What to do in a gap year to prepare for a Physics + Math degree

[BalinesePhysicist]

As the title says, I am now in a Coronavirus induced gap year. I have been accepted at a university, which for some reason requires us to do a double major. Hence I chose math as my second major alongside Physics since it has the most overlap, and I'm also very interested in theory. In school, I have learned some single variable calculus, up to integration techniques. For those who are familiar with it, I did the A level Mathematics curicullum. However, having spent a month or two not dong anything in particular and just enjoying free time, my math skills is a bit rusty. I enter college March 2022, so I basically have a year to do anything I want.

What should I do now in order to prepare for college so that I could excel? I want to become a researcher in theoretical physics, and I have heard that it is incredibly competitive. So what can I do with my time now to maximize my chances of enterring this career?

I have read So You Want To Be A Physicist - but only Part I as that is the information most relevant to my current situation. I will read more in the future. Their suggestion is to master basic mathematics (algebra, geometry, trig), which I have already done in school.

A common advice that I have heard is to learn calculus, which I plan to do. I have copies of multiple calculus books. The books that I am interested in doing are Thomas' Calculus (12th edition, if that makes any difference) as well as Spivak's calculus. I know Spivak is recommended here a lot, but my impression is that it is more meant for those interested in pure mathematics as it has little to no applications, and a lot of proofs. Books like Stewart and Thomas gets a bad rep here for being plug and chug with no theory, but I've read the reviews for my edition of Thomas online and there were a bunch of engineers who complained that it had too much proofs and theory in it, so it may be perfect for an aspiring physicist like me, as a cursory glance tells me it also has a lot of applications.

Plus, while I have learned Calculus in school, I haven't masterred all the computations yet. If you asked me to do an integral by trigonometric substitution, i probably can't do that, and I don't remember the derivatives/integrals of trigonometric functions by heart. Plus the A level curicullum doesn't teach limits. I've heard that it's better to get a good background in Calculus first before embarking in Spivak. Your advice would be appreciated here. Furthermore, the first chapter of Thomas includes a review of algebra and trigonometry, and while I'm already confident in my abilities on basic math, this should sharpen my skills.

Other than this, what else should I do? Learn programming? If so, what language? I already know python. I also have an online copy of University Physics with Modern Physics, so maybe I should start working on that. Honestly though I'm afraid what I'm learning now will be redundant since I will be relearning it later at college, but on the other hand I would have to spend less time studying later on and probably get better grades. Again, your advice will be appreciated.

Thank you.

 

[Zexuo]

Overall, the Thomas calculus textbook will likely mirror the beginning calculus course better. Read it through and do all the odd or even numbered exercises. If you have the time do all of them. Same with physics text.

If you already know Python, learn to use the numpy, scipy, matplotlib, and pandas libraries. Some of the models in the scikit-learn library can come in handy as well.

 

[BalinesePhysicist]

Overall, the Thomas calculus textbook will likely mirror the beginning calculus course better. Read it through and do all the odd or even numbered exercises. If you have the time do all of them. Same with physics text.

If you already know Python, learn to use the numpy, scipy, matplotlib, and pandas libraries. Some of the models in the scikit-learn library can come in handy as well.

IF I finish the Thomas book before I start college (which is a big if, as college is 10 months away), what math book should I read? I'm planning to work through Strang's linear algebra alongside Thomas, right before I get to the multivariable part of the book as I've heard linear algebra could be useful for that. Other than that, I've seen "mathematical methods for the physical sciences" recommended a lot here. Maybe that could be useful?

 

[Zexuo]

With a restricted timeline you might want to switch to Boas for linear algebra and multivariable calculus. She covers those topics in the early chapters. Since you plan to major in math as well you'll take a complete linear algebra course at some point but Boas gives you enough to proceed with the later topics. Make sure you get through improper integrals, numerical methods, conic sections, and indeterminate forms in Thomas before considering a switch.

 

[WWGD]

I suggest you go through the material you will encounter; the actual books if possible, without putting too much pressure on yourself to understand it. That way once you actually take the classes the material, notation used will be familiar to you.

 

[MidgetDwarf]

IF I finish the Thomas book before I start college (which is a big if, as college is 10 months away), what math book should I read? I'm planning to work through Strang's linear algebra alongside Thomas, right before I get to the multivariable part of the book as I've heard linear algebra could be useful for that. Other than that, I've seen "mathematical methods for the physical sciences" recommended a lot here. Maybe that could be useful?

I personally do not like Strangers at all. It is too wordy. I suggest Anton Linear Algebra, and Serge Lang: Introduction to Linear Algebra (together).

Your goal is to learn Calculus. What edition of Thomas do you have? Have a look at the third edition. It is a much better book. Editions past the 4th do not contain the original spirit of book written by Thomas. He died, and the publisher just use the name.

 

[Mondayman]

I've never seen an older edition of Thomas Calculus, so I can't say how much better it would be. When there are 15 editions, the older ones are almost always better.

But for the most the part, the newer 9th Edition does the job for most intro university curriculums. Another good one is Calculus: A Complete Course by Adams.

I enjoyed Anton and would recommend it as a first step into linear algebra. Fried egg is a good second step.

Edit: The fried egg autocorrect for Friedberg was too good to change.

 

[WWGD]

If you have the option , go to your/a college library , browse through the Math/Calc session and see which book somehow feels right for you, or find out which book will be used for your classes.

 

[BalinesePhysicist]

I personally do not like Strangers at all. It is too wordy. I suggest Anton Linear Algebra, and Serge Lang: Introduction to Linear Algebra (together).

Your goal is to learn Calculus. What edition of Thomas do you have? Have a look at the third edition. It is a much better book. Editions past the 4th do not contain the original spirit of book written by Thomas. He died, and the publisher just use the name.

I have the 12th edition since it's the only one I could find. Plus I have the solutions manual. I'm not sure which book you mean by the third edition. Is it Calculus and Analytic Geometry? Is there really a significant difference with the 3rd edition? The 9th edition seems to have a lot of good reviews on Amazon while the 3rd one barely has any reviews at all. Plus this forum thread seems to indicate that the 9th edition is just as good if not better than the 3rd.

For what it's worth, I've started with the twelfth edition and worked through several sections, and it's perfectly fine so far. Would it be worth the effort to switch from my current version to the 9th edition? Shipping textbooks to my country using Amazon takes months, and I can't seem to find an online copy of the third edition you mentioned.

If you have the option , go to your/a college library , browse through the Math/Calc session and see which book somehow feels right for you, or find out which book will be used for your classes.

Unfortunately I currently live in a developing country with really no good infrastructure for getting English textbooks such as local libraries, plus the college I've been accepted to is thousands of miles away on a country I can't enter due to the coronavirus, so I can't access its libraries. I've looked at the Calculus courses in my college and for Single variable calculus, they list Stewart's Calculus as "reference for routine exercises" and Spivak's Calculus as "reference covering advanced topics", while multivariable just uses Stewart and some course notes. I took a peek at Stewart and didn't really like what I saw; I preferred the Thomas book.

 

[Mister T]

You say your math skills are a bit rusty but you have mastered algebra, geometry, and trigonometry? I would start by taking a placement test at your local college to see just how well you do in those topics. And then take it from there. For example, if you're good at algebra and trigonometry you shouldn't have much trouble learning how to do an integral that involves a trigonometric substitution.

You of course need to be good at math to be good at physics, but there is more to physics than just the math. Or in just being able to find the right answer to a test question or problem. I recommend a good book on the concepts of physics. Look, for example, at the stuff Paul G. Hewitt has written.

 

[WWGD]

I have the 12th edition since it's the only one I could find. Plus I have the solutions manual. I'm not sure which book you mean by the third edition. Is it Calculus and Analytic Geometry? Is there really a significant difference with the 3rd edition? The 9th edition seems to have a lot of good reviews on Amazon while the 3rd one barely has any reviews at all. Plus this forum thread seems to indicate that the 9th edition is just as good if not better than the 3rd.

For what it's worth, I've started with the twelfth edition and worked through several sections, and it's perfectly fine so far. Would it be worth the effort to switch from my current version to the 9th edition? Shipping textbooks to my country using Amazon takes months, and I can't seem to find an online copy of the third edition you mentioned.Unfortunately I currently live in a developing country with really no good infrastructure for getting English textbooks such as local libraries, plus the college I've been accepted to is thousands of miles away on a country I can't enter due to the coronavirus, so I can't access its libraries. I've looked at the Calculus courses in my college and for Single variable calculus, they list Stewart's Calculus as "reference for routine exercises" and Spivak's Calculus as "reference covering advanced topics", while multivariable just uses Stewart and some course notes. I took a peek at Stewart and didn't really like what I saw; I preferred the Thomas book.

Ok, then maybe you can use any books Or online resources available . Good luck and come back with any questions.

 

[Choppy]

One thing about trying to read through some textbooks without the structure of a formal course is that a lot of people seem to stall out when they attempt this. A big reason for that is that there is no specific goal beyond something like "learn calculus." Further, there's no forced deadline. So whenever the choice to study comes up against something with a deadline... it's rare that study wins out.

Here are a few other things to consider if you have a gap year to fill in...

• Read up on the things that really interest you. You'll have lots of formal structured learning when you get to university. Now is a great time to spend learning about the things that really drive your curiosity. You may not have a lot of time for that when you're studying at school. Read biographies of scientists you admire. Read popular science books and online introductory articles. Read through Physics Forums Insights.
• Take up a hobby that helps you to develop some practical skills. Electronics. Programming. 3D printing. Build a drone. Etc. Skills with these things can help you immensely in a career in the physical sciences.
• Get a job and earn as much money as you can while spending as little as you can. Build up a nest egg so you won't have to work as much through university, or to put you in a position where you can afford a nicer apartment, better food, etc. will help you to focus on your studies that much more when the time comes.
• It's also important to try to get into a job where you can pick up practical skills. Even things like retail sales help you to develop a unique and useful skill set that you can apply through your entire career. You can also gain practical skills though volunteer work.
• Usually I'd tell people to travel, but that's not reality at the moment. But the point is more to expose yourself to new situations, explore the world and learn about yourself.
  

 

[BalinesePhysicist]

One thing about trying to read through some textbooks without the structure of a formal course is that a lot of people seem to stall out when they attempt this. A big reason for that is that there is no specific goal beyond something like "learn calculus." Further, there's no forced deadline. So whenever the choice to study comes up against something with a deadline... it's rare that study wins out.

Here are a few other things to consider if you have a gap year to fill in...

• Read up on the things that really interest you. You'll have lots of formal structured learning when you get to university. Now is a great time to spend learning about the things that really drive your curiosity. You may not have a lot of time for that when you're studying at school. Read biographies of scientists you admire. Read popular science books and online introductory articles. Read through Physics Forums Insights.
• Take up a hobby that helps you to develop some practical skills. Electronics. Programming. 3D printing. Build a drone. Etc. Skills with these things can help you immensely in a career in the physical sciences.
• Get a job and earn as much money as you can while spending as little as you can. Build up a nest egg so you won't have to work as much through university, or to put you in a position where you can afford a nicer apartment, better food, etc. will help you to focus on your studies that much more when the time comes.
• It's also important to try to get into a job where you can pick up practical skills. Even things like retail sales help you to develop a unique and useful skill set that you can apply through your entire career. You can also gain practical skills though volunteer work.
• Usually I'd tell people to travel, but that's not reality at the moment. But the point is more to expose yourself to new situations, explore the world and learn about yourself.

Thanks for your tips, you're the only one I've heard who suggested doing anything other than studying :) I've actually been implementing some of the tips you mentioned!

Your suggestion about getting a job is interesting. I've asked my parents about this and they said that it would be hard to find someone willing to hire me due to my age (I'm only 17) and also my lack of qualifications. I've heard of people working in retail/fast food as teenagers in the US, but it just doesn't work that way in my country (Indonesia). However, I discovered something interesting recently, and I'm not sure if this counts as a job.

For the past few months I've actually been picking up a new hobby, which is game development. This involves a lot of coding, and, surprisingly, math. I uploaded some videos to YouTube, including a VLOG documenting my experience making a game as well as some tutorials. They were surprisingly well received and I received a handful of views and subscribers. With the current rate of growth, I predict I'd be able to monetize my channel in a couple days (it requires 1000 subscribers) and gain money from it. If I actually put the time into it, I could actually make some serious money out of this. I did my research into channels which are in my niche, and between advertisements, sponsorships and patreon, the money they make is not insignificant.

My concern is that if I start to focus my time on this endeavor, I'll have less time and energy to work on math and physics / preparing for my degree. Coding, making art and music, editing, etc. takes a lot of time and effort, and I found that if I spend a couple hours coding I basically have little to no brainpower or willpower left to study. Vice versa is also true. Reading "pop-sci" Physics books also surprisingly takes a lot of brainpower and effort, though it is incredibly fun. Reading "Six Easy Pieces" was not "easy" at all and I had to sketch out some things to actually understand Feynman's explanations.

The point is, in any given day I have a finite amount of time and energy to spend. I'm looking for advice on how best to spend them. Working on my "job" - if you can even call it that - or on preparing for my degree. To what extent (or: how much time should I spend) studying right now to make sure I can excel later on?

 

[Choppy]

The answer here is going to be different for everyone. It's a multi-objective optimization problem. You only have some much time and energy, and you can't do everything. (My list of suggestions was not a checklist, but just an attempt at brainstorming some options.)

Your YouTube game development VLOG is a great idea! If it's something you enjoy, then I'd say go for it. I suspect that actually making serious money on this kind of thing is rare, but you never know. You could fall into a niche that could land you some income. More importantly though, it's something that will help you develop practical programming skills, and if you fast forward to your graduation... let's say grad school or academia doesn't work out... you could be in a place where you've got a double major in physics and mathematics, and lots of documented, practical game development and programming experience. That's not a bad fallback option!

To balance that with studying, one thing you could try is setting yourself a reasonable studying goal. Say, dedicate one hour every day to study. One hour doesn't sound like much, but the point is not to make it too high, set yourself up so it's easy to accomplish. Even a half hour might work in the beginning. Then give yourself specific tasks, like working your way through the problem sets in a given textbook. See how far you can get in one month. Then at the end of the month, based your progress, extrapolate out and set a goal for yourself to accomplish by the end of the next nine months. Maybe that's three textbooks where you've solved all the problems for which you have verifiable answers. That would put you in a great place to start university, keep your skills sharp, but not overwhelm you with insurmountable goals, and hopefully leave you with lots of time to fill the rest of your day with other things.

 

[DaveE]

Have you, or can you, ask some of the professors at the school you will be going to. You can't expect a lengthy reply, but it should be easy to get some general guidance from them like textbooks and subjects to study. It seems to me if they know you'll be a student next year, they should be willing to offer more informed advice than us.

My advice is to focus on really understanding the calculus that you have already, or will be studying. Don't try to go too fast yet, a really clear understanding of the basic foundations is really important. Same for basic physics.

 

[Dr. Courtney]

Take the ALEKS pre-calculus course until you complete 100% of the "pie."

If you can do that, you are ready, and anything else you can do in preparation will be gravy.

If you cannot complete the ALEKS pre-calculus pie by the time you start, you are in a tough spot, and anything else you do is tilting at windmills.