I understand the physics but struggle with the math on tests

• Testing
• BearShark
In summary, the person is struggling with long algebra in their physics studies, despite having a solid background in math. They have tried various strategies, such as writing out their thought process and drawing diagrams, but still struggle with tedious algebra, such as matrix multiplication and solving linear systems. They have a learning disability in writing, which gives them extended time for exams, but they still feel at a disadvantage compared to their classmates. They are seeking tips and strategies from fellow physicists to improve their algebra skills and achieve better grades.
BearShark
Hey,
I guess anyone in physics have seen it a lot but I have trouble looking for tips and strategies for solving my problem so I thought I'll try here.

Problem: I currently take Waves and Optics. I already passed Mechanics, Electricity and Magnetism, Analytical Mechanics, Thermodynamics and PDEs. I feel like I understand the martial and sometimes develop solid intuition, and I solve the weekly exercises on my own or after help from the TA. However I struggle with long algebra.

I have a solid background in math, I got a B+ in my calculus class, so I do understand the math, I just get confused when a lot of algebra is involved so if there is a problem that requires thinking about physics, doing some math then thinking again, I might get stuck with the math so I will not be able to solve the problem from there.

What I'm doing so far:

1. If I can't do the math, I write what I would do if I could solve the equations, and if I have an idea how would the solution look like I write that. I managed to pass exams where I could solve only half of the math like that, but I don't get full score so I get C's when I use this approach.
2. I try to draw a diagram of the geometry of the problem which helps but not applicable to all problems.
3. I try to be as organized as possible but if the math is long enough, it does not always help.
4. Needless to say I also practice a lot before the exam. However, this hurts the effectiveness of my studying because I often have to solve the problem a couple of times because each time I find an algebra mistake.
5. I do "sanity checks" whenever possible, but knowing there is a mistake often means I have to find it and then repeat the derivation which takes a lot of exam time.

The university has a learning disability counselor, and she has good tips, but she is not in physics and I feel like this is a problem physicists are more familiar with so I'm asking here. I want to start getting Bs and As instead of Cs soon because I want to go to grad school, and I feel like this is what is holding me back.

Thanks!

You seem to be already at a high level if you've studied PDEs. Can you give an example of the level of maths you can manage and an example of what is beyond your current capability?

PeroK said:
You seem to be already at a high level if you've studied PDEs. Can you give an example of the level of maths you can manage and an example of what is beyond your current capability?
Thank you for your response. I do ok when I need to solve classes of problems I am already familiar with.

For example I can usually do Fourier transforms ok because I am familiar with the theorems like the shift and convolution theorem, which allows me to skip a lot of algebra.

I am also familiar with most of the simple solutions of PDEs like the wave equation, so solving the wave equation for simple boundary conditions in a variety of symmetries is not that much of a problem, unless for example there is a situation where the Bessel function appears when there is no apparent drum symmetry so I have to get to the Bessel equation by simplifying the equation. If does not happen often but sometimes it does.

I struggle for example with multiplying a lot of matrices. It happens in Waves and Optics with ABCD and Jones matrices. Often an exam problem asks to chain a couple of matrices and I end up making mistakes in this process. I always check my answer by multiplying the base vectors and seeing if I get an expected result but it is not always possible and if I see I got it wrong it often means repeating pages of derivations.

I also struggle with finding transmittance and reflectence coefficients in scattering problems. I can set the equations and boundary conditions fine, but often get lost in the tedious algebra that follows, and a lot of times we are required to use the expressions we found in the next parts of the questions, which often results in unsolvable math if the expression is not right.

Summery: Basically if there is physical intuition \ meaning I can use to either guide me through the math of significantly simplify it I do ok, but if there is tedious "means to an end" math like matrix multiplication or solving a linear system with a lot of expressions and variables I tend to get lost.

Last edited:
You may get a better answer but I don't think there is an obvious way to do lots of difficult algebra without mistakes. I wish I could do it. I usually try to break a calculation down into manageable chunks. But on any sufficiently complex problem I'll usually make at least one error somewhere.

PeroK said:
You may get a better answer but I don't think there is an obvious way to do lots of difficult algebra without mistakes. I wish I could do it. I usually try to break a calculation down into manageable chunks. But on any sufficiently complex problem I'll usually make at least one error somewhere.

Thanks. I do realize everyone makes mistakes, but no matter how much I practice I don't seem to manage to do as well as my classmates seem to do in this area. This is frustrating for me because it puts me at a disadvantage.

You mentioned the "learning disability counselor." Do you have a learning disability (dyslexia in particular)?

DrClaude said:
You mentioned the "learning disability counselor." Do you have a learning disability (dyslexia in particular)?
I have have Dysgraphia, like dyslexia with writing, and I get an extended time accommodation in exams. It does help because it gives me more time to go over errors. I would still like to make less errors because I'd rather use the time to think about the problems rather than do algebra most of the time.

I think it helps to approach calculations as you approach a job like replacing a window or repairing a floor. Before you do a step in such physical jobs, its best to visualize how things are going to turn out. The can't be done exactly, but if you don't imagine how things will turn out and instead begin to execute steps, there are often surprises.

For example before you multiply two matrices together, you can visualize the general process - which rows time which columns are going to produce a lot of terms? Will any of the terms be "like terms"? How many different "species" of terms will there be?

When you're doing something like a Jones matrix are you writing everything out or subbing dummy variables in during the calculations? Some of them are hideous and it's easier for me to just rename all those trig functions/stuff A, B, C... etc. and then do the math subbing back at the end.

It makes it easier for me rather than rewriting messy expressions over and over again while actually doing the simple algebra stuff, you might want to try something like that.

1. Why is it important to understand both physics and math in tests?

Understanding both physics and math is crucial in tests because physics relies heavily on mathematical concepts and equations. Without a strong foundation in math, it can be difficult to solve physics problems accurately and efficiently.

2. What are some strategies for improving math skills in physics tests?

One strategy is to practice regularly and consistently, as math skills require repetition to master. It can also be helpful to review basic mathematical concepts and formulas, and to seek help from a tutor or teacher if needed.

3. How can I better connect the physics concepts to the math problems on tests?

One way to connect physics concepts to math problems is to focus on understanding the underlying principles and relationships between different variables. This can help in applying the correct equations and formulas to solve problems.

4. What should I do if I get stuck on a math problem during a physics test?

If you get stuck on a math problem during a physics test, take a deep breath and try to break the problem down into smaller, more manageable steps. You can also use any available formulas or resources, and don't be afraid to ask your teacher or classmates for assistance.

5. How can I overcome test anxiety when it comes to math problems in physics?

One way to overcome test anxiety is to practice relaxation techniques before the test, such as deep breathing or positive self-talk. It can also be helpful to arrive early and familiarize yourself with the test format and questions. Remember to stay calm and focused, and to use your time wisely when solving math problems.

Replies
60
Views
4K
Replies
2
Views
1K
Replies
4
Views
2K
Replies
11
Views
1K
Replies
8
Views
706
Replies
5
Views
1K
Replies
14
Views
2K
Replies
10
Views
2K
Replies
7
Views
2K
Replies
9
Views
2K