Mathematics

We found 14 articles

How to self-study mathematics
Mathematics is a topic that is notoriously difficult to learn on one’s own. Sadly, this often causes people to think they’re not “math people” or that learning mathematics perhaps isn’t for them. In the contrary, I think that learning math is something that is accessible to everyone, but requires a different approach from reading a novel, or ...
A brief introduction to the infinite
Set theory is the branch of mathematics that studies the infinite. The discipline was founded by Georg Cantor in the late 1800s. Cantor is responsible for many of the notions we discuss here. A set, according to Cantor, is a collection of definite, distinguishable objects conceived as a whole. A set consists of its elements. There is exactly one ...
Motivating matrices: why do we care about linear maps?
If you’re reading this, you probably already know what a matrix is. But just to be clear, a matrix is a rectangular array of numbers. Here is an example:
Solving systems of equations by graphing (even after Algebra 1)
When learning about lines in Algebra 1, you likely learned how to solve a system of (linear) equations, such as the following, by graphing:
How to think like a mathematician
Behind every mathematician is a beautiful mind: one that has been forged through years of critical thinking. Their minds are molded by countless failed attempts at solving problems and refined by the exposure to remarkable ideas explored along a lifetime of learning. How can we train our minds to see the world more like mathematicians do? The map ...
Making mistakes in math class
Learning math often feels like it’s all about right or wrong, like success or failure are the only two possible options and that all of your math expertise is visible as soon as you take a test. What I experienced as a student studying math and now as a math teacher is that this couldn’t be further from the truth. Some of my greatest learning ...
A math puzzle (for fun!)
I'm going to introduce you to my favorite math puzzle. It's a doozy, and I hope you'll find it as intriguing as I do. And maybe a bit more intuitive than I did when I first encountered it.
The magic of induction
What is the sum of the first n positive integers? Phrased mathematically: 1 + 2 + 3 … + n -1 + n = ?. The answer, it turns out, is n * (n + 1) / 2. How do we show this is true though? How do we prove this?
How to approximate the value of pi
I always tell my students not to be afraid to ask why. In so many parts of our lives, we are asked to defend our opinions and ideas—to offer evidence and to explain our thinking or reasoning. But sometimes, it feels this is missing from math education, especially in middle school and high school. Math becomes about memorizing formulas rather than ...
How to prove the Pythagorean Theorem
The Pythagorean Theorem plays an essential role in many facets of math from Euclidean Geometry to complex numbers to trigonometry. Today we’ll explore one of its many proofs.
How to approach initial value word problems
We’ve all been there: on a homework set or in an exam, you turn to the final page and, to your dismay, it’s a wall of text. The dreaded Word Problem. Some of the words are useful, but some of them are meant to distract. Let’s look at a strategy for answering initial value word problems.
An introduction to enumeration using generating functions
In the year 1202, Italian mathematician Leonardo Fibonacci published the extremely influential Liber Abaci (Book of Calculations). The book's most significant contribution was to bring to Europe the Hindu-Arabic number system that we all use today. But it also contained a curious thought experiment about the reproductive patterns of rabbits, which ...
The math tutor: simplifying probability
Probability is one of those topics that haunt children from grade school days, asked to determine the likelihood of picking out red marbles from a box. Even my most advanced math tutoring students sometimes feel bamboozled by it. Why? Because probability and statistics can quickly become overwhelming with the many different distributions and ...
Standardized Test Math Mechanic: SAT geometry prep
I thought that it would be fun to tackle a geometry problem on today's post. I know what you're thinking, fun and geometry – can these two words even go in the same sentence? But yes, geometry can be fun; let's see as we work together through the details of a particular problem.
topicTopics
academics study skills MCAT medical school admissions SAT college admissions expository writing English MD/PhD admissions writing LSAT GMAT strategy GRE physics chemistry math biology graduate admissions ACT law school admissions interview prep test anxiety language learning academic advice MBA admissions premed personal statements homework help career advice AP exams creative writing MD study schedules Common Application summer activities test prep history computer science philosophy organic chemistry secondary applications supplements economics PSAT admissions coaching grammar mathematics research law statistics & probability psychology 1L ESL CARS SSAT covid-19 dental admissions legal studies logic games reading comprehension USMLE engineering Spanish calculus parents Latin verbal reasoning DAT PhD admissions case coaching excel mentorship political science AMCAS French Linguistics MBA coursework Tutoring Approaches academic integrity chinese medical school Anki DO English literature Social Advocacy admissions advice algebra astrophysics biochemistry business classics diversity statement genetics geometry kinematics mental health presentations quantitative reasoning skills study abroad time management work and activities IB exams ISEE MD/PhD programs STEM adjusting to college algorithms art history artificial intelligence athletics business skills careers cold emails data science functions gap year international students internships letters of recommendation logic mechanical engineering poetry resume science social sciences software engineering tech industry technical interviews trigonometry 2L 3L AAMC Academic Interest DMD EMT FlexMed Fourier Series Greek Health Professional Shortage Area Italian Lagrange multipliers London MD vs PhD MMI Montessori National Health Service Corps Pythagorean Theorem Python Sentence Correction Step 2 TMDSAS Taylor Series Zoom acids and bases amino acids analysis essay architecture argumentative writing art art and design schools art portfolios biomedicine brain teaser campus visits cantonese capacitors capital markets cell biology central limit theorem centrifugal force chemical engineering chess chromatography class participation climate change clinical experience community service constitutional law consulting cover letters curriculum dementia demonstrated interest dental school dimensional analysis distance learning electric engineering electricity and magnetism enrichment escape velocity european history executive function finance first generation student freewriting fun facts genomics graphing harmonics health policy history of medicine history of science hybrid vehicles hydrophobic effect ideal gas law induction infinite information sessions institutional actions integrated reasoning intern investing investment banking lab reports linear algebra linear maps mandarin chinese matrices mba medical physics meiosis microeconomics mitosis music music theory neurology neuroscience office hours operating systems organization pedagogy phrase structure rules plagiarism potential energy pre-dental proofs pseudocode psych/soc qualifying exams quantum mechanics relativity