Advanced Mathematics to Kids
I’ve often thought that we could do a lot better job of explaining “advanced” mathematics concepts in simple language for the benefit of a wider audience. As a student, I never liked being told, “We’ll explain that to you next year.” As a teacher, I’ve always wanted be able to give real answers to students’…
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How to Read Mathematics
Ranked a top 100 research university, VCU is a place where discovery and creativity go hand in hand. Located in downtown Richmond, Virginia, its more than 200 programs emphasize hands-on learning, creativity and engaging in the world around us.
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The Mathematics of 2048: Counting States by Exhaustive Enumeration
How many board configurations are there in the game of 2048? Let's try to enumerate them.
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Down with Determinants (1995)
This paper was published in the American Mathematical Monthly 102 (1995), 139-154.
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Connections between Abstract Algebra and High School Algebra (2015)
by Erin Baldinger, University of Minnesota; Shawn Broderick, Keene State College; Eileen Murray, Montclair State University; Nick Wasserman, Columbia University; and Diana White, Contributing Editor , University of Colorado Denver.
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Andrew Wiles on the struggle and beauty of mathematics
Roger Highfield explores the beauty of mathematics at a recent event at the Science Museum
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Building a Regex Engine in Fewer Than 40 Lines of Code
A blog about programming and modern web development, particularly Node.js and React
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Theoretical Machine Learning Lecture Series: Deep Learning and Cognition
Deep learning, which is the reemergence of artificial neural networks, has recently succeeded as an approach towards artificial intelligence. In many fields, including computational linguistics, deep learning approaches have largely displaced earlier machine learning approaches, due to the superior performance they…
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Deep image prior 'learns' on just one image
Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is…