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High School Physics is almost always the same as “College Physics”: a non-calculus based college physics curriculum. For more information, see College Physics.
Unfortunately, high school students can sometimes have an additional challenge: the people who teach High School Physics are often not qualified to teach physics: they get “stuck” teaching a course they dislike, and can teach their students to dislike it as well.
AP Physics is always a calculus-based University Physics class. Students who take this class have two goals, which are unfortunately, not always aligned:
• They want an A. Of course.
• They want to pass the AP Exam. Naturally.
These two goals are not always aligned in the sense that the learning style for grades is not the same as the learning style for standardized tests.
A student maximizes their grade by spending lots of times and worrying about the small details to get everything completely correct.
On the other hand, to pass an AP Exam, you need a different skill set: the ability to quickly figure out which answers are clearly wrong. Once the student crosses off the answers that can’t be right, only then can the student determine whether they should actually roll up their sleeves and solve the problem. I would estimate that about 50% of the AP Exam can be done without any calculation at all, and the reason why this is important is because you have a very stringent time component. Like other standardized tests, the test taker needs to quickly select the answer, and quickly move on to the next question.
You can see the competing goals here: deep, accurate problem solving versus a clever combination of estimation, approximation, calculation, and perhaps luck. This is both the blessing and curse of standardized tests.
Our goal is two-fold: make sure you maximize your grade, but also, make sure you pass the AP Exam.
Note: This is a great class if you intend on entering pre-med, nursing, architecture, etc. For students who desire to become physicists, engineers, or applied mathematicians, my recommendation is to pass the AP Exam, but go ahead and take the freshman class anyway. Even at the best high schools, AP Physics teachers are not always the most qualified to teach Physics, and you want to know the fundamentals down cold!
Also called “College Physics”, this non-calculus based course is usually two semesters long, and is designed for students who want to pursue technical fields in the non-hard sciences. Some examples would be pre-med, nursing, architecture, psychology, and others.
Sadly, this is a course that’s very difficult to teach correctly. One of the paradoxes of mathematics is that the harder the subject is, the easier it makes everything else, and this is no exception.
Learning calculus is not trivial: it requires a lot of hard work, however, it does make learning physics a whole lot easier!
Without calculus, the teacher has to jump through a lot of hoops to deliver a lecture which really doesn’t amount to much more than a string of equations to memorize strung together by hand-waving arguments.
Is possible to do a good job at College Physics? Yes, it’s just a lot harder, for both the professor to teach, and the student to learn. But, more often than not, this class amounts to memorizing formulas and hoping you use them correctly in the correct context.
This 3 semester course is usually divided up into mechanics (starting with kinematics and ending with oscillators), electricity and magnetism (starting with electrostatics and usually culminating with EM Waves or radiation theory), and then an “ugly duckling” class which includes everything not covered by the first 2 classes: thermodynamics and statistical mechanics, geometric optics, hydrostatics (and possibly a bit of hydrodynamics).
This is the standard course that all Physics majors and Engineering majors take. If this is you, I guarantee that this is the one course you want to ace. Not only does this set the “tone” of your scholastic career, but having strong fundamentals makes the advanced courses much easier. Putting in your work now will pay back, with interest, later on.
I am more than capable of teaching any physics course for majors. As you can see from my Examples of Work, I have a very deep, very intimate knowledge, and I can communicate that knowledge extremely well, with minimal jargon and “fluff”.
Some examples of classes that fall under this heading would be quantum mechanics, junior-level electricity and magnetism, junior-level classical mechanics, special relativity, modern physics, thermodynamics, and the list goes on.
Do note that I’m qualified to teach many undergraduate engineering classes as well. Mechanical and civil engineers always need to take courses in Statics and Dynamics, which is nothing more than advanced applications of Newton’s laws. Electrical engineers usually take a course on electrical networks: network theorems like loop analysis, nodal analysis, and Kirchhoff’s Law, equivalency theorems like Thevenin circuits, non-linear devices like transistors and diodes, etc. These are all things I’m intimately familiar with, and can help you with your studies.
This one is tricky.
Graduate classes are not trivial, even for the PhDs that teach them. In the past, I have lectured and TA’ed for Electrodynamics (i.e. “Jackson”) and am qualified to tutor the standard 2-year curriculum: Classical Mechanics, Quantum Mechanics, Thermodynamics, etc.
I’m also qualified to tutor classes on classical General Relativity and Cosmology.
I received an A in all my Quantum Field Theory classes, but would not be comfortable tutoring them unless you’re completely lost, in which case, I can definitely help you become “unlost”. Just realize that these classes are very difficult for everyone, and I’m not as facile in this topic as I am with the other topics. Statistical Mechanics probably falls under this heading as well.
If you’re seeking help with graduate classes, let’s discuss and see if we can formulate a plan of attack.
Standard one semester high school algebra curriculum.
Standard one semester high school trigonometry curriculum.
I remember this course being difficult for me. Thinking back, a few things jump out at me:
First, problems often have multiple ways of attack: there’s often more than one solution for a problem.
Second, many high school students are lacking in their facility for fractions, and trigonometry is about nothing if not fractions!
Third, my 2nd point is untrue! I consider high school trig to be an incomplete course. The study of sinusoidal functions has so much breadth, applications, and utility that it’s often difficult to see what this course is really all about. People think of trig functions as being related to triangles. They are, but I think the subject would make more sense if it were taught from the point of view of circles rather than triangles.
I would give this more rich and full view of trig only if specifically requested, otherwise, we will study flagpoles like the millions of other trig students in the past!
Standard one semester high school curriculum.
This class can be slightly disorienting: after calculation-based arithmetic and definitive solution-based algebra, the student gets the first glimpse of how math can be an art: each problem can have multiple solutions, all of which are correct. Furthermore, the student gets a first glimpse of how the process is much more important than the answer. Some students find this jarring.
This is usually a 4 semester course, although I’ve seen it done (poorly) in 3 semesters, and even (horribly) in 2 semesters.
The first semester is always Derivatives: rates of change.
The second semester is always Integrals: area under the curve.
Third semester is devoted to series and summations. This is where you do Taylor expansions, infinite summations, and convergence tests. The class often goes into the separate topics of parameterization, coordinate systems, and conic sections, which can be tough. This is where most people meet Polar (2D), Spherical (3D) and Cylindrical (3D) coordinates for the first time.
The last semester is usually a “baby vector calc” class (aka “vector calculus”), but it can be pretty difficult. It usually covers integration of 3D conic sections, which can be difficult to visualize (but this visualization is key!) It also covers, briefly, the integral theorems: Gauss’s theorem and Stokes’ theorem.
This class is usually reserved for math majors and physics majors, although engineers can benefit from it as well.
The class usually focuses on proofs, rather than computation. It’s usually the first time an undergraduate performs math that’s independent of the number of dimensions of the space we’re in.
The class also gives deep insight into things we take for granted in calculus, like Jacobians, L’Hôpital’s rule, and the integral theorems covered by the last semester of freshman Calculus.
If you’re lucky, your professor will show you the metric tensor and how it relates to the coordinate bases.
This class can be tough, but it’s a lot of fun.
This class falls into one of two types:
The class for math and physics majors is largely a proof-theoretical class. It makes half-hearted attempts at presenting real-world applications, but more often than not, the attempt flops. Nevertheless, this is an honestly difficult class.
The class for everyone else is generally a “let’s get things done” kind of class. You learn how to formulate a null hypothesis and then use standard statistical tests to prove (or not) that hypothesis. It focuses on datasets and real world applications. For example, this is where pre-med and psychology majors learn the student-T test. This class can also be difficult, to be honest. Understanding often takes backseat to calculation, so even when you do well with the homework or tests, many students often end up scratching their heads and wondering what the heck does it all mean.
There are a number of classes that fall under the heading “differential equations”. Many math departments have 3 versions of this class:
Differential Equations for math majors and physics majors is a proof-centric class. You certainly get your hands dirty and solve a lot of equations of various types, but theoretical concerns and proofs play a central role in how the material is presented to the class.
Differential Equations for engineering majors (and other science-related pursuits) is a little like freshman calculus. You study a number of different types of equations and how each one is solved. The entire class from start to finish is “Here’s a differential equation of type X. Let’s see how to solve it. Now here’s a differential equation of type Y. Let’s see how to solve it.” And so on, and so forth.
Lastly, many departments offer a class on partial differential equations, which is a truly tremendous and difficult pursuit. I’ve never seen a school offer more than one semester of PDEs, yet I don’t think you can make an honest study of them in just one semester. Consider physics majors: one can label a physics major as someone who solves differential equations for 4 years. There are SO many ways to approach this topic, it’s insane. Usually, the professor of a PDE class needs to carefully craft the class in a way that doesn’t overwhelm the students.
The goal of Real Analysis is to formalize the study of numbers and functions, and to investigate important concepts such as limits and continuity with the most careful eye to formalism, rigor, and detail. This is considered the hardest class a math major will take. This class is even more theoretical than what most physics majors will tolerate (although some of us love this kind of formalism! :) )
Complex Analysis has a similar goal, but with complex numbers, complex-valued functions, and functions of a complex variable. It’s generally an easier course because computation is often a large part of the class whereas Real Analysis has pretty much no computation at all. For example, you’ll be computing contour integrals, inverse integral transforms, conformal transformations, Laurent series, and all kinds of good stuff. This was easily my favorite class when I was an undergrad.