Collegemath

We found 17 articles

How to solve (almost) any math problem
Math is all about problems -- questions for which you don’t currently know the answer -- and problems can be really frustrating. That feeling of being stuck, for me, goes from a scattered confusion to a mind-numbing blankness. It’s really easy to shut down and give up, so the first step to solving any math problem is to persist! Don’t let the ...
Einstein’s proof of E = mc^2
In this post, we’re going to prove the most famous formula in all of science, E = mc^2! We’ll do this using a simplified version of Einstein’s original 1905 proof. In this post I will assume that you are familiar with special relativity and Lorentz transformations.
Can you “hear” the Fourier Series on a guitar?
As a musician, I had always wondered why different instruments sound dis tinct from one another, despite being in-tune and playing the same note. Why is it so easy to distinguish someone singing a C major scale versus someone playing the same scale on the piano? Timbre, tone color, or tone quality of a sound are those characteristics separate from ...
Slide rules, logarithms, and analog computers
Growing up, one of my favorite films was Studio Ghibli’s The Wind Rises—an animated historical drama about a 20th-century Japanese engineer named Jiro Horikoshi. Each time I rewatched it, I was always intrigued by a device that Jiro used for performing calculations. It consisted of two wooden rulers, with the top one able to slide freely. Somehow, ...
Think quickly: can you ace the world's shortest intelligence test?
Below is the world's shortest intelligence test. See how many questions you can answer!
Calculating flood risk using probability and statistics
If at some point you ever want to buy property near water, a variation of this question will undoubtedly pass through your head: what are the chances that my {insert name of your expensive piece of property close to water} floods?
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.
Introductory statistics: are my data normal?
Statistics is fun, I promise! But before we can start having all the fun, it is important to describe the distribution of our data. We will need to handle problems differently depending on the distribution.
What is implicit differentiation and how does it work?
One topic that seemed a bit mysterious and magic to me when I first learned calculus was implicit differentiation. In this post, we’ll start by reviewing some examples of implicit differentiation and then discuss why implicit differentiation works.
How to survive a proof-based math class
Probably the most common challenge that I see my students struggle with is understanding and writing out mathematical proofs. Although most higher-level college math and computer science courses rely heavily on proofs, there aren’t many courses that really prepare students before they’re thrown off the deep end. I wanted to discuss some tips and ...
Which is bigger?: Set cardinality, injective functions, and bijections
Comparing finite set sizes, or cardinalities, is one of the first things we learn how to do in math. From a young age, we can answer questions like “Do you see more dogs or cats?” Your reasoning might sound like this: There are four dogs and two cats, and four is more than two, so there are more dogs than cats. In other words, the set of dogs is ...
The key to mastering mathematics? Quit memorizing.
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. 
An introduction to proofs: the structure of induction
  Induction.  It's a mathematical concept that is no doubt familiar to any student taking an introductory proof class.  It is also a concept that can bring complex feelings---the excitement of learning a new cool proof technique, the fear of being asked to prove something "obvious", or the confusion of where to start.  
Revolving curves to make solids
Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?
topicTopics
academics study skills MCAT medical school admissions SAT expository writing college admissions English MD/PhD admissions GRE GMAT LSAT chemistry writing strategy math physics ACT biology language learning test anxiety graduate admissions law school admissions MBA admissions interview prep homework help creative writing AP exams MD study schedules summer activities history personal statements academic advice career advice premed philosophy secondary applications Common Application computer science organic chemistry ESL PSAT economics grammar test prep admissions coaching law statistics & probability supplements psychology SSAT covid-19 legal studies 1L CARS logic games reading comprehension Spanish USMLE calculus dental admissions parents research Latin engineering verbal reasoning DAT excel mathematics political science French Linguistics Tutoring Approaches chinese DO MBA coursework Social Advocacy academic integrity case coaching classics diversity statement genetics geometry kinematics medical school skills IB exams ISEE MD/PhD programs PhD admissions algebra astrophysics athletics biochemistry business business skills careers data science letters of recommendation mental health mentorship quantitative reasoning social sciences software engineering trigonometry work and activities 2L 3L Academic Interest Anki EMT English literature FlexMed Fourier Series Greek Italian Pythagorean Theorem STEM Sentence Correction Zoom algorithms amino acids analysis essay architecture argumentative writing art history artificial intelligence cantonese capacitors capital markets cell biology central limit theorem chemical engineering chromatography climate change clinical experience cold emails community service constitutional law curriculum dental school distance learning enrichment european history finance first generation student fun facts functions gap year harmonics health policy history of medicine history of science information sessions institutional actions integrated reasoning intern international students internships investing investment banking logic mandarin chinese mba meiosis mitosis music music theory neurology operating systems phrase structure rules plagiarism poetry pre-dental presentations proofs pseudocode school selection simple linear regression sociology software study abroad teaching tech industry transfer typology units virtual interviews writing circles