We found 62 articles

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 ...
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 ...
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.
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.
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 ...
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 ...
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 ...
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 ...
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’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: It is not an actual charge but rather a form electron book-keeping. The sum of formal charges should equal the compound’s actual charge.
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 ...
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 ...
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 ...
Guide to nuclear magnetic resonance spectroscopy (NMR) analysis: part 2
If you haven't read Part 1 of this blog, please do so now. How to Solve an 1H NMR Spectrum 1. Calculate the degrees of unsaturation (DOU). Calculate the DOU from the molecular formula, or the number of double bonds or rings. In order to solve an NMR spectrum, a molecular formula must be provided. If not, only generalities can be determined about ...
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: 
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 ...
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 ...
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 ...
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. ...
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 ...
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.
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.
Which college literature classes should I take?
  Congratulations! You’ve gotten to college, and now you never have to read another book in your life! But that’s exactly the opposite of what books can do for you in college. Instead of a book being something you have to read, think about college literature classes as your opportunity to get to read. Whether or not you’re a humanities major, odds ...
Converting Polar to Cartesian Equations in Five Easy Steps
If polar equations have you second-guessing your future as a nuclear physicist, fret not!  Almost every pre-calculus student I have tutored has struggled here, and it isn’t surprising at all.  Remember the first time you saw an equation and were introduced to these strange x and y variables?  It may seem like second nature now, but you were ...
An introduction to the branches of linguistics
Many students start college with no idea what linguistics is, and it’s possible they won’t even brush past it throughout their entire college career. Today, I’ll demystify and explain exactly what linguistics is and hopefully encourage you to at least take an introductory class! When I tell people that I'm doing a PhD in linguistics, there are ...
The ambiguous case of the law of sines explained
Trigonometry should be simple—you’re just using the given information to solve for only one answer, right? Well, with the Law of Sines, sometimes there is more than one right answer. This situation is also known as the Ambiguous Case.  Before we dive into the Ambiguous Case, let’s review the Law of Sines and Congruence.
A guide to deciphering chemistry arrows
Chemistry is confusing enough with IUPAC nomenclature procedures to know, and the difference between E/Z and cis/trans alkene descriptions, and so many other new terms, models, units, and symbols. But the most common and important symbol in chemistry is the arrow.
The basics of retrosynthesis
People often dismiss organic chemistry as “all memorization”. I disagree – organic chemistry is just a series puzzles based on a few basic concepts (electronics, sterics, orbitals) that come together to answer almost any problem you might encounter on your homework or tests.
What are heuristics? Representative vs. availability heuristics
One topic that many of my psychology tutoring students get confused about is the topic of heuristics, which comes up when they study judgment and decision-making.
How to read and interpret economic graphs
Learning to think like an economist can be a daunting task for beginners. Introductory economics courses often begin with a jargon-loaded discussion of opportunity costs and marginal benefits versus marginal costs—in other words, what is the benefit of continuing to read the rest of this post, and what else could you be doing with your time?  In ...
How to tell if a bond is inter- or intra-
As you go over the material in your chemistry course or your SAT/AP test prep, you most certainly spend a lot of time learning about bonds—what they are, how they differ, how strong they are, and so forth.  Also, you have probably read about them being classified into intramolecular bonds and intermolecular bonds.  During my many one-on-one ...
How to remember the steps of photosynthesis
Over the years, I have tutored many students studying for the AP biology exam and I have noticed that the majority of them find photosynthesis and cellular respiration very difficult and confusing. These are very important processes that frequently appear on the AP exam. However, there is so much information, so much detail, and so many terms, ...
What is love of wisdom in philosophy?
The word “philosophy” comes to us from ancient Greek and means “love of wisdom”.  Someone who pursues philosophy, then, was supposed to be someone who was seeking the attainment of wisdom.  What is wisdom, though, and what is it to love wisdom?
Evocative vs explicative language
We’ve all been subjected to that lecture in middle school Language Arts class about the differences between “showing” and “telling” with our writing—about the stylistic separation between providing sensory details around a piece of information and just stating that piece of information outright. In the context of seventh-grade compositions, this ...
How to identify unknown solutions in a chemistry lab
One of the most common general chemistry lab experiments, both in advanced high school classes as well as introductory college courses, is the identification of a series of unknown chemicals.  As a chemistry tutor, I am well equipped to break it down for you.