Doing a Math major on top of computer engineering/science

[RoboNerd]

Hi everyone. I am a rising high school senior. This summer, I plan to study for fun Electricity and Magnetism from a college textbook that a friend gave me, do some calculus, and do some C++ programming [C++ How to Program is the book I am using].

I am a mathematically, logically constructed person. I am taking AP calculus BC next year, and took AP Physics C mechanics this year.

What I really enjoyed in my physics class was reading the textbook and then deriving the differential equations [doing the proofs] for torsional pendulums, simple pendulums, etc. That really got my juices flowing, so I think I am cut out towards liking mathematical proofs.

As of now, I have an inkling of getting into the cybersecurity field, and plan on doing computer science or computer engineering [while getting an appropriate dose of how hardware and digital electronics work]. On top of that, I am considering doing a math double major.

Now, I would like to gain an opinion if doing a math double major is valuable for masters admissions, doing cybersecurity work [I think it would help with cryptography], or if doing one specific major and specializing in depth would help me more.

Please advise...

Thanks!

 

[Jaeusm]

Now, I would like to gain an opinion if doing a math double major is valuable for masters admissions, doing cybersecurity work [I think it would help with cryptography]

The most important thing for masters admission is doing very well in what ever you choose as your major. Having a double major will not hurt you, but it will require more work.

or if doing one specific major and specializing in depth would help me more.

The point of a BS is to gain a breadth of exposure to topics in your major. You won't be specializing. That's for grad school.

In my opinion, a double major is not worth the extra effort, especially if your primary goal is just to gain another credential. If you plan on earning a graduate degree, a second bachelors degree doesn't mean much.

 

[chiro]

Hey RoboNerd.

For cyber-security you will be well suited to study pure mathematics with an emphasis on discrete mathematics (up to the graduate level with a treatment of graduate algebra) and some computer science to put these things into perspective.

Additionally it will help to understand the practical aspects of security in information systems to some degree (simple things like bad passwords and bad network protocols help).

Also realize that computer, information, and network security has many branches and mathematics based security consists of lots of mathematics (mostly algebra and discrete structures but also across many branches that connect to things like number theory and the ability to use those results).

Information is quantized and that translates into discrete mathematics (which includes number theory and eventually abstract and graduate algebra of discrete structures).

 

[RoboNerd]

Thank you jauesum and chiro for your inputs.

chiro, why pure mathematics and not applied mathematics? I thought applied mathematics was more practical?

 

[onoturtle]

Thank you jauesum and chiro for your inputs.

chiro, why pure mathematics and not applied mathematics? I thought applied mathematics was more practical?

I don't really know what's considered applied vs pure mathematics. I suppose traditionally I think of more analysis subjects that are commonly applied to physics and engineering (e.g. differential equations). But of course physics and computer science use abstract algebra, graph theory, etc. So I guess pure vs applied just depends on how the subject is taught (focus on theory or applications). OP seems to be more interested in applications.

As for double majoring, are you interested in mathematics in general? If you double major, you need to go through the entire program's requirements, including courses you may not care for. You may be better off picking and choosing the few that you truly are interested in and/or useful to your field (cryptography makes use of abstract algebra, number theory, probability, information theory; I'm not sure what maths would be useful for cybersecurity in general), which also frees up space in your schedule to pursue courses in other subjects of interest as well (perhaps more physics in your case since you appear to enjoy that) since you skipped required course that maybe you're not so into (say real analysis). On the other hand if the entire mathematics program does sound awesome to you and you don't care for taking classes in other fields as much, then maybe a double major is for you.

Bear in mind that your career trajectory may change. I personally studied comp. sci. and took mathematics courses, but not double major. I too was targeting security and then coding theory, so I took the subjects I mentioned above. Ultimately, I ended up changing course in grad school since coding theory research wasn't working out for me, and I ended up doing a PhD in bioinformatics and machine learning. So some of the math I studied in undergrad isn't really of use to me any longer, but the mathematical maturity they bring will help give you the skills to learn additional math on demand. Anyway, just saying I think studying more math is a great idea but you don't necessarily need to double major.

 

[chiro]

Basically because a lot of the stuff you will need to know regarding high level number theory, discrete mathematics and abstract algebra is done in pure mathematics.

When information is quantized you deal with discrete structures and this translates in some form or another to number theory.

The other thing to note is that abstract algebra looks at a lot of general results that apply to discrete mathematics if the field (basically the structure of the number itself and the constraints that define it) is a particular kind of field. If it's a whole number (integer, natural) or rational then it can connect with number theory and discrete mathematics in some way.

Most problems in cryptography can be translated to problems in discrete mathematics and abstract algebra involving very particular fields.

This is why it is useful to know these fields for cryptography since one has to be able to understand the current theoretical and practical approaches behind the different mathematical constraints and what is known to "crack" these algorithms. If one knows it from the pure perspective then it will be a lot easier to understand.

Number theory is not the same as calculus which is what most applied mathematics involves in some way and this is the reason why cryptography is a little different since the techniques and structures in applied mathematics are typically not the same as cryptography.

 

[RoboNerd]

Thank you for your kind inputs everyone!

I see that people are building a consensus that abstract math would help me here as cryptography is different from applied maths.