What is Spectral Geometry?

Posted by Isaac S on 4/5/17 9:00 AM

All shapes, from strings to bridges to carrots, resonate

You’re having breakfast in the kitchen when you start to hear a series of slow and repetitive thuds – someone is coming down the stairs. Without having to ask or look up, you can instinctively guess who it is. That’s because the cadence and volume of one’s footsteps is unique from person to person, depending in a significant way on the geometry of their gait and body structure. Of course, it isn’t too surprising to suggest that geometry and sound are interrelated; you can hear the difference between strings of different thicknesses and drums of different widths. The shapes of these instruments affect the frequencies they resonate at.

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Tags: math

What is a Limit, Anyways? Mathematical Concepts Explained

Posted by Abu on 3/15/17 5:59 PM

Let’s talk about a concept that can be confusing when you’re first studying calculus: limits. When you’re first introduced to limits, you’ll often hear your professor say things like,
What is the limit of f(x) =  as x approaches 5?

When worded like that, limits don’t sound very natural or intuitive – but in today’s post, I’m going to convince you that limits are a very natural way of looking at the world. I’ll also go over some examples of limits that we can solve without doing any “math” at all!

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Tags: math

How to Help Your Child with Math Homework: 5 Easy Questions You Can Ask

Posted by Meghan on 1/9/17 6:22 PM

If you’re the parent of a teenager, chances are good that a few years have passed since you had to graph a polynomial or find a derivative. Since high school math covers topics that people working outside of STEM don’t come across very often, many parents don’t feel like they can give much help to their teenage children with their math homework. But you’re an adult who solves problems every day! You have a lot to offer your teenage student about how to approach problems productively, utilize resources, and access their own abilities. 

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Tags: math, high school

Revolving Curves to Make Solids

Posted by Abu on 1/6/17 5:28 PM

Have you ever wondered where the formulas for volumes that you studied way back in geometry come from? It’s not too surprising that the volume of a cube is , but why is the volume of a cone ?

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Tags: math

Data Science and Intuitive Mathematics

Posted by Isaac Solomon on 5/13/16 9:30 AM

Sitting at the cross-roads of mathematics, statistics, and computer science, the emerging field of data science (ranked by many as the top career in the US) seems daunting to those still developing strong technical skills. At the same time, a host of dynamic and highly-efficient libraries give coders the power to treat complex areas like machine learning as a black box.

There is, however, middle ground: an intuitive understanding of mathematics that makes

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Tags: statistics & probability, math

Why logarithms are actually useful: Simplifying Arrhenius temperature dependence using log tricks

Posted by Patrick on 3/18/16 9:30 AM

Learning about logarithms is one of those times in math class where you wonder if this will ever be useful in any way. I see lots of students struggle with topics like logs, since they can seem abstract and they aren’t obviously useful. But I’m here to explain why they are actually incredibly important and describe so much of the world we live in! Let’s take a look at an example from chemistry and physics that shows just how powerful logs can be - the Arrhenius Equation.

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Tags: physics, math

Converting Polar to Cartesian Equations in Five Easy Steps

Posted by Maryam Amr on 8/12/15 11:00 AM

If polar equations have you second-guessing your future as a nuclear physicist, fret not!  Almost every Pre-Calculus student I have tutored has struggled here, and it isn’t surprising at all.  Remember the first time you saw an equation and were introduced to these strange x and y variables?  It may seem like second nature now, but you were learning about a whole new way to communicate about points and curves.  

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Tags: math SAT subject test, math

SAT Math Section Tips: Triangles

Posted by Tyler Lau on 8/7/15 11:00 AM

Triangles can be very different!

The SAT math section is full of triangles. They’re the most basic 2D shape that you can create and they can be found everywhere, so the SAT wants to make sure that you have the basic facts down pat. So let’s look at some tricks and facts about triangles. We’ll start by looking at the triangle below (not drawn to scale).

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Tags: math SAT subject test, SAT, math

The Ambiguous Case of the Law of Sines Explained

Posted by Maryam Amr on 7/27/15 10:30 AM


In math, art, or life, it's not hard for things to get ambiguous... [image source: Magritte]

Trigonometry should be simple-- you’re just using the given information to solve for only one answer, right? Well, with the Law of Sines, sometimes there is more than one right answer. This situation is also known as the Ambiguous Case.  Before we dive into the Ambiguous Case, let’s review the Law of Sines and Congruence.

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Tags: math

The Math Tutor: Simplifying Probability

Posted by Eriene Sidhom on 3/2/15 12:08 PM

Dungeons and Dragons is complicated. Mastering probability doesn’t have to be.

Probability is one of those topics that haunt children from grade school days of the determining the likelihood of picking out red marbles from a box. Even my most advanced math tutoring students in Cambridge sometimes feel bamboozled by it. Why? Because probability and statistics can quickly become overwhelming with the many different distributions and definitions.  The key is to find the underlying patterns and to stay organized.

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Tags: math