Hi there and welcome to my blog! This is my first post, with hopefully many to follow.
In my undergraduate years, I learned about a very curious summation discovered by the great Ramanujan. Since then, whenever a student tells me that they hate mathematics and that it is stupid, I show this to them and they almost always see math in a new
and enthusiastic light. Here, I will explain the series to you, and hope that it brings you as much excitement and curiousity as it first brought me.
Consider the series 1+2+3+4+5+6+... The series is simple, we simply add two to one, then add three, then four, then 5, and keep going forever. The series is called a "monotonic series", meaning that it is ever increasing. This should be intuitive, since
if we look at the first few terms, we have
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
If we continue the process,...
In recent months, I’ve felt the need, as one who has made a study of the laws of physics, to educate the general public and dispel myths that abound in society today.
Today, I’d like to talk about fans. This is a topic of great personal significance to me in that, growing up, my parents wouldn’t turn the air conditioning on unless the temperature inside the house got up into the 80’s (about 27-29 Celsius). Instead, we were
told to just turn the fan on. Knowing what I know now, I can say that that wasn’t the best of ideas.
To find out why I say that, let’s look at a fan from the standpoint of thermodynamics*. When you turn a fan on, you bring in a steady flow of energy into whatever room the fan occupies. Friction guarantees that, given enough time, all of this energy will be
turned into heat. What this means is that, unless the energy is allowed to escape, then it will just continue to build up, heating the room. The good news is that the electrical energy brought into...
Displacement is the distance between the starting position and final position. It is the change in position. This might seem easy enough but one thing about displacement is that it is the net change in position. Meaning it doesn't matter the path you took,
all that matters are the initial and final locations. So if you ran around a jogging track, and ended in the same place you started, your displacement would be 0.
Velocity tells us how fast an object is moving. It is described as the displacement divided by time. Going back to the track example, since your displacement is 0 in this situation, the average velocity would be zero. This is because velocity is a vector.
It has both magnitude and direction. Take the direction away and you only have magnitude, in this scenario that gives us speed. Speed is different that velocity in that it is a scalar, it has no direction, only magnitude.
Two types of studies that many people despise the most are Science and Mathematics. Some people cannot even stand to hear them mentioned. Truth is, whatever you are actually extremely good at, others may need some improvement. Although there are scientists
and mathematicians out there who are able to analyze and engineer scary and complex looking graphs and three-dimensional shapes and models, they do have some weaknesses. One of my weaknesses in academia is reading (especially when it is uninteresting to me).
I have struggled with reading for quite some time and there are times where I actually have to force myself to read, not because I can't do it, because I can. This is the same for many others, it's not that you do not like math/science, its just you were
taught to memorize it and not understand it. Back when you did adding and subtracting, math was pretty fun right? Well I am sure you will find science and more complex...
My favorite resources found online vary greatly, in regards to which subject help is needed in. For math intermediate level and down, math-drills.com and mathfactcafe.com can be very useful. Although I don't tutor in Physics currently, physicsclassroom.com
is a good online resource to help a student get kind of warmed up before learning a new lesson. For any elementary topics, greatschools.org/worksheets/elementary-school/ is a good resource. All of these are free and easily found. Also, simply typing in your
subject of interest followed by practice problems, can guide to a large exploration of online help 24/7.
I am studying stoichiometry with a student right now. It can be confusing sometimes to think about the two or three steps required to reach your final answer. We ran into a problem that required converting weight to moles of reactants, converting moles
of reactants to moles of product using mole ratio, converting moles of product back to weight, and then finally calculating the percent yield. Anybody can get lost in this soup. Take the time to write down the units at each and every step. If your units don't
add up, then you know that you didn't do the problem right.
When you're down and they're counting
When your secrets all found out
When your troubles take to mounting
When the map you have leads you to doubt
When there's no information
And the compass turns to nowhere that you know well
Let your units be your pilot
Let your units guide you
They will guide you well
Part of studying mathematics is accepting that we do not know all there is to know. Its possible, daily even, for our understanding of reality to be challenged or even changed. Think of how different our idea of the universe was 100 years ago. Think
of how different it could be in 100 years, even!
Rigor is something that is emphasized frequently in higher levels of mathematics and physics, and it has always been something that I appreciated. Unfortunately, with increased rigor often comes a decreased number of people who can understand an argument.
One pedagogical ploy that has been used to great effect has been to offer "proofs" of rather difficult concepts on the basis of certain tricks that are not themselves rigorous. I call these things "lazy proofs", and they suffer from the problem of leading to
outright contradictions and nonsense if taken to far. This kind of problem, usually, is swept under the rug by the person (usually a teacher) offering the proof in hopes that the misconceptions that could arise never rear their ugly head. Sometimes they never
do. Other times, they cause problems down the road.
One example of such a lazy proof is the following argument that the centripetal acceleration is
a = v2/r. ...
This blog post will discuss some of the physics behind the things molecules do – as gases, liquids, or solids – and also get you thinking about the concepts momentum, kinetic energy, rate (of a physical molecular-scale process), and equilibrium constant
(of a physical molecular-scale process). These may all sound like difficult, high-level ideas – but if molecules, which don’t have much in the line of brains, can act according to these ideas, you, with brains, can follow them too!
What are molecules? First, at their simplest, they’re just clusters of atoms stuck together in such a way that they don’t come apart on their own. (If they did, they would do so immediately; there’s no such thing as delayed disintegration, the way that isotopes
of some elements are radioactive.) Wait a minute, you say, what if I heat a pure substance and it breaks down? That happens when one molecule of the substance crashes into another molecule of the substance with enough energy to break at least...
Please check out my tutoring policies here:
Gerrit's Tutoring Policies (It's
very important that you read those!)
Here are some useful resources for help with physics problems:
Guide to solving problems.
Here is a helpful guide I created to illustrate from start to finish all of the steps involved to properly go about solving a physics problem. It outlines a tried-and-true proven method for approaching physics problems that is thorough, structured, simple,
and (most importantly) breaks down problems making them much easier to solve. Please adopt it, practice using it, and try to incorporate it into all of your future physics assignments; it
will make your life easier.
Steps to Solving Physics Problems
Comprehensive lists of high-school physics equations:
Official AP Physics Exam: Equations List
MCAT Physics Equations with Explanations
Here are some of my favorite Science resources. Check back again soon, this list is always growing! I also recommend school textbooks, your local library, and used bookstores.
(Gr. 9-12) CellsAlive.com – Learn about the life cycle of a cell, including reproduction, structure and live cell growth videos.
(Gr. 9-12) Zooniverse.com – A fabulous resource for science projects; you can even participate in someone else’s live science project (some are even from NASA). Focuses on astronomy, biology, and chemistry.
(Biology) KhanAcademy.org/science/biology – Tutorials and information on all things Biology related
(Biology) SpellingCity.com/biology.html – Provides a list of vocabulary terms typically seen in Biology courses
(Biology) Biology-online.org - Provides quick explanations of concepts, with examples
(Bio/Anat/Physics) BiologyCorner.com – Lessons, tutorials, definitions, and practice problems.
Now that finals have passed for most of the college students on the semester schedule, I'd like to reflect on the panic that arises when students in required introductory physical science classes come to the end of a course and realize that they haven't
retained anything! What is the correct approach to triaging such situations?
Of course, the best way to engage with material is by answering questions that are similar to those that will be on the examination, and most professors will be kind enough to tell you what the format and types of questions will be. Generally, there are two
types of questions you will find: qualitative and quantitative. I'll deal with the best way to study for each type of question in turn.
The tendency here is to think that cramming and memorizing facts is the best way to go to answer such multiple choice, free response, or essay questions on qualitative subjects. However, this is not often the case....
Final exams are coming up and you are freaking out!
There are steps that you can take in order to help you prepare for the upcoming exam.
Do not wait until the night before to start studying. Start going over the material weeks before the final.
Previous exams - use the midterm and any other exams to help you study material from earlier in the semester. Problems that you saw on these exams may also show up on the final.
Practice finals - many professors sometimes hand out practice problems or practice finals in order to help you study. Go over these problems and make sure you know how to solve every problem.
Take a break from your study routine occasionally. Your brain will thank you!
I have found that most people have an intuition about mechanical physics that is generally correct before the algebra and calculus starts to confuse them. This comes from the fact that before we could speak, we were learning how to exist in the world around
us (a world that is governed by physics). For instance, a child knows that your food will remain on the table unless he/she adds a force to push it onto the floor. Or that a ball thrown straight up into the air will eventually come to a stop, reverse direction
and come right back down to earth. The most common issue people seem to have with physics is that, when they add in the math they forget to look at the larger picture of what is really happening.
With that being said, there are several important steps that can help you with physics problems.
Identify all the information given and write it down at the top of the page.
(It helps if you are labeling a diagram)
I've always had an opinion that conceptual Physics (and even advanced Mathematics) should be introduced at the primary school level.
It's just amazing that when I'm beginning to draw an airplane for an example problem explaining vectors, my 12 year old student goes off on a tangent when she explains in laymen's terms - Bernoulli's Principle.
I probably should've started drawing a curve ball instead. Lol
In the spirit of giving, starting on 11/29/2013, I will be offering a few brainteasers/ trivia questions where the first 3 people to email me the correct answer will receive a free, one hour, tutoring session in any subject that I offer tutoring for (via
the online platform)! That's right free! Get your thinking hats on everyone!
Andrew L. Profile
I used to do this and I see a lot of students who do this common mistake when studying. Maybe you are working through old homework problems to prepare for an exam in math or physics and you have the solutions in front of you. You get to a certain point
and you get stuck, so you check the solution, see what the next action you have to take is, and then continue working through the problem. Eventually you get an answer that may (or may not) be right and check the solution again. If it is, you feel great and
move on. If it isn't you compare the work and see what you did wrong and understand the mistake so you move on. All this is a fine way to start studying, but the major mistake is that most students don't go back to that problem and try to do it again. Even
if you were able to understand the solution or the mistake you made, you never actually got through the problem completely without aid. So now if you come to this problem on your test, this will be the first time you actually...
Many times students look at graphics and word problems as perfect storms. If the problem is analyzed and related to a real life situation, I bet concepts should be easily understood. Today I was tutoring a senior student on Physics. She looked at a graph
of time vs velocity with a question mark on her face. What I did was to place her on a real life case in which she is driving from home, speeds up, see a well known police officer in this area, so.... slowing down, then driving at constant speed (flat section
of graph with acceleration = 0) and then slowing down again when getting to her friend's house before stopping. That was an AHA moment indeed!
One day I was sitting in the student union at the University of Utah when I noticed two students sitting near me working on a physics problem. One student was having trouble and the other was explaining how to do it using big hand motions. The first student
nodded he understood. The second student left his friend to work on the problem on his own, and I watched him work for a while, then turn to his laptop, where he entered his answer into an online homework site and submitted it. This site gives you a little
green checkmark when you get the right answer, and when the checkmark appeared, he pumped his fist. It seemed this little tutoring session went perfectly.
There was just one problem. The second student's explanation was completely wrong; he was literally 'handwaving'! So how was it, exactly, that the first student was able to solve the problem with such bad information? Beats me. What I can say is that tutoring
is more than just the transfer of information...
Galileo was a famous astronomer who was the first scientists to point his telescope towards the heavens and view the moon, rings of Saturn and other amazing objects. When he began to study the moon he noticed that there were craters and plains on it. He
also noticed that there were mountains on the moon by noticing light patterns on the moon.Many people would have gone on to the next observation, but Galileo began to measure these mountains.
I, like many other students, would always ask "what is the point of math?" "when will I ever use this?" so on and so on.Well depending on the career path you may never need the high level math you are required to take, but I hope that you at least appreciate
math for the power that it holds in unlocking mysteries of our universe. Think about it the moon, is 238,900 miles!!!! And in the 1600's without any sophisticated gadgets like we possess, a humble scientist was able to measure the height of a mountain...