academics

We found 191 articles

Clarifying summary, analysis, and synthesis
Many writing assignments in college, especially in the liberal arts, will require elements of both analysis and synthesis. Understanding the differences as well as the complementary relationship between these two moves will help you write stronger essays. 
The puzzle pieces of an argument
When learning about argumentative writing, my students regularly freeze. The terms claim, reasoning, evidence, and explanation all appear to be the same. They are unsure where to start and where to end. So let’s break it down together.
Three tips for writing a persuasive essay
At some point in your academic career, you’ll likely have to write an essay where you argue for or against a specific point of view. This may be for a standardized test or for a class you’re taking, and it’s important to always follow the directions that are specific to that assignment. Still, I’m going to offer some advice about writing ...
Capacitor confusion: basic pointers to salvage your sanity 
You have recently started to learn about electrical circuits, and even though the occasional, particularly tricky circuit still proves challenging to solve, you feel like you “get” what batteries and resistors are and are starting to grasp fundamental concepts such as voltage and current. Forever dedicated to your torture, your physics teacher ...
How to become a successful software engineer
The realm of software continues to evolve, as does the architecture within education to become a software engineer. While some experts come from various university programs in Computer Science, others break into the industry through boot camps or self-guided study programs. Unfortunately, not every program can cover every base, and as the field ...
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.
What are the soundness and completeness theorems in logic all about?
If you’re interested in logic, you’ve probably heard of the soundness and completeness theorems. They’re the first major results proved in a logic class. Their proofs can get messy and technical, especially the proof of completeness. What the theorems are really supposed to tell us and why it’s interesting often gets lost in all that technicality. ...
Simple linear regression: what you need to know for data science
Given the recent rise of big data, there continues to be growing interest in the field of data science. One of the most basic, yet most useful tools for a data scientist is the linear regression model. Let's walk through the basics behind simple linear regression—a statistical model used to study the relationship between two variables.
The value in understanding algorithms from a theoretical perspective
Computer science majors across many universities often dread their introduction to algorithms course, especially if it is proof-based. It can feel out of place compared to the rest of their classes that focus more on learning standard coding practices, the fundamentals of how computers work, or just generally courses that seem to directly prepare ...
Demystifying operating systems
I have tutored a great number of students in undergraduate operating systems. Personally, I enjoy the topic. My dissertation is in the field of distributed systems. Distributed systems is an academic offspring of operating systems research where partial failures are expected and allowed. The operating systems course is almost universally taught ...
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 ...
Units: the hints hidden in every physics and engineering problem
In many science and engineering classes, units can be seen as an additional step that needs to be taken into consideration when completing a problem. In some problems on the Fundamental Engineering exam, mismatched units are intentionally used in an attempt to confuse students and measure their understanding of key concepts. Nonetheless, units ...
5 weird moments in European history
Some people say “reality is stranger than fiction,” and throughout the course of human history, this has definitely been true. Here are just five of those moments that were as strange – or stranger – than something you would find in books or on tv:
How to study for Chinese dictation quizzes
听写 (dictations) have been used to evaluate how much effort students put into learning Chinese. Dictation often tests vocabulary memorization. How do you study/prepare for 听写 effectively? Do you spend hours of writing characters? Have you experienced cramming with flashcards, only found that you forget everything on the day of the quiz? 
An introduction to phrase structure rules and word order typology
Fluent speakers of any language will have intuitions on what word order sounds "natural" or "correct", but languages differ in what order they put words in. Linguists (specifically syntacticians) are interested in figuring out what ways languages can differ in how they organize sentences, as well as how they are similar. In this blogpost I will ...
How to ethically use WolframAlpha, Mathway, and Photomath
As a middle school and high school math teacher, I’ve seen my students try to get out of doing work in all sorts of ways. If you haven’t heard of WolframAlpha, Mathway, or Photomath, you may want to stop reading this article now - the temptation may ruin your hard-work ethic.
Understanding the central limit theorem
The central limit theorem (CLT for short) is an enormously powerful tool that makes much of what we do in statistics possible. But if you just read the actual definition, which you can find below, it’s pretty hard to understand why this theorem is so important. This blog post will help you understand both what the CLT is and why it is important ...
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.
The dreaded “P” word
What’s the most dreaded letter that could appear on a transcript? I’ll wager that it’s not a “B,” or, gulp, a “C”, but a “P” as in “plagiarist.” In fact, if Hester Prynne were a 21st century student, instead of the protagonist of Nathaniel Hawthorne’s 19th century novel The Scarlet Letter, she’d probably be less concerned about having the letter ...
Suitcases and schedule scrapes: “packing” more punch into limited study time
In his book, Outliers, Malcolm Gladwell lays out criterion that in some ways has become the anecdotal darling of pop-academic culture. You’ve likely heard of it: the 10,000-hour rule. Mastery, Gladwell purports, is a matter of numbers. Put 10,000 hours of focused practice, and you can achieve mastery of a complex set of skills. Imagine the ...
Succeeding as a STEM major
So you’ve decided to major in STEM. Congrats! If you haven’t already, you’re probably going to hear all about how there are certain courses that are absolutely horrible in your major, whether they’re meant as weed-outs, taught by, well, let’s call them distant professors, or just plain hard. This post is meant to give you a few tips for how to ...
Good writers start as good readers
Writing is a conversation. Whether you anticipate your audience to be a friend, a panel of scientists, a room full of legislators, the owner of a pizza shop, the divine universe, or oneself, to write is to put forth one’s wish to be heard. By extension, to read is to be in the position of the listener. Just as we learn to speak and to express ...
Linkage and association mapping in genetic analysis
When geneticists want to see how closely related two genes are, they have two main ways of doing so: linkage analysis and association mapping. 
Why medical students should care about the history of medicine
It’s undeniable that medicine and science have transformed our world. From novel therapeutics that combat various diseases, new technologies that allow us to better understand how our bodies function, to transformative surgical interventions. Yet, often, since we know that medicine and science “work”, we fail to interrogate and challenge the ...
Where ideas come from
A lot of people who sit down to write a story are worried they don’t have any ideas. They think people who do have ideas are very special, or different in some way to people who don’t. It’s for this reason that authors are so often asked where they get their ideas from. The people asking think that the author will reveal the magical secret of ...
How to tell the difference between mitosis and meiosis
If you’ve ever taken a biology class, you’ve most likely come across the concept of the cell cycle. Put simply, the cell cycle is the growth of cells, the replication of DNA, and the subsequent division of DNA, organelles, and cytoplasm that creates new cells. For eukaryotes, cell division is an essential part of both growth and reproduction. ...
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 ...
To ask or not to ask? That should NEVER be the question
My family often refers to me as “the questionnaire” because I am constantly peppering people with questions during all of our conversations. What can I say? I spent four years as both an English literature student at Bates College and a reporter/editor for my college newspaper. I simply always have questions to ask of myself and those around me. ...
Pseudocode: a must-use tool for Computer Science
My number one piece of advice for someone entering college and studying computer science is the following sentence: write pseudocode before writing your actual code. If you follow this piece of advice, you will save yourself hundreds of hours over the next four years of your life.
Why I chose neurology
According to the Association of American Medical Colleges (AAMC) database, there are between 2,000 and 3,000 future neurologists looking to specialize in neurology each year. So what exactly does a neurologist do? How do you become one, and why should you consider becoming one?
How to use an outline to your advantage when you’re writing
How often do you start writing an essay with a great idea in mind, only to lose steam—or worse, lose track of your argument—well before you meet the length requirement? Have you ever reread a paper draft only to realize what you’re arguing on the first page isn’t quite the same thing you’re arguing on the last one? These sorts of problems are ...
Introduction to Functions
You’ve made it through algebra: now it is time to start talking about functions. While functions are often used to make upper-level mathematics easier to understand, they can be confusing at first. So – what is a function? How do functions relate to the algebraic equations we have used before? And how do they help us with mathematics and computer ...
How to succeed in college-level history courses
Success in college-level history courses requires that students develop a specific set of habits and practices, few of which are ever clearly spelled out by history instructors. While this is not an exhaustive list, the following paragraphs offer a few tips to help you get the most out of your history courses and excel while you are at it.
It’s time to rethink your note-taking strategy
During your time in school, you may have encountered the following scenario. After a long day of in-class learning, you have to muster the energy to complete homework assignments. With darkness falling, you have to prioritize these assignments, beginning with the most pressing. Once you’ve gotten through that punishing problem set and polished ...
The beauty of a reverse outline
Are you having trouble organizing your thoughts for an essay in your Humanities class or for an application? Have you tried outlining before writing only to feel defeated before you even get started? Do you struggle with editing a paper you’re sick of looking at, one that you know has some gaps that need to be addressed? Look no further than your ...
Artificial Intelligence: breaking ground or repeating the past's mistakes?
Artificial Intelligence (AI) has become embedded in nearly every aspect of our lives. The purchases we make, the people we virtually connect with, even the mechanisms to unlock our phones (if the phone was made in the last four years) are all influenced by AI. That said, should there be a limit to what parts of our lives AI touches? Moreover, how ...
Data science in risk management: value-at-risk and expected shortfall
Have you just started your investment journey and wondered how much to invest? Did you follow promising strategies but still see your account in red? Are you worried about the risk that you cannot foresee in your holdings? If you are nodding along these questions, know that you are not alone. In fact, these are what professionals like quants, ...
How to identify and avoid dangling modifiers
One of the most common grammatical pitfalls students encounter when writing essays and personal statements is the dangling modifier.
A brief primer on the secretory pathway
The secretory pathway is arguably one of the most important pathways in the body. It deemed ‘Secretory’ primarily because it’s the pathway that controls how the cell secretes proteins int extracellular environment.
Computer science buzzwords explained
Computer science can be intimidating! Especially when people use lingo you aren’t familiar with. The goal of this blog post is to help you start understanding some of the computer science buzzwords.
Chromatography: purifying your understanding
Maybe you were studying for the MCAT or just in your college chemistry lab when it dawned on you: why are there so many different types of chromatography? What do they have in common and what are their differences? 
How to communicate better: unlocking language’s hidden meanings
We all know that language is a powerful tool for communication. Sometimes it can be surprising how much meaning is conveyed in the shortest of sentences. Language is composed not only of the direct meaning of the words used, but also of many additional layers of meaning that arise through prior knowledge, background information, word choice, and ...
5 easy steps to good writing
Great chefs don’t cook wonderful meals on the first try. They’ve been in the kitchen for many sessions trying things out before they put a dish on the table. Writers need to do this too. Plan, practice, and prepare for the writing project you have in front of you. Break it into manageable chunks of about 2-3 hours each. These chunks need to be ...
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, ...
Why I love teaching English
“I’m not good at writing.” “I don’t really like reading.” “I don’t think of myself as a writer.” “Why do I need to learn how to write? I’m going to study engineering!” 
Why I love teaching Spanish
In the spring of 2020, when we were all locked down due to the pandemic and feeling cooped up and anxious, I got an email that lifted my spirits. It was from a former student who wrote to thank me for writing him a letter of recommendation for an internship with his local congresswoman that led to a job after graduation. He revealed something that ...
What I love about psychology
I have always been fascinated by human emotions and behaviors, as well as the unique ways in which we interact with ourselves, others, and the world. I initially learned about a field that addresses these very phenomena—that is, the field of psychology —when I was in high school. However, I didn’t consider it as a possible career path until ...
What I love about history
It’s not uncommon for people to find history the most boring subject in school. It often gets a bad rap in popular culture, too. In Harry Potter, for example, the History of Magic teacher, Professor Binns, drones on and on and frequently puts his students to sleep with boring lectures about arcane material. When I tell people I study history, they ...
What I love about physics
What if I told you that there’s a way to describe the waves of the ocean, the winds in the skies, the motions of celestial bodies — almost everything around us — and harness that information to create great things? This tool does exist, and it’s a science so fundamental that its principles guide our understanding of everything from microbes to ...
How to streamline a draft
One way to make sure your writing is clear (beyond writing "good sentences") is to take a look at the content of your paragraphs. The technique I'm going to detail in this post is perfect for a first draft, but can be used for final drafts too. I like to use this method when I need to cut some words to make a paper shorter, or before and after a ...
How to plan and organize historical research
Designing and executing historical research for a short essay, seminar paper, or thesis can be daunting. How do you find a primary research question, and how do you know which sources will help you answer this question? How do you read and take notes on sources once you've found them?
How to ask for feedback that will actually improve your writing
We’ve all received feedback on our writing that just wasn’t very useful. Maybe you wrote a paper for class and received back a list of grammar and spelling mistakes that you’ll never look at again. Maybe you showed your personal statement to three different people and were confused when you received three contradictory pieces of advice for ...
Tips for studying biology
I am often asked the question, “Brooke how do you study for biology?” We know to use practice problems to study for physics, or pathway diagrams for chemistry, but biology is different: it is a lot of memorizations!
Working out your brain
My first day in the gym was intimidating. I always thought the gym wasn’t for me, and so I had tried to avoid it as much as I could. I remember feeling slightly embarrassed as I picked up the smallest weights in the gym with my slender arms. However, overtime I was able to pick up heavier weights and noticed that my arms were slowly filling up the ...
What’s the difference between stiff, strong, and tough?
Though the average person might think the words stiff, strong, and tough mean the same thing, engineers know that they in fact have very different meanings. Learning the difference between these terms will help you sound like a pro when discussing material properties. 
The role of insurance and common threats in health insurance markets
Growing up, the GEICO Gecko and Allstate’s Mayhem were frequent fixtures of TV nights with my family. “15 minutes could save you 15% or more on car insurance” and “You’re in good hands” were slogans I knew for as long as I could remember. Clearly, the services these companies were selling – different types of insurance – were marketed as taking ...
How to solve an empirical formula problem
In this blog post, we will review how to determine the empirical formula of a compound using the mass percentages of the elements from which it is formed.
Quantum numbers
In this blog post, we explore the four quantum numbers, which allow us to describe the properties of each electron within an atom. According to the Pauli Exclusion Principle, no two electrons can share the same combination of quantum numbers. A carbon atom has six electrons, for example, and each of these electrons can be described by one of six ...
A painless introduction to VSEPR theory
Today we will discuss VSEPR (pronounced “vesper”), which stands for valence-shell electron-pair repulsion. The basis of VSEPR is that the electrons in bonds and lone pairs repel each other. To minimize the instability that results from these repulsions, a molecule will adopt the shape that places electron groups as far apart as possible. VSEPR ...
A language study routine that actually works
So you're studying a new language, and you've been told that you need to make time to review and study vocabulary regularly. That makes sense. You tell yourself you'll do it. You may even make some flashcards and spend time drilling them two or three times early in the semester when you are full of good intentions. But if you're like me, the ...
How to read legal statutes like a lawyer
Legal statutes can be a daunting task. Statutes are filled with legalese, numerical codes, and several headers that can make you feel stuck in a labyrinth of law. However, have no fear! Following these simple steps can turn that labyrinth of written statutes into a nice roadmap and summary of any legal statute. 
So you want to be an engineer...but don’t have a degree in engineering
I was getting my degree in environmental science, at a school without an engineering program, when I realized I wanted to be an engineer. Engineering first called to me in Cambodia, home to the magnificent Angkor Wat complex of temples. The Angkor people constructed a series of motes and irrigation systems at a scale that rivals that of many ...
Tips for success in organic chemistry courses
Organic chemistry is historically considered a “weed-out” class for pre-medical students and often the cause of much frustration for students. After spending 3 years during college serving as a teaching assistant and tutor for organic chemistry courses at my undergraduate university, here are some tips for studying for your organic chemistry ...
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!
Ask the right questions: how to know what you don't know you don't know
Have an assignment due tomorrow, and have no idea where to even start? In office hours or class and so lost that you don't even know what your question is? No matter the context of your confusion, you're not alone! 
The finals crunch: a roadmap to working smarter, not harder
It’s the end of term, and your grade comes down to just one score: the final exam. On top of that, you’ve got a whole term’s worth of material to review! Fret not — we’ve all been there. Here’s how to make the best of it!  
Reading is hard. But it doesn’t have to be.
There is no denying it. In the age of the attention economy, bright stimulating screens, and exhausting schedules it is very hard to sit down and read with focus. Whether we are talking about a novel for English class, a source for AP U.S. History, or that dense SAT Reading passage from the Federalist Papers, it is hard to truly dig in and read ...
Tips for getting a 4.0 in engineering
College is intimidating enough as is without overworking yourself in pursuit of a perfect GPA. However, if you have decided that graduating with a 4.0 is a top priority for you, here are some tips that helped me achieve a 4.0 in engineering.
What makes a good descriptor?
Cliche is natural; originality, not so much. Pre-packaged phrases like “bring to the table,” “at the end of the day,” or “read between the lines” are overused and now lack their meaning, becoming a kind of automatic thinking, according to George Orwell. But why? Because triggering automatic thinking in a listener is helpful to a speaker if he or ...
How to balance redox reactions in acidic and basic solutions
Balancing redox reactions is an essential skill for the Chemical and Physical Foundations section of the MCAT, the GRE Chemistry Subject Test, and the AP Chemistry Exam. Today, we will learn how to use the half-cell method for balancing redox reactions in acidic and basic solutions. We will first balance a redox reaction in acidic solution, then ...
Top grammar errors to avoid
Throughout the years I’ve spent reading and writing, I’ve seen my fair share of grammar errors. But few are peskier, or more pervasive, than the two I’ll discuss in this post. So common are these two grammar errors that I regularly encounter them in professional writing — sometimes even in articles by full-blown professors! These two errors often ...
Hormones of the female reproductive system
The female reproductive system can at times feel like a difficult jumble of hormones that all seem to be related, but fluctuate in unpredictable ways. To make sense of the particularities of the female reproductive system, especially for exams like the MCAT, it is important to not only know what hormones are involved, but also to understand what ...
Gametogenesis and spermatogenesis and oogenesis, oh my!
Meiosis is one of those processes that we all learned about in high school biology as a deceptively simple concept. You take the diploid cell, divide it twice, and it becomes four haploid gametes that are each capable of participating in fertilization. Easy, right?
How to use root words to learn vocabulary
Retaining new English vocabulary is challenging, whether you’re learning English for the first time or studying for standardized tests like the SAT or GRE. The challenge arises, in part, from the sheer volume of words in English. English’s massive lexicon comes from words in several other languages, and learning some of these words—more often ...
The Intermediate Value Theorem explained by everyday life
Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.
What I learned about the writing process from bread baking
Working from home means I can adapt myself to the capricious schedule of bread making. Dough waits for no one (and it will not rise more quickly if prodded!). I’ve loved baking since childhood, but I discovered bread more recently.
S’more fun: simplifying limiting reactants using chocolate
Stoichiometry: it’s the bane of many chemistry students’ studies. It’s so easy to get tangled up in a jumble of numbers without any idea of what’s actually going on.
Tips for success as a third-year medical student (MS3)
Clinical clerkships can be some of the most exciting times of medical school, but they can also be some of the most frustrating. Academic medicine tends to be very hierarchical, making it difficult for students to advocate for their own learning. Residents are often busy and stressed. Asking questions is often disincentivized – shouldn’t you just ...
How to make sure you don’t fall behind during distance learning
Let’s be real: it’s hard to focus on school at home. And as COVID-19 cases persist and online learning remains part of our lives, it is important to not fall behind. Here are some tips to help you stay on top of your work while learning from home:
Pituitary gland hormones made simple
What is the pituitary gland? Even though the pituitary gland is about the size of a pea, it plays a very important role in regulating a lot of our body’s endocrine functions. Located in an area known as the sella turcica at the base of the brain and suspended from the hypothalamus by a stalk, the pituitary gland consists of two parts: the ...
The middle school writers’ workshop: 3 steps to a great literary essay outline
Writing literary essays can be scary. Learning how to analyze texts through writing is one of the most challenging but fundamental skills that you’ll need in your academic career. Particularly for younger students, this task can be daunting. However, if you follow a few simple steps, it doesn’t have to be!
How to write more clearly in six steps
Whether you’re writing a medical school admissions essay, a high school book report, a college research paper, or a personal statement for graduate school, clarity is key. But writing clearly is trickier than it looks. In my ten years of experience as a writing teacher and tutor, I’ve found that there are a few steps that students can take to more ...
Understanding a confusion matrix
One of the major tasks in machine learning and statistical testing is classification. In classification problems, we use a training set of labeled data to train our model to classify an unlabeled observation into one category or another. At the simplest level, this method uses observable data to make a related yes-or-no classification (like: will ...
Five quick and easy English words to elevate your writing
Anyone studying English will at one point or another recognize that the language is quite a hodgepodge. Centuries of outside contact – from Viking and Norman invasions to importations of Latin during the Renaissance – led to what would become the rich vocabulary of Modern English. But what should a savvy writer do with so much variation when ...
Explaining eight common Chinese idioms (“chéngyǔ”)
“Chéngyǔ” (成语) are Chinese idioms that usually occur in groups of four characters and often originate from old fables in classical Chinese writing. As a testament to China’s long history and rich culture, chéngyǔ have persisted as a fundamental component of modern Chinese language in both formal writing and in everyday language. There are over ...
Six ways to brainstorm more effectively
At its core, writing is about discovering relationships between words and ideas. Your brainstorming process can and should reflect that central goal from the very beginning of the writing process. Here are a series of investigative approaches to help you expose and explore these relationships:
I just want to be a doctor, so does organic chemistry really matter?
Imagine: you’ve made it through your first semester or two of undergrad and weathered all the storms that come with this transition. And, now you find yourself facing a dreaded academic giant that has stricken fear in the hearts of scores of pre-medical students. A chemistry course unlike any other. If you are anything like most pre-medical ...
A beginner’s guide to analyzing historical documents
Most high school and college-level history courses will require that you read, interpret, and analyze a document or set of documents from the past—otherwise known as primary sources. In this post, I will provide five basic questions that you should ask about your document(s) that will kickstart your thinking about the past and serve as a starting ...
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.
Working with lenses and mirrors: how to draw a ray diagram
Ray diagrams can look intimidating, but they don’t have to be! In this blog post, we will tackle five examples of ray diagrams.
Statistical mediation and moderation in psychological research
One of the most commonly identified challenges in statistics for psychology is differentiating between mediation and moderation. Fully understanding these concepts can seem overwhelming, but it doesn’t have to be that way! All concepts that seem tricky can be broken down into simple, comprehendible steps.
Studying at home: how to keep up with work while learning online
In the early stages of the COVID-19 pandemic, most of us had to deal with the sudden reality that we could not go to school physically. We might have had have school content posted online or packets of work to complete, but we were likely not allowed to physically be at school with our teachers and classmates. We were, essentially, homeschooling.
Where do Taylor series come from and why do we learn about them?
Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by
But what is “dx” really? Calculus terms explained
The symbol “dx” comes up everywhere in calculus. For example:
Pareto efficient allocations and fairness in economics
A very important concept when it comes to thinking about markets in economics is the idea of Pareto efficiency. An allocation of resources is Pareto efficient if it is not possible to make anyone better off without making someone else worse off.
Two common grammatical mistakes to avoid in polished writing
There are no hard and fast rules in writing. But even if an experimental poet or an avant-garde novelist has dispensed with capitalization or written an entire novel without the letter E (yes, a novel like this really exists!), this does not mean that you need to follow suit. Your personal statement, for example, is not the place to defy the ...
Writing: knowing your audience
“Where do I even begin?” is probably the most common question students ask me about writing—and understandably so! Many writing projects can seem almost impossible to visualize, much less to get started on. So what to do when facing that blank screen?
The music of Mandarin: learning the five tones of the language
Learning Chinese is challenging but fun! Even the parts that require repetitive practice can be enjoyable with the right framework and point-of-view.
Learning the basics of Game Theory
Imagine that you and a friend are going to the movies. You like comedies more than action movies, while your friend likes action movies a lot more than comedies. If you go to see a movie alone, however, you’re probably not going to have as much fun, regardless of what type of movie you see. What is the optimal behavior for each person in this ...
Homonyms
English is one of the languages in which spelling is a big deal. Spelling bees were created in English, and the concept is not present in other languages in which words are more often pronounced just like they look. In English, we have words that are pronounced the same but have different meanings and spellings (homophones). We also have a lot of ...
Grammar: one to 1
When learning a new language, students almost always begin with the alphabet and numbers. We use letters, of course, to form words, which form sentences that express ideas of varying complexity in a form that people who read this written language can understand. Numbers designate a different kind of language, one that conveys equations and ...
Betwixt and between: difficult grammar rules explained
English is not the easiest language to learn. This may be because of the many exceptions to its rules or because the same combinations of letters can be pronounced in many different ways. English also has one of the largest vocabularies of any recorded language, which means English speakers can say what they mean in a lot of different ways, but ...
Checking your answers in physics
Having worked through a long physics problem, you finally have an answer. How do you know if it’s right and all that work wasn’t for naught? In this post, I will cover a few quick strategies that can help rule out wrong answers.
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 ...
An application of calculus: finding optimal road networks
Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.
Understanding elasticity of demand in economics
You may have heard in your econ class about a good’s elasticity of demand, or about “elastic” or “inelastic” goods. Consumers’ elasticity of demand is just a fancy way economists talk about how sensitive people are to changes in a good’s price.
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 ...
High school chemistry: What is it? Can I be good at it?
The word “chemistry” inspires so many emotions. To some, it brings about the excitement of mixing together glowing liquids and crafting the perfect radioactive potion that, when consumed, will turn you into the Incredible Hulk. To others, it’s discombobulated numbers and letters on a piece a paper in a classroom, a concatenation that strikes fear ...
What physics equation sheets can do for you, and what they  can’t
In your time taking physics courses, you will likely run into one that deals with equation sheets. These can be note cards or an entire sheet of paper, and anything that can fit on it is fair game and can be brought into a test. The natural reaction might be to try to cram and squeeze an entire textbook on those sheets using really, really tiny ...
So, what is chemical engineering for, anyway?
Chemical engineering is a comprehensive and vast field of study with far-reaching impact. I have been a practicing chemical engineer in the biotechnology industry for the last 5 years, and prior to that, I earned my doctorate in chemical engineering at the University of Wisconsin, Madison. Over the last 10 years, I have seen the evolution and ...
5 tips to improve your writing
I was recently helping someone with a comparative essay they had to write for school. This person did not like writing—a common enough state of affairs. They felt that they had no talent for it. The process frustrated them. I could see that they were struggling in part because they were trying to do everything at once (come up with ideas, write ...
How to write with clarity and brevity
1. Harshly criticize everything you write as you write it Ask yourself: is this sentence necessary? Could it be five words instead of ten without losing meaning? Is it a digression into something you find interesting useful, or a distraction?
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. 
Complex solution composition problems: knowing where to start
Thanksgiving dinner conversations can be uncomfortable… but solution composition problems don’t have to be! Recall that a solution is a homogenous mixture of two or more substances. Chemists have come up with many ways to describe the composition of a solution. Some ways are more appropriate than others depending on the situation. 
What is a thesis statement?
Every paper you write in college should have it. Sometimes professors call this a “thesis statement,” sometimes a “claim,” and sometimes they don’t really specify what it is. But it’s essential — and sometime elusive. But it shouldn’t be! 
A guide to limiting reactant problems... using sandwiches
An everyday limiting reactant problem You’re expecting company and totally forgot to go grocery shopping. What on earth will you feed your guests? Sandwiches! You have some ingredients to whip up some sandwiches. So, let’s assume you are going to go through with making these sandwiches. You need 2 slices of bread, 3 slices of meat (can’t be ...
Dimensional analysis: why the factor-label method is a lifesaver
Ever lost points on a test because you forgot to write the units? Rightfully so! Numbers have no meaning without their units of measurement. Two can be greater than 12. Three can equal one. This is all dependent on the unit of measurement being used. In your general chemistry class, you will encounter measurements of all sorts. These measurements ...
Electron configurations: a must know hack
Imagine this...you’re taking your general chemistry midterm and you’ve decided to shuffle through the exam and complete all the hard things first. You’ve totally underestimated how much time those problems were going to take you and now you have three minutes left to write the electron configuration of 10 elements. Untimed, this would be easy to ...
Formal charge: what they didn’t tell you in your chemistry class
Formal charge is the charge that a bonded atom would have if its bonding electrons were shared equally. Note:
Tips for writing an exam essay in 80 minutes
We've all been there.  The teacher is at the front of the classroom with a pile of blue books.  She begins handing them out.  You scrawl the name and date on the front and wait for her to start the timer.  As you open the first page, an overwhelming white page stares back at you.  And you panic. Luckily, there are ways to prepare for essay exams ...
3 ways to better analyze poetry
“Cikgu Tess!” “Pagi.” “Miss. Look lah.” “Alyaa—why?” “Girl’s bathroom,” she says. “Cikgu, you touch?” Our state has the highest concentration of venomous snakes in the region. “Is it poisonous?” I mime the action of being bitten (by my hand) and then dying. “Mm, don’t know.” In 2017, I taught ESL, literature, and political science at a rural ...
An introduction to supply and demand
What is supply and demand? In economics, supply and demand is the relationship between the quantity of a commodity that producers wish to sell at various prices and the quantity that consumers wish to buy.  Though it is a seemingly straightforward relationship, in practical application it can become quite complicated.  In this blog, we will use an ...
The physics of martial arts
As a practicing biomedical engineer and martial artist, I belong to two communities that, at a glance, seem to conflict with one another; engineering requires rigorous thought and thorough validation of proposed innovations, while martial arts focuses on sensing subtle body motions and quickly reacting to one’s environment. When I first became ...
How to make introductory physics exciting (when you're bored out of your mind)
Why do many students find physics so boring?  Cutting-edge physics research gets to address amazing, deep questions: "What is all the stuff in the Universe fundamentally made of?” and “Where did all this stuff come from anyway?” Yet college-level introductory physics courses on Newtonian mechanics can feel quite...mechanical. Why does introductory ...
The power of anecdote: creative strategies for academic writing
Many of the freshmen I instruct at CUNY enter the first few sessions of my Expository Writing class wearing metaphorical top hats and monocles, armed with—and comforted by—the five-paragraph essay structure and other basic compositional building blocks. College-level essay writing, in their understanding, requires a stuffy, exacting formality—a ...
An introduction to choice theory: are humans really 'rational actors?'
If you are a student of economics, one of the first axioms you are instructed to adapt is that everyone should be considered a “rational actor.” What this means is that all people who take part in economic decisions and transactions are informed by self-interest and do so in a manner that maximizes their potential self-benefit.  This is essential ...
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 ...
How to keep your middle schooler's backpack organized In 8 easy steps
Have you ever opened a middle schooler’s backpack to find a mess of papers, crushed pencils, and uneaten snacks? The emoji-themed folder that your child was so excited to pick out in the beginning of the year torn to shreds? The "math" section mysteriously also becoming the catch-all for notices about PTA potlucks, field trip reminders, and ...
3 surprising reasons why Social Science prepares you for medicine
One morning during winter break, as I was sitting on my couch with a mug of coffee in hand, I remember reveling to my mom: “It’s incredible how much majoring in anthropology kept on proving itself useful in medical school.  Who would have known?” In college, I chose to major in a social science, anthropology—surely the less traditional route for ...
Introduction to physics: the language of the universe
 In elementary and middle school, we learn mathematics for the sake of mathematics, we are never told what mathematics can ultimately be used for or why mathematics is useful other than the fact that it can help us make change and do our taxes one day. What they should be telling you is that the laws of the universe are written in a language that ...
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.  
How to write a killer essay in 3 easy steps
We’ve all been there: staring at a blank document, practically able to feel the creeping imminence of our paper’s deadline. For so many of us, it’s really hard to sit down and actually channel our thoughts into a coherent form, let alone one that’s structured and based on an argument worthy of praise.
What are lymphocytes? A guide to your immune system
The immune system is designed to prevent disease and fight infection and is critical for human survival. It specializes in the ability to attack foreign microorganisms, but what stops your immune system from eating you alive? Given that cells of the immune system can essentially eat microorganisms, you may be wondering what mechanisms are in place ...
Solving the “I’m not good at math” problem
You’ve heard it before. Or you’ve said it. I’m not good at math. I hear it from seventh graders struggling with fractions, high school students preparing to take the SAT, friends at a restaurant when splitting a check, and even from parents assuring me that their child’s own difficulties are in fact genetic. And while I’ve heard it countless ...
Orgo 2 strategies: “taking home” carboxylic acid derivatives
I’ve already covered how to easily manage carboxylic acid derivative formation and manipulation using the Reactivity Hill. Say we’re tired of whatever derivative we just created and want to bring the derivative back to its parent acid (the particular acid the derivative came from). There are two ways to “take home” any acid-derivative. We can ...
Golden rules to nuclear magnetic resonance spectroscopy (NMR) analysis: part 1
Nuclear magnetic resonance spectroscopy, or NMR, is a fundamental analytical technique used by chemists to determine the structure of organic compounds. Unlike other analytical techniques, such as infrared spectroscopy or mass spectroscopy, NMR allows for the complete interpretation of molecular structure and can be quantitative.
The top 3 reasons you should study Latin
There comes a moment in the careers of most middle- and high-schoolers learning Latin, and also among some college students considering it as a possibility when picking classes; a moment when they ask themselves (or their parents, or their teachers), “Why do I need to study this?”  After all, Latin is a dead language; unless you plan to become a ...
What is graduate level economics like?
  Is graduate level economics very different from undergraduate level economics? To many extents, undergraduate and graduate economics is similar, to many others very different. Their similarities reside in the fact that the core ideas and ways of approaching problems are the same. That is, because knowledge builds in layers, they share a common ...
How to solve kinematics problems: a guide to vectors
This article is the third chapter in a series on how to understand and approach kinematics problems. The first chapter covered position, velocity, and acceleration. The second chapter covered solving kinematics in one dimension Now we are going to take a quick detour into vectorland so that we’re ready to approach kinematics in two (and even ...
Two ways to determine equilibrium position in organic chemistry
A common exam question that comes up in both Orgo 1 and Orgo 2 requires students to determine a reaction’s equilibrium position. The question usually looks something like this: 
Orgo 1 strategies: finding and comparing alkene hydration products
We all know Orgo 1 professors love stereoisomers. Consider the equation A + B = C. Most professors expect you to fill in the question mark with all possible products and then indicate the major product(s), while other professors may provide you a potential C and then ask you if the statement is True or False.
How to get oriented to organic chemistry: 7 pillars of the course
Organic Chemistry (OChem or Orgo) seems like a scary course. But it should not be if you know what to expect. This road map is your guide to orientate yourself to Orgo1. It teaches you about the main topics covered in Orgo1 in the typical order they are taught in class. So, take a breath and sit back as you read, skim, or view the images that ...
How do enzymes work? Catalytic strategies and models of substrate fit
In this post, we are going to do a brief Q and A to review what enzymes do and how they work. This post will be slightly beyond a basic introduction so it is probably most appropriate for a student who already has a sense of what enzymes are.
Orgo 1 strategies: protocol for acid-base problems
  Determining which of two molecules is more acidic is tricky if you haven’t yet organized those factors that influence acidity. The protocol is a method I learned from my mastermind Orgo 2 professor to keep these ideas in order when they come into conflict. Namely: Size is more important than Electronegativity, which is more important than ...
What is the phospholipid bilayer and what determines its fluidity?
All cells are surrounded by a cell membrane that forms a barrier between the cell and its surroundings. This membrane is often referred to as the phospholipid bilayer. As you can probably tell from the name, a phospholipid bilayer is made up of two layers of lipids. The fluidity of this membrane must be maintained within a certain range for the ...
An introduction to blood types: genotype, phenotype, inheritance, transfusion, and more!
What determines blood type? Contained within their cell membranes, some red blood cells have special glycolipids called A and B glycolipids. People with blood type A have the A glycolipid in their cell membranes, people with blood type B have the B glycolipid in their cell membranes, and people with blood type AB, have both glycolipids in their ...
Why does English borrow so many words from other languages?
The Canadian blogger and free-lance reviewer James Nicoll created the following epigram on the English language: "English doesn't borrow from other languages. English follows other languages down dark alleys, knocks them over and goes through their pockets for loose grammar."
How to sketch any graph by eye
Equations in math are useful but they’re also kind of inefficient – for each x value, you have to do a separate calculation to figure out what y is. Graphs take that equation and turn it into a visual, something you can look at and immediately see what happens at different values of x, how the function changes, and more!
How do we classify mutations in biology?
In the previous post, we discussed some of the built in mechanisms that help to prevent mutations. Sometimes, however, mutations occur in spite of these systems. There are a few different ways that mutations are typically classified in an intro biology course and there are often overlaps between these categories. Here is a brief review of some of ...
What is moment and how do you calculate it?
When I tutor my physics students, I want them to understand the fundamentals of the concept, not just how to plug in numbers into an equation. I wished when I was learning physics, my teachers drew upon real life applications more, things we already understand about the world to help us really get it.
How to use probability trees to evaluate conditional probability
  If you’re majoring in economics, you will likely also need to take a statistics course.  One of the trickiest concepts is dealing with conditional probabilities.  In most classes, they teach you a fairly complicated equation known as Bayes’ Theorem. While this isn’t a hard formula to plug values into, it doesn’t give an intuitive understanding ...
5 key differences between American and British spelling conventions
Before America became a nation, the colonists who arrived to establish the country spoke English. From England. As there was not yet an authoritative source for how to spell words correctly in English, the colonists spoke English they were used to back home and wrote much the same way, using the way language was written in English literature as a ...
How to write an excellent history paper
I love the film Bill and Ted's Excellent Adventure and I've seen it more times than I can count. It is about two teenagers on the brink of failing high school, unless they ace their final history exam. The Hollywood twist? The protagonists acquire a time machine that allows them to travel through different eras of history. Throughout the film, ...
Four mathematicians you should know
Math has changed a lot over the years. When most people think of math, they likely think of someone sitting quietly at a desk with a book or some paper. It’s an unmoving image. When we think of people who are good at math, we conjure up people who blaze through problems quickly and alone. They follow the rules in math and in life. But this is a ...
Preventing and repairing DNA mistakes during the cell cycle
If you are currently studying biology, you have probably learned that mistakes in DNA can create very big problems, including cancer. These DNA errors often (but not always) occur during replication. Whenever they occur, it is very important for the cell to have a set of systems in place to both prevent and repair these errors. In this blog post, ...
Tips for interpreting pedigree charts and understanding inheritance patterns!
Different traits are inherited in different ways. Many intro biology classes will expect you to be able to identify different patterns of inheritance and parental genotypes based on either a pedigree or the rates of a given phenotype in the offspring. It is helpful to be familiar with the phenotype ratios, pedigree charts, and the specifics of the ...
How to solve kinematics problems, part 2
This article is the second chapter in a series on how to understand and approach kinematics problems. The first chapter covered position, velocity, and acceleration. Now that we understand these quantities, we are going to use them to solve problems in one dimension. 
Essential tips for learning the anterior pituitary hormones
Learning the anterior pituitary hormones for your biology class or the MCAT can be a little overwhelming. It is easy to get lost in the weeds and struggle to see how it all connects. One thing that helped me when I was learning the anterior pituitary hormones was to visualize the connections between the most important structures. This both helped ...
Don't actually 'break a leg': common English idioms explained
One of the recent lessons I gave to my English Language Learners involved English idioms and their origins. An idiom is a saying that does not mean what the words literally express, but rather it has some representative meaning behind the words. Often, the reasons for the meanings of idioms are obscure; in this post, I will try to bring to light a ...
Breaking down nephron functioning into six easy steps!
The nephron is the kidney’s smallest functional unit. It works to ensure that the urine you excrete leaves your body in the correct volume and concentration. This is a complicated process, but once you master it, it is exciting to understand this important function of the human body!
What is kinematics? Physics answers made simple
How to use this guide This blog post is the first in a series on how to understand and approach kinematics problems. It is meant to supplement your class and textbook. I will focus on practical applications, how to solve problems, and common mistakes that students make. If you want to learn the basics of kinematics, I recommend a textbook, but if ...
Marginal Rate of Substitution (MRS), Marginal Utility (MU), and how they relate
In this post, I start off by explaining the Marginal Rate of Substitution (Sections II-IV). Then, I cover the concept of Marginal Utility (Sections V-VII). In both cases, I start with a story explanation, then give a formal definition, and finally provide some other useful information about the concept. After that, I connect the two concepts ...
Back to the basics: past, present, and future tenses in English
As an English teacher and literature major in college, I am passionate about the English language. I am a self-identified stickler for grammar, and I will correct a text to a friend if I notice it lacks an apostrophe or contains an erroneous punctuation mark.
3 ways to implement teacher feedback to improve your work
Most of us know what it feels like to put significant effort into an assignment, and to have it returned with a barrage of red comments cascading down the pages, recommending innumerable changes for improvement. It can feel disheartening and frustrating – and sometimes dampens your motivation to want to try at all to work on a revision!
Tips and mnemonics for memorizing amino acid structures
Learning amino acid structures is a challenging part of biology and biochemistry coursework. Many students feel totally overwhelmed by the task. The best way to master this skill is lots of repetition (here is a link to a Sporcle quiz that may help you with the repetition part) but it can be helpful to have tricks and mnemonics to get you started. ...
Revolving curves to make solids
Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?
What is the subjunctive tense in English?
One grammar category that seems to be widely untaught is the names and functions of various verb tenses. For those who have studied a foreign language, the existence of these constructions is not so foreign, but native English speakers rarely learn what the subjunctive – in English – even is, let alone how to use it correctly. The same goes for ...
Turn back the clock on that grade! How to revise a bad college paper
After you receive your grade and read your professor’s comments, you might have a lot of those “if only” thoughts. “If only I had looked up that concept.” “If only I had taken extra time to proofread that.” “If only I had read the assignment more carefully.” “If only I had started earlier and done more research.” “If only I had realized I was ...
A list of common homophones and their differences
What is a Homophone? There are many more words in the English language than one might expect, given how similar their pronunciation and spelling can be. They're usually nouns and adjectives, except for those that function as conjunctions or contractions. Once you accept that English contains many pairs or groups of deceptively similar words with ...
4 tricks for solving any physics problem
Physics can be intimidating—all those pulleys and protons and projectile motion. If you approach it with the right mindset, however, even the hardest problems are usually easier than you think. When you come up against a tough question, don’t panic. Instead, start with these short, easy tricks to help you work through the problem. 
The most common English prefixes and their meanings
The English language comprises a plethora of words that can change meanings with the addition of a prefix or a suffix. For example, the prefix re signifies that the base word to which it attaches is happening again, as in "do" and "redo". In theory, one could add re an infinite number of times to the front of a word, and the effect would continue ...
Possessive plurals and plurals' possessives
Within the realm of punctuation, apostrophes on plurals and possessives can also lead to questions. There are patterns for forming plurals, though, and so that you do not have to wonder about when and where to put an apostrophe.
Three essential things to remember when citing parenthetically
For a lot of students, parenthetical citations may seem like the bane of their existence. You've just written a ten-page essay, you're happy with your argument and the conclusion you thought of in the middle of the night before it was due to submit, but you still have to check all the quotes. Especially in today's digital age, in which reading and ...
Five habits for improving and maintaining reading and writing skills
The first few months after my college graduation, I began my 9-5 job and was disappointed by how much less time I had to read.  After majoring in English and becoming accustomed to finishing multiple novels a week during the semester, I wished that I could dedicate more time to that pursuit.  Furthermore, after a few months of working forty-hour ...
The best ways to prepare for an essay exam
College students are often intimidated by essay exams, a common final exam format for courses in the humanities and social sciences. Because the exam itself provides so little structure for your answers, it can feel impossible to get all of your thoughts on paper in an organized way without running out of time. As someone who has graded a lot of ...
Physics: learn, don’t memorize!
Intro to Physics Blues    As a high school student, I took physics my junior year and struggled to stay afloat in the class. While I was interested in understanding and applying the theories I learned, it was difficult to make sense of them in my head. As a result, I began my first collegiate physics course with a lot of excitement, yet some ...
How to succeed in pre-med lab classes
Nearly all of the science pre-med requirements (intro bio, intro chem, org, physics, sometimes biochem) come with an associated lab class that counts either for a significant portion of your class grade or for an entirely separate grade listed on your transcript. It is just as important to succeed in these sections as it is in the exam portion of ...
How to use logarithms to simplify Arrhenius temperature dependence
  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 ...
How to study for AP Biology
When I was in high school, it was actually my AP Calculus teacher who gave me this AP Bio study tip. I used it with great success that year in AP Bio, and it continued to serve me well throughout college as I majored in molecular biology.
Choosing between AP and IB: an in-depth guide
I went to the International Academy (IA), which, for two years, was ranked the number one public high school in America by USA Today. As a metric, they used the number of IB or AP tests each student took.  My high school was an all IB school, one of the first in the country, and as an IB school, it required every student to take 6 IBs.
Five ways to reduce procrastination while studying or writing papers
  The night before every exam or paper deadline is always the same for me: Me: Why did I spend the last two weeks working on the opening sentence?! Roommate: Didn’t you also watch the entire first season of Game of Thrones? Me: For inspiration! Roommate: [Raises eyebrows] On rodent neurogenesis? Me: It’s ok—I have the rest of the night to work on ...
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