What math subjects should a physics major master?

[Zack K]

Throughout a degree as a physics major, you take a bunch of math courses, and it's safe to say that you should have a good understanding of all the calculus and algebra courses. But what math subject/specific course should I master at a spiritual level? Especially ones that are needed for astrophysics/cosmology because that's my field of interest.

 

[Klystron]

Master Probability and Statistics. Minor in computer programming.

Note: specific computer languages are not as important as a thorough understanding of data structures, software design, and advanced software packages in your field to remain adaptable.

 

[Zack K]

Master Probability and Statistics. Minor in computer programming.

Note: specific computer languages are not as important as a thorough understanding of data structures, software design, and advanced software packages in your field to remain adaptable.

What's the best method of learning about said computer science theory?

 

[Dr. Courtney]

Throughout a degree as a physics major, you take a bunch of math courses, and it's safe to say that you should have a good understanding of all the calculus and algebra courses. But what math subject/specific course should I master at a spiritual level? Especially ones that are needed for astrophysics/cosmology because that's my field of interest.

Not even sure what it means to master a math subject at a spiritual level.

There is ample room in many physics majors for a few extra math courses, often enough to comprise a math minor at many schools. But the recommended path often depends on whether the future is likely to be more experimental, more computational, or more pencil and paper theory. My view is that this distinction is more important when choosing math courses than the field of physics (atomic, condensed matter, astro, etc.) Further, in my experience one's field of physics is more likely to change after the middle of your undergrad years than your likely emphasis between experiment, computation, and pencil and paper theory. Give that some thought, and you're likely to get better advice on preferred math courses.

But when you pick some courses, be satisfied with earning an A. Earning an A is usually a good enough launch pad to productively use the math mastery in later work. My view is it probably takes a couple thousand hours of using a math skill set to have really mastered it. Coursework builds a launch pad for the independent use that provides real mastery.

 

[ZapperZ]

Throughout a degree as a physics major, you take a bunch of math courses, and it's safe to say that you should have a good understanding of all the calculus and algebra courses. But what math subject/specific course should I master at a spiritual level? Especially ones that are needed for astrophysics/cosmology because that's my field of interest.

I'm puzzled as well as to what you mean by ".. at a spiritual level.."

The easiest and quickest way for me to point to the mathematics that you need as a physics major is to point to a text such as Mary Boas's "Mathematical Methods in the Physical Sciences". Those are the basic areas of mathematics that you will probably need as a physics major.

Zz.

 

[Zack K]

I'm puzzled as well as to what you mean by ".. at a spiritual level.."

It was more of a metaphor emphasizing the depth of knowledge.

The easiest and quickest way for me to point to the mathematics that you need as a physics major is to point to a text such as Mary Boas's "Mathematical Methods in the Physical Sciences". Those are the basic areas of mathematics that you will probably need as a physics major.

I skimmed through a PDF of that I I don't find it as a good resource for learning, it's more of a reference after you learned it because they don't go into much theories.

 

[alan2]

When I was an undergrad in physics the degree requirements included calc, ODEs, linear algebra, one semester of advanced calc, and 3 math courses at the senior level chosen from complex variables, Fourier series and BV problems, vector calc, and probability, as well as a methods course taught by physics. Schools seem to have gotten away from that but those courses all seem fundamental to me.

 

[bhobba]

What's the best method of learning about said computer science theory?

I like the following book:
https://www.amazon.com/dp/0691125651/?tag=pfamazon01-20

Not that I think probability and stats is most imortant - my favorite book is Boas's:
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20

Thanks
Bill

 

[ZapperZ]

It was more of a metaphor emphasizing the depth of knowledge.I skimmed through a PDF of that I I don't find it as a good resource for learning, it's more of a reference after you learned it because they don't go into much theories.

From the Preface of Mary Boas's book:

this book is particular intended for the student with one year of calculus who wants to develop, in a short time, a basic competence in each of the many areas of mathematics needed in junior to senior-graduate course in physics, chemistry, and engineering... It is the intent of this book to give these students enough background in each of the needed areas so that they can cope successfully with junior, senior, and beginning graduate courses in the physical sciences. I hope, also, that some students will be sufficiently intrigued by one or more of the fields of mathematics to pursue it further.

You asked for the "math subjects" that a student like you needs. That's what this book provides. It gives further references for anyone who wish to go into detail any of the type of mathematics that is covered.

https://www.physicsforums.com/threads/boas-methods-good.855156/#post-5556864
https://www.physicsforums.com/threa...-the-physical-sciences-by-mary-l-boas.665434/

Take it from someone who has gone through the entire process, and have also done enough teaching at various level. This text can be a lifesaver. But you are welcome to ignore this advice, because it is not me that has to learn all of this.

Zz.

 

[Dr. Courtney]

Ignore ZapperZ's advice regarding Boas at your own peril. Since most Physics Majors I know about already include a Boas-based course called something like "Math Methods in Physics" I was assuming yours did also and providing advice regarding math courses over and above the Boas-based physics course. But if your school does not provide anything like a Boas-based course, then that would be the place to start.

If you are going to succeed in Physics, you need to separate what you do not like from what you do not need. You will need many things you don't like. The material in Boas is essential. Not that Boas is the only place you can get it, but avoiding those topics is a recipe for failure in Physics.

 

[Zack K]

Ignore ZapperZ's advice regarding Boas at your own peril. Since most Physics Majors I know about already include a Boas-based course called something like "Math Methods in Physics" I was assuming yours did also and providing advice regarding math courses over and above the Boas-based physics course. But if your school does not provide anything like a Boas-based course, then that would be the place to start.

If you are going to succeed in Physics, you need to separate what you do not like from what you do not need. You will need many things you don't like. The material in Boas is essential. Not that Boas is the only place you can get it, but avoiding those topics is a recipe for failure in Physics.

I just looked it up and my university has a 300 level course of "Mathematical Methods of Theoretical Physics", Would that be the equivalent of what you described?

 

[Dr. Courtney]

I just looked it up and my university has a 300 level course of "Mathematical Methods of Theoretical Physics", Would that be the equivalent of what you described?

Probably. But it would also be worthwhile to compare a topical listing of that course with Boas. My concern would be the emphasis on "Theoretical" might leave out some essential topics in Boas that are regarded as more for experimental and/or computational physicists.

 

[ZapperZ]

I just looked it up and my university has a 300 level course of "Mathematical Methods of Theoretical Physics", Would that be the equivalent of what you described?

When, in your curriculum, are you expected to take this class?

The problem with many mathematical physics classes at many schools is that it is often offered too late in an undergraduate program. You need the math in such a class to be able to do QM, CM, etc. It is a bit too late if you take this class after already taken those. You do not want to come across the phrase "orthonormal" or "Bessel function" or "Fourier transform" for the first time in a physics class.

The Boas text, if you read the Preface, is meant for someone in the Sophomore year, i.e. often before one takes the advanced undergraduate courses. She teaches you the tools that you might need BEFORE you have to use them.

Zz.

 

[Zack K]

When, in your curriculum, are you expected to take this class?

No It's not mandatory, which I think is terrible to not make it required. Though I was talking a professor I'm working with and he recommended I take his computational astrophysics 300 level class which is a "Computer-based approach[e] to solving complex physical problems".

The Boas text, if you read the Preface, is meant for someone in the Sophomore year, i.e. often before one takes the advanced undergraduate courses. She teaches you the tools that you might need BEFORE you have to use them.

I just realized the book you mentioned was not the one I was referring too, my bad. It seems highly recommended and I'll check it out over the summer.