Mathematical induction is a common and very powerful proof technique. At its core, it’s an appeal to an intuitive notion that Induction proofs often pop up in computer science to proof that an algorithm works as intended (correctness) and that is runs in a particular amount of time (complexity). In this tutorial we’ll break down a classic induction problem in mathematics, and in the next post we’ll apply the same techniques to a classic computer science problem. As a warmup we can look at a classic example used to teach induction, namely the proof that the sum of integers from 1 to n is equal toRead More
Preparing for both mathematics sections on the SAT can be a bit intimidating. You can’t expect yourself to know every topic that might come up, and the time limit adds to the stress. Much more efficient than trying to learn everything you might come across is to start with what you have already learned in high school and use examples to apply it more widely in the SAT. The most classic sort of example is what teachers have been drilling for ages: plug in numbers. However, mathematics is all about generalizing rules and strategies, so I want to talk about how to expand plugging in numbers to the art of creating your own examples.Read More
There are many misconceptions when it comes to the subject of mathematics. One of the most common myths I encounter is related to the way one approaches learning math.Read More
How do you feel about math?
Let’s take a minute to think about math and how we feel about it. Good memories or bad? Or both? If I were to draw an analogy about math and anything else, it would be a foreign language. You can’t forget what you learned in arithmetic and expect to do well in algebra, just like you can’t forget how to conjugate French verbs and expect to write a full sentence. Math requires a great foundation and, once that foundation is built, everything else comes after. I am here to help you build that foundation. I am here to tell you that math isn’t supposed to be scary or cryptic or over your head and I’m not just saying this because I am a tutor, I am saying this because I have been there, staring at a problem and blanking, putting the pencil down, getting scared, when another second spent ‘braving the storm’ made all the difference.Read More
Step 0 – Make Sure the product makes sense!
Say we’re given two matrices A and B, whereRead More
Are you looking to present college admissions committees with a competitive application for programs in engineering, science, math, finance, or economics? Math is a basis for all of these subjects, and demonstrating mastery in math can really help your applications. By coupling high scores on the SAT or ACT math section, SAT Math Level 2 Subject Test, and an AP math exam, you can bolster your portfolio to impress colleges. In this blog post, we’ll specifically focus on the Math Level 2 SAT Subject Test, and discuss ways to improve your score and go into the exam room feeling confident.Read More
Whether you’re applying to a university with strict test requirements or you’d like to showcase your unique academic strengths on college applications, scoring well on the SAT Subject Tests can really help in the college admissions process. In this blog series, I’ll discuss some tips unique to individual Subject Tests in a variety of areas. This first post is on the Math Level 1 Subject Test, so let’s begin!Read More
It’s a Tuesday night, and you’ve just remembered that you have a huge algebra 2 test tomorrow. Panic starts to sweep over you as you think back on all you’ve learned this semester. How will you ever succeed? You call up your friend to ask how you can study, and he calmly tells you he has just spent about an hour reviewing the main concepts from the unit, and he feels confident about the test. The question, then, is what is his secret?Read More
There is a humorous, misguided stigma associated with math. Just the mere utterance of the word “math” conjures up, for many, the image of intimidating, arcane equations strewn about blackboards and calculators gone on the fritz. For many, math was a painful experience in grade school (and beyond) -- myself included! In fact, I did not become interested in pursuing a math major until my sophomore year of college. The purpose of this post is not to philosophize on the state of mathematics curriculum in America’s schools, but rather, to explain how I eventually saw meaning beneath the seemingly endless exercises.Read More
SAT, ACT, SSAT, ISEE, GRE. What do these acronyms all have in common? Well, they’re all standardized tests, but more importantly, they all have multiple-choice math test sections. Despite whether or not they’re accurate indicators of student performance in the classroom, lab, or office, they are all essential for entry into some educational career path. So whether you want to be a lawyer or you want to get into a STEM-focused private high school, it helps to do well in a standardized, timed math test to get there.Read More