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Years ago, while working on an explanation of the Fourier Transform, I found this diagram: (source) Argh! Why aren't more math concepts introduced this way? Most ideas aren't inherently confusing, but their technical description can be (e.g., reading sheet music vs. hearing the song.) My learning strategy is to find what actually helps when learning a concept, and do more of it. Not the stodgy des
The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s the formula: Years to double = 72 / Interest Rate This formula is useful for financial estimates and understanding the nature of compound interest. Examples: At 6% interest, your money takes 72/6 or 12 years to double. To double your money in 1
This is a realistic learning plan for Calculus based on the ADEPT method. I have a few minutes for Calculus, what can I learn? 1 minute: The Big Aha! Level 1: Appreciation Calculus is the art of splitting patterns apart (X-rays, derivatives) and gluing patterns together (Time-lapses, integrals). Sometimes we can cleverly re-arrange the pattern to find a new insight. A circle can be split into ring
The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations: Yikes. Rather than jumping into the symbols, let's experience the key idea firsthand. Here's a plain-English metaphor: What does the Fourier Transform do? Given a smoothie, it finds the recipe. How? Run the smoothie through filters to extract each ingredient. Why? Recipes are ea
Despite two linear algebra classes, my knowledge consisted of “Matrices, determinants, eigen something something”. Why? Well, let’s try this course format: Name the course Linear Algebra but focus on things called matrices and vectors Teach concepts like Row/Column order with mnemonics instead of explaining the reasoning Favor abstract examples (2d vectors! 3d vectors!) and avoid real-world topics
I’ve been on a web tweaking kick lately: how to speed up your javascript, gzip files with your server, and know how to set up caching. But the reason is simple: site performance is a feature. For web sites, speed may be feature #1. Users hate waiting, we get frustrated by buffering videos and pages that pop together as images slowly load. It’s a jarring (aka bad) user experience. Time invested in
Git is a fast, flexible but challenging distributed version control system. Before jumping in: Understand regular version control Understand distributed version control Along with a book, tutorial and cheatsheet, here are the insights that helped git click. There's a staging area! Git has a staging area. Git has a staging area!!! Yowza, did this ever confuse me. There's both a repo ("object databa
Here’s a collection of time-saving math shortcuts, great for back-of-the-envelope estimates. Time and Distance 60 mph = 1 mile per minute Going 60 mph and the exit is in 10 miles? That’s 10 minutes. Been driving a half hour? That’s about 30 miles at highway speeds. Feet Per Second = MPH * 1.5 MPH = Feet Per Second * 2/3 (derivation) 60 mph is about 90 feet per second (88 exactly), so just multiply
Compression is a simple, effective way to save bandwidth and speed up your site. I hesitated when recommending gzip compression when speeding up your javascript because of problems in older browsers. But it’s the 21st century. Most of my traffic comes from modern browsers, and quite frankly, most of my users are fairly tech-savvy. I don’t want to slow everyone else down because somebody is chuggin
Browser buttons (bookmarklets) are shortcuts that act like a simple browser plugin. Their advantages include: Fast installation: Just add a link to your bookmarks Convenient: Use features while on your current page Easy to write: Bookmarklets are just like making a webpage; there’s no need to write a whole browser plugin Cross-browser: The same bookmarklet can work in IE, Firefox, Opera and Safari
Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference: I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method: Learning isn’t about memorizing facts to pass a test. It’s about unlocking the joy of discovery when an idea fi
Traditional version control helps you backup, track and synchronize files. Distributed version control makes it easy to share changes. Done right, you can get the best of both worlds: simple merging and centralized releases. Distributed? What’s wrong with regular version control? Nothing — read a visual guide to version control if you want a quick refresher. Sure, some people will deride you for u
Version Control (aka Revision Control aka Source Control) lets you track your files over time. Why do you care? So when you mess up you can easily get back to a previous working version. You’ve probably cooked up your own version control system without realizing it had such a geeky name. Got any files like this? (Not these exact ones I hope). KalidAzadResumeOct2014.doc KalidAzadResumeMar2015.doc i
I’m glad people liked the introduction to Rails; now you scallawags get to avoid my headaches with the model-view-controller (MVC) pattern. This isn’t quite an intro to MVC, it’s a list of gotchas as you plod through MVC the first few times. Here’s the big picture as I understand it: The browser makes a request, such as http://mysite.com/video/show/15 The web server (mongrel, WEBrick, etc.) receiv
Ruby on Rails is an elegant, compact and fun way to build web applications. Unfortunately, many gotchas await the new programmer. Now that I have a few rails projects under my belt, here’s my shot at sparing you the suffering I experienced when first getting started. Tools: Just Get Them Here’s the tools you’ll need. Don’t read endless reviews trying to decide on the best one; start somewhere and
Javascript is becoming increasingly popular on websites, from loading dynamic data via AJAX to adding special effects to your page. Unfortunately, these features come at a price: you must often rely on heavy Javascript libraries that can add dozens or even hundreds of kilobytes to your page. Users hate waiting, so here are a few techniques you can use to trim down your sites. (Check out part 2 for
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