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Within all of our cells, we have millions of proteins, nucleic acids, lipids, and carbohydrates serving various biological functions. Many of these molecules have structure which play key roles in understanding how the mechanisms of those biological functions work. Scientists who study structural biology seek to determine the structure of these ...
These three words are enough to strike fear into the heart of even the most intrepid anatomy, pre-clinical, or clinical student. There’s so many nerves, some in front and some behind, some looping around – it’s easy to get tripped up trying to make sense of this complex structure.
One of the most important equations in econometrics – and in economics in general – is the equation for omitted-variable bias. This simple equation is a powerful tool for reasoning about the ways in which correlations we see in the data may differ from the causal relationships we care about. In this post, we'll begin by learning exactly what the ...
Picture this - you’re at a car dealership and you’re eager to purchase your first car. You settle on a brand new Honda Civic, and your representative asks: sedan or hatchback?
You have your paper topic, maybe you even have a thesis statement ready to go. But before you can charge into the depths of the writing process, you’ve got put together your bibliography. In some cases, this part seems easy: you’re already familiar with the scholars who work on the topic; your instructor has given you a list of sources; or you are ...
This is a blog post about understanding linear maps and a special number associated to them called the determinant. A linear map f from Rn (n-dimensional Euclidian space) to Rm (m-dimensional Euclidian space) is any map which satisfies the following properties:
I’ve taught expository writing in the Ivy League for several years now, and one of the most common problems I see is student papers that overstate their argument. Fortunately, there’s an easy way to fix this issue—a trick that makes pretty much all argumentative claims much more convincing.
The unit circle is a handy tool that can help students learn the trigonometric values, sine, cosine, and tangent, of certain angles (30°, 45°, and their multiples) that the math “Powers-That-Be” have determined to be important. Unfortunately, for a lot of students, the unit circle can feel like tedious rote memorization with unfamiliar numbers ...
The mention of mathematics often evokes mixed emotions among biologists. While some embrace it as a powerful tool, most merely view it as a black box for their collaborators to navigate for them or as intimidating and unrelated to their study. However, as a Biology PhD student, I firmly believe that math is not scary and an essential and ...
Intermolecular forces (IMFs) are “electrostatic” interactions between molecules – a result of all the charges floating around and interacting in the system. IMFs influence the properties of substances that we can observe and interact with – for example, the phase of the substance or its boiling point.
The first Shakespearean play that I had to read in school was A Midsummer Night’s Dream; I was in eighth grade. I found the kooky language insurmountable, and, truthfully, thought the plays were pretty boring. These challenges continued year after year, as we moved on to Romeo and Juliet, Macbeth, Hamlet, and more. In short, I hated ...
Truss Analysis was the first engineering concept I learned at Cornell. It involves the Balance of Force and Moments, and can be quite confusing at first. I will break it down into a couple of steps that you can apply to every Truss you see!
In my experience as an instructor and teaching assistant at the University of Washington, I have worked with many students who are biology or chemistry majors desperately trying to stay afloat in introductory physics. They describe the experience as a painful one and feel their hard work does not pay off. If you feel similarly, the good news is ...
Competition in nature is relentless. Predation, famine, disease, and disaster all threaten to prevent individuals from reproducing. In this competitive environment, mutations that make survival more likely are more likely to appear in future generations, and mutations that make survival less likely probably won’t stick around in the population for ...
Looking back after almost thirty years of using science to build new technologies and companies, I realize that learning science in college could have been much more efficient and enjoyable for me. I spent almost all my time focused on details of how to do the coursework (to balance an equation, to get the right answer, to figure out what was ...
Revision is an essential part of the writing process, but it can feel daunting. You’ve toiled over ideas, finally gotten words onto the page, and now you need to revise. This step can seem overwhelming, especially if you’re pressed for time or tired of looking at the same draft.
Potential energy can be easy to understand, tricky to define, and confusing to use. Here, we not only define potential energy, but explain what it means, why physicists use it, how physicists calculate it, and examine why potential energy is only associated with certain types of forces.
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 ...
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 ...
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:
Are you ever nostalgic of the days of long division? Or annoyed that a tape measure makes determining the dimensions of a new couch so simple?
The beginning of the school year is an exciting and slightly overwhelming time during college. Start off your science classes right with these tips for effective note-taking and studying techniques!
Imagine sitting in a car and pressing the gas. You can tell you're moving since you feel the car's acceleration and see things moving around you. Once you're traveling at a constant velocity, you no longer feel the acceleration but see the outside world moving around you.
Some writing anxiety is inevitable and even useful. But if your anxiety is keeping you from producing your best work, try the strategies below to improve your writing process.
There are very few among us who haven’t seen or heard of electric vehicles (EVs). When thinking of EVs, what comes to mind might range from wishing for a stylish Tesla to wondering how anyone could put up with so little range and charging infrastructure. However, it’s tough to have an academically informed opinion when so much information comes ...
Many if not most humanities papers, essays, and articles require that you make a scholarly intervention into an academic conversation. The nature of this intervention varies: if you are doing advanced research, it will be expected that you have read other criticism on the text(s) or object(s) under consideration and respond to a body of criticism ...
Fictitious forces such as the centrifugal force are fake forces – they don’t really exist! However, fictitious forces are helpful when working in non-inertial reference frames (a fancy term for reference frames that are accelerating, like when we use the rotating Earth as a reference frame). In these frames, F = ma doesn’t hold, and you’ll need to ...
If you’ve taken a high school physics class, you probably started by learning about position, velocity, and acceleration, ubiquitous concepts in physics that are also well-motivated by our daily life experiences. But soon after that, the course probably moved on to less familiar concepts, such as energy and simple harmonic oscillation modeled by ...
If you've clicked on this blog, you must be captivated by the beauty of relativity, quantum mechanics, dark matter, or black holes. Now, you're eager to delve deeper into these subjects. Maybe this moment just happened recently or a few years ago. Regardless, you want to get paid to study nature and attempt to describe it using mathematics. As I ...
Escape velocity is the speed an object needs to escape the gravitational influence of another object. Here, we explain escape velocity, derive the right equation, and discuss what this equation does (and doesn’t tell us) about how objects actually move in space. For example, how fast would you have to throw a tennis ball for it to fly off into ...
All you’ll need for this project is a computer that can run Python, 30 hours of free time, and an 18-foot aperture parabolic antenna.
The dreaded weed-out class. A pre-med’s worst nightmare. Students often approach organic chemistry with apprehension, and a particularly sore spot in the class is mechanisms. Arrows, electrons, charges, and structures all drawn out like a map. Now, make that 10 maps – or 20! What’s a pre-med to do?
One thing I wish I had learned as an undergraduate (who geeked out on medieval lit) was how to find and read facsimiles of original manuscripts. The Internet is a treasure trove of public works, with classic, canonical, and contemporary literature available in html or as PDFs. This is awesome. It meant I could teach a survey course of British ...
So, you’ve finished the first draft of an essay, paper, short story, or personal statement! You’ve done the first hardest part: sitting down and putting pen to paper. But writing, like any other creative pursuit, is “10% inspiration and 90% perspiration.” In other words, the first draft is just a start. Revising is where the real work happens.
Poetry can try the patience of even the most willing of readers. John Milton’s extended similes mysteriously belabor seemingly arbitrary comparisons; T.S. Eliot’s famously infuriating footnotes obscure more than they reveal; and Lyn Hejinian’s non-sequitur-fueled “sonnets” boggle the mind, refusing sense and logic at every turn. If you’ve ever ...
If we had to pick one go-to answer to explain as many things as possible in biochemistry, it would probably be “the hydrophobic effect.” It’s responsible for protein structure and function, cell membrane organization, and the distribution of drugs and metabolites. It’s often an important consideration in drug design. But what is it, and how does ...
Have you ever wondered how our brains work? Our every thought, every emotion, and every movement are generated by our brain through a vast network of cells called neurons. Neurons make connections and talk to each other through electrical signals called action potentials.
Among the most important topics covered in any college-level microeconomics course is that of how to solve constrained optimization problems, which involve maximizing or minimizing the value of some objective function – such as a utility or cost function – subject to one or more constraints – such as a budget or production target. Although these ...
While you might not think about it very often, gases are everywhere around us, from the air you breathe to the natural gas you might use to heat your home. To use gases safely and effectively, chemists use the ideal gas law to understand how much gas is in containers and pipes.
On October 21st, 2004, the International Human Genome Sequencing Consortium published a near-complete draft of the human genome, a 100 million dollar initiative to understand the genetics of our species. By 2022, the cost to sequence the human genome neared $1000. This drastic price reduction has led to new advancements in understanding cellular ...
When I first started studying biology, I thought the discipline was mostly about memorizing facts and figures about different organisms and their characteristics. In high school, I was more interested in physics and chemistry, which seemed to involve learning general principles and laws that could be applied to many problems. In other words, I ...
There’s nothing quite like the feeling of dread that settles in the pit of your stomach when you sit down in front of yet another blank Google Doc with a paper due at midnight. You might even tell yourself you’re not getting the grades you want because you’re just not good at writing.
“One Oreo McFlurry, please.” I hand the cashier my card, take the receipt, and then wait. “Pull up to Window 3, sir, to get your order.” Stretching out in front of me are four windows in a series, one after the other, after the other. But I can't get to the third window without waiting for the car at window two to finish. The system is inane. ...
You may have the best proposal to present to a Principal Investigator at a T1 research institution. You may have drafted a fascinating schematic imagining a new building for an architecture program. Your work is solid but you need to connect with others outside of your narrow field to show how your proposal engages a wider audience. What can you ...
You started your electricity and magnetism course and now all you hear about are potentials, potential energies, fields, and forces. It’s overwhelming. The purpose of this post is to help you understand each of these quantities and how they are related.
Acid-base chemistry is a fundamental unit in orgo that provides a platform for many of the other reactions you’ll learn about throughout the semester. Not only that, it’ll follow you to many other classes (like biochem and inorganic chem). If you’re still puzzling over what acids and bases even are, let’s take a minute to get everything straight. ...
For those who are not naturally math inclined, the first exposure to economics can be daunting. With a little extra work, those of us with a math aversion can grow fond of the subject. I employed some of the following strategies to get the most out of my economics courses and share them with the hope that they will help you too.
Students are expected to think and write with greater sophistication, specificity, and self-direction as they get older. This can be a stumbling block for writers used to receiving topics from instructors. One day, instead of a general prompt, you’re handed an unfamiliar novel and asked to determine your own line of research and argument. It’s ...
Before we consider how computers play chess, let’s talk about how humans do it.
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?
Arguably one of the most important topics you will learn in your organic chemistry course, resonance is something that seems like it makes absolutely no sense upon first glance. What does it mean, why should I care about it, and how do I use this information to supplement my understanding of organic chemistry at large? All great questions!
Writing, in all forms it takes, can be very scary. This is because writing is hard! If you’re anything like me, you may also worry about what others will think of your writing. It’s inevitable that some people won’t like or agree with what you say, but what you can do is make sure that your writing is as foolproof as possible. You’ve probably ...
Whenever I tell people what I’m studying in grad school, they seem pleased for a moment, but it doesn’t take long for them to look totally perplexed. It’s as if I told them I study gopher economies.
One of the things that makes art history such an interesting analytical discipline is that it examines both the anthropological and creative value of an artwork. Artworks are historical objects that can give us insight into the culture of a particular place and time. Yet artworks also transcend their time and place through their creativity, ...
I wouldn’t be surprised if you’ve heard the word “quantum” before. It’s a real buzzword: “quantum computing,” “quantum gravity,” “quantum information,” “quantum entanglement”. But what is quantum mechanics, really? My goal in this post is to give you intuition for what quantum mechanics is, where you can find it in real life, and why it’s so ...
In school, we devote time and energy to learning many different skills, in many different subject areas. Some of these skills may feel more relevant than others. A student who dreams of becoming an artist may bemoan the hours spent calculating derivatives in Algebra, while a future chemist might wonder why she should bother with Social Studies’ ...
Reading is a fundamental mode of communication and therefore a prerequisite of active participation in today’s world. There are two components to reading: decoding and comprehension. Decoding refers to understanding the relationship between letters and sounds, otherwise known as phonics; comprehension refers to a student’s ability to make sense of ...
The advantage in fuel economy that comes from driving a hybrid-electric car instead of a non-hybrid has not one major contributing factor, but three. Even if you don’t drive a plug-in hybrid, these innovations drastically improve the vehicle’s efficiency using clever applications of physics and optimization.
Computer science is a major with some of the most varied outcomes for their students. Computer science majors will go on to be professors, software engineers, hardware engineers, machine learning engineers and data scientists. A good computer science program will provide introductory coursework that offers glimpses into each of these various ...
You can stare at or redraw the pathway for glycolysis to memorize it, but obtaining a deeper understanding of cellular and tissue metabolism requires an understanding of the regulatory mechanisms governing glycolysis. Below you can find a figure of the steps for glycolysis as a reference as we discuss the regulation.
The time has come. You are past the introductory chapters of your organic chemistry class and now must dive into one of the hard parts: synthesis problems. These types of questions can be intimidating at first because they rely on your knowledge of a variety of reactions and can be like little puzzles. However, there is no need to be scared. By ...
For most of us, entering a new environment or learning a new topic can really shake up our usual routines. Maybe your high school study habits just aren’t working for college courses, or your AP class is way more intense than expected. You might find yourself treading water to keep afloat while fighting the ever-growing burden of a large workload ...
Before dive in, here are a few things that will hopefully make the whole process of writing a thesis a bit less stressful. First of all, it’s important to remember that your thesis will change throughout the writing process and that’s perfectly fine (even good!). Second, your thesis doesn’t have to be just one sentence; two, or even three, ...
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.
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 ...
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 ...
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 ...
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.
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. ...
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.
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 ...
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 ...
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 ...
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 ...
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:
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?
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 ...
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 ...
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.
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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.
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.
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 ...
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 (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 ...
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, ...
One of the most common grammatical pitfalls students encounter when writing essays and personal statements is the dangling modifier.
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.
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?
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 ...
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 ...
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, ...
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 ...
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 ...
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?
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 ...
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!
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 ...
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.
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 ...
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.
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 ...
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 ...
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 ...
Below is the world's shortest intelligence test. See how many questions you can answer!
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!
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!
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.
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 ...
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 ...
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 ...
Consider the following questions:
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 ...
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?
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.
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.
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 ...
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 ...
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 ...
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 ...
“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 ...
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:
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 ...
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.
Ray diagrams can look intimidating, but they don’t have to be! In this blog post, we will tackle five examples of ray diagrams.
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.
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.
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 ...
“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?
Learning Chinese is challenging but fun! Even the parts that require repetitive practice can be enjoyable with the right framework and point-of-view.
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 ...
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.
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 ...
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.
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 ...
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 ...
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 ...
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 ...
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?
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.
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.
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!
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 ...
Formal charge is the charge that a bonded atom would have if its bonding electrons were shared equally. Note:
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 that ...
“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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.
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.
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 ...
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 ...
If you haven't read Part 1 of this blog, please do so now.
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.
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 ...
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 ...
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:
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.
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 ...
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.
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 ...
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 ...
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 ...
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 ...
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 of ...
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, ...
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 ...
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 ...
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!