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The Ultimate Guide to Majoring in Math

What’s Covered:

 

 

Math is one of the first subjects that most students encounter in their lives, and also one that they are consistently required to take until they graduate high school. This ubiquity and math’s myriad applications to real-life scenarios make it a common consideration amongst high school students who are exploring prospective college majors. If you’re reading this, chances are you’re thinking about majoring in math. In this article, we’ll dive into more detail about what exactly majoring in math entails so that you can gain more context around whether the subject is a good fit for you. 

 

Reasons for Majoring in Math

 

1. You’ve enjoyed math so far.

 

Perhaps the most obvious, though commonly overlooked, reason you’d want to major in math is simply if you like it. You’ve probably encountered this subject throughout your life, whether in the form of basic counting, algebraic equations, or even an AP Calculus class. At this point, your familiarity with the subject has probably allowed you to form an opinion on it, or at least some idea of where it ranks amongst the other subjects you’ve taken over the years. If you’ve enjoyed almost every math class you’ve ever taken, that’s a great starting point for considering math as your college major.

 

2. The world is becoming increasingly quantitative.

 

From a pragmatic perspective, the world is more quantitative than ever, with an increasing demand for people who are skilled at quantitative problem solving – and math is fundamentally about solving problems. In general, being able to understand the world from a more quantitative perspective is a really big plus to majoring in math.

 

There are also many fields tangential to math that are really important right now, such as computer science, physics, and engineering. Even if your goal is to go into those fields, it can be really helpful and really fun to have a double major in math. This is because building a strong background in math can supplement the learning you do in other subjects; for example, in physics, advanced math is quite important. For subjects like computer science, there are some really interesting aspects of discrete math and abstract algebra that will allow you to gain increased understanding of and appreciation for the field.

 

Aside from academia, math is common in the fields of finance, data science, and consulting. Many math majors gravitate towards these high-performing careers because the skills built in pursuing math set a solid foundation for the demands of those types of jobs. Just the experience of learning math and getting in that very specific problem-solving mindset can be really, really beneficial and open doors to a host of well-paying opportunities.

 

3. You want to explore math research and academia.

 

And finally, you might want to major in math… to learn more math! If you’re interested in research mathematics and math academia, that is absolutely a great reason to major in the subject. The concepts you’ll learn as you progress through degree programs will build upon each other, and so focusing on having a solid foundation early on will prepare you for success in future endeavors.

 

What You Can Expect to Learn as a Math Major

 

Getting started: calculus

 

Whether you’re considering majoring in math or absolutely set on it, it’s important to get an understanding of the student experience. The topics you learn in classes will form an integral part of your college experience, and even though you may not understand all of the math-related jargon yet, just hearing about these concepts can inform your future research into the math major.  

 

By the time you graduate high school, you will probably have taken some form of calculus; but if not, you’ll usually start your math major by taking the triumvirate sequence of calculus: calculus, one, two, and three, with the third course being multivariable calculus. These courses are pretty standard, but different colleges will divide up the sequence a little bit differently, with some of them incorporating the next level of courses into this first set for a more advanced curriculum. 

 

Linear algebra and differential equations

 

The next two concepts you’re almost certainly going to encounter are linear algebra and differential equations. Linear algebra is the study of what are called linear transformations, linear referring to lines, but in higher dimensions. If that sounds abstract, know that linear algebra shows up all over the place: in physics, engineering, and computer science. It’s a really important fundamental class with far-reaching implications across all of these subjects.

 

Many schools will offer two different kinds of linear algebra classes. One that’s more focused on applications to subjects like computer science, physics, and engineering, and another that zeroes in on the theory. The latter involves more abstract ideas including vector spaces, fields, and matrices. 

 

The subject of differential equations is all about studying solutions to problems involving derivatives, where the function is an unknown. This is very important in the physical world. You may have already experienced some kinds of differential equation-like problems if you’ve taken a physics or chemistry class. Generally, everything that we know in physics about how to describe the world is some form of a differential equation, or at least the solution to some form of a differential equation.

 

Abstract mathematics and proofs

 

You may have started to learn about proofs if you’ve taken Geometry at the high school level. In college, and depending on what your background is or the school you go to, you may take a Discrete Mathematics class or an Intro to Proofs class. 

 

Proof is this very special fundamentally mathematical idea of being able to show that something is true and there is no other possibility. In any experimental science, we can get data, and have facts, but there’s always the idea that maybe this isn’t the full picture. With math, when something is proved, it is true permanently, for the rest of time. Many math majors find this beautiful and incredibly gratifying – but working with proofs requires a pretty fundamental paradigm shift in the way you think about math, which can be difficult at first. 

 

In these abstract math classes, you’ll look at subjects like set theory, number theory (which involves working with prime numbers) and some forms of Euclidean geometry that surface in a way that’s a little bit more advanced than what you may have come across in high school. 

 

Higher-level abstract courses

 

There are three general areas that constitute the more abstract and more foundational higher-level courses in math. Those are roughly grouped into abstract algebra, analysis, topology and geometry. 

 

Abstract algebra can be thought of as the study of things defined by equations. Instead of thinking about equations involving numbers, whether they be integers or real numbers, the subject defines structures like groups, rings, fields, and modules. Vector spaces from linear algebra also come in here. 

 

In advanced abstract algebra, students get into Galois theory, which manifests at the high school level through the quadratic formula. There is also a cubic formula and a quartic formula, which get increasingly complicated – but there is no quintic formula. There is no general way to solve a degree-five polynomial using radicals; this is proved by Galois theory, which you’ll probably encounter in your later undergraduate years. 

 

Next is analysis, which can be described as the study of infinite decimals, or the theory behind calculus. This subject explores continuous functions, differentiable functions, and integrals from a very abstract perspective. Students may end up proving the fundamental theorem of calculus, which is not as easy and obvious as it sounds. Within analysis, there are a whole bunch of other more specific fields: for example, complex analysis is a particularly beautiful field that deals with differentiable functions with complex numbers.   

 

Finally, the third field is topology and geometry, which have to do with shapes and spaces. And there are a number of classes that you might take in this field, such as point-set topology, which explores continuity, compactness, and connectedness. 

 

Then there are different kinds of geometry. One is differential geometry, which uses techniques from analysis and differential calculus to study sorts of spaces. This ends up being really helpful in physics because Einstein’s theory of general relativity is all about differential geometry on a four-dimensional manifold.

 

You also have algebraic geometry, which studies the geometry of things defined by polynomial equations. In high school, you’ll graph a bunch of polynomials – algebraic geometry studies those. And there are so many more subjects; applied mathematics, statistics, probability, mathematical modeling, and so on. There is no shortage of mathematical subjects for you to explore.

 

If a lot of these words don’t mean anything to you, that’s totally okay! These subjects are all starting points of investigation that you can research to learn more about math in-depth. Investigating these topics in detail can help you decide if math is right for you, or just get a sense of what to expect when you go to college.

 

How to Find a Good School for Math 

 

Once you decide if you’re studying math, it’s important to consider where you want to pursue the subject. Not all higher education institutions are created equal, and the different cultural norms and resources at each will influence your academic and social experience. Above all, you want to do research into specific factors related to your learning style and personality to see if the school is a good fit for you. To start your search, ask yourself the following questions:

 

Is the mathematics department reputable?

 

As you consider a major in math, you might be wondering which schools are best for the subject. A number of these should probably be unsurprising for you – the Ivies are good for math; in particular, Harvard and Princeton are two of the top math schools in the world, let alone the country. On the same level, Stanford, MIT, UChicago, and Northwestern all have very reputable math departments with distinguished faculty. But a really great shared characteristic of these top schools, besides the excellent professors there, is that they have many motivated students.

Additionally, a lot of state schools such as UCLA, UC Berkeley, University of Illinois Urbana-Champaign, UT Austin, Rutgers, and Penn State have excellent math programs. UCLA and UC Berkeley in particular are up there with the Ivies, Stanford, and MIT. Carnegie Mellon also has an excellent program, particularly if you’re interested in the math relating to computer science and logic. 

 

Do the school culture and resources encourage collaboration?

 

And with math, more so than most other fields of study, the students you are around can really influence how you learn, almost more than the professors there. Talking through complex, abstract concepts is almost fundamental to better understanding math, especially because many times, topics can take a while to digest. The ability to have a support system that learns and grows together can really make your college experience, from an academic perspective in addition to the social perks. Schools with tight-knit communities might even have a dedicated study lounge where all the mathematicians congregate, and you can surround yourself with students who also are very interested in math and further your education in an enjoyable manner.

 

Are there a variety of courses in your area(s) of interest?

 

A lot of small liberal arts colleges also have good math programs, but you won’t generally be able to take the breadth of courses that you might at a larger university. This is especially true for the math major because as you continue along in your studies and hone in on specific topics you want to explore more in-depth, you may want to take graduate-level courses. At small, liberal arts schools, they just don’t have graduate students and therefore, many of those advanced courses are not as readily available.

 

It’s also important to consider that part of a great math program comes from your internal drive to make it work for you. And this comes down to learning on your own, reaching out to professors, taking independent study courses, and learning with your peers. It’ll be much easier to do this at a school already has established resources specific to your academic interest, so you can be more supported on your unique academic path. 

 

For a full list of top schools for math, check out our college rankings, where you can filter my major, location, and various other factors to build a school list that personalized to your goals.

 

How to Increase Admission Chances for Prospective Math Majors

 

In this section, we’ll discuss what you can be doing right now to both prepare yourself for a math major and make yourself a stronger candidate in the eyes of the admissions office.

 

Establish intellectual curiosity.

 

One of the best things you can do is pursue more academic opportunities related to math. This means taking more math classes, taking harder math classes, and self-studying. If possible, take all the math classes that your school offers; you can double up on courses like AP Calculus and AP Statistics in the same year if your school has both. 

 

If you have access to a community college or a four-year university nearby, you can also enroll in some dual-enrollment classes there. Not only will these really help you determine which parts of math you want to continue exploring in your higher education journey, but you can also demonstrate an intellectual curiosity for the subject to admissions officers by illustrating your appetite for the subject outside of the typically required coursework.

 

If your school or local community colleges don’t have readily accessible courses, you can always pick up some textbooks from the library and read through them to get a better handle on concepts of your choosing. You can also use the Internet towards these research goals; a great place to start is by looking up YouTube videos about linear algebra and differential equations. Sometimes it’s a little hard to parse through all of the resources out there, so be sure to try a few to determine which sources are most attuned to your learning style.

 

Pursue research.

 

Another possible extracurricular you can pursue that will demonstrate your propensity towards math is to engage in research in the subject. This is a little bit more difficult than learning on your own, as at the high school level, it can be tricky to get into mathematics research and find opportunities. At first, through your own studies, you can accrue some significant background to guide you in the right direction for research. Why is research in math so difficult? Well, a lot of the open problems in math are things that have taken centuries of development to even be able to state. But, it is possible to find active labs and join them. 

 

However, you’ll want to avoid reaching out to big-name professors or researchers. A lot of students erroneously think that reaching out to a really famous mathematician or professor will result in an almost instantaneous research position. Not only is this unlikely, but professors often get annoyed by messages from students when it appears they’re just trying to reach out to make their application look a little bit better. Most of the universities with really strong math programs have extremely strong postdoc students there, who are more often willing and ready to help you. 

 

Try math-related extracurriculars.

 

You could also take part in Math Olympiad and similar math competitions. These establish your expertise in the subject and also give you the ability to build up the Achievements section of your application.

 

If your school has a math club, that can also boost your application. Targeted extracurriculars like this help develop a spike to your application. A spike is formed in a student’s application when they have several extracurriculars concentrated in a particular subject or field. Spikes are a great addition to your application as they help admissions officers determine where you fit in with their incoming class, and provide more context into your interests as a prospective student than a well-rounded profile would. 

 

However, not all of your extracurriculars have to be explicitly math-related. There’s opportunities at the high school level in computer science, data analytics, physics, engineering – anything that uses math to do other things can look great on your application. And you can learn interdisciplinary applications that can inform your future studies and career as they relate to your mathematical pursuits. 

 

Want to know how your extracurriculars affect your chances of admission? You can learn how different types of involvement affect your profile with CollegeVine’s free Admissions Chances Calculator. Our calculator will take into account your GPA, test scores, extracurriculars, and more to give you a personalized estimate of your chances at the schools of your choice!

 

Frequently Asked Questions (FAQs)

 

What are ideal extracurriculars for success in math and computer science?

 

The more that you experience the problem solving aspects of math, the better your grasp of the subject and the easier it will be to convey that to admissions officers. Particularly, self-studying through a text that’s about proof or problem-solving more than just computing integrals, or computing derivatives can translate really well. For computer science, learning set theory, category theory, and logic are really helpful subjects to start with to establish more of a foundation in the subject. In particular, category theory is a fascinating and powerful foundational and organizational system that applies across math fields. Choosing to start with these foundational skills and explore them academically will be helpful as you continue your studies.

 

What are the different career options for math majors? 

 

Common career fields for math majors include finance, data science, consulting, research. There are many careers at national laboratories, especially those including physics and engineering. A lot of national laboratories also hire pure mathematicians to do research for defense purposes. It’s possible to research and do pure mathematics, both at a university and at a company.

 

There are also plenty of options in applied mathematics. careers in computer science include software development, front end, back end, data analytics, and even computer engineering. For physics, theoretical physics and experimental physics are also common options.

 

How do you get into math research as a high school student? 

 

One of the best things you can do is to start learning more math, now. In order to get into research, you will generally need a heftier math background than what is often taught in high school.

 

You can talk to one of your math teachers at your high school, or look on the internet for people at a four-year university conducting research. Postdoctoral candidates are ideal to reach out to over professors, as they are usually more willing to help. If you find someone whose research you find really interesting, you can send them an email. At the very least, they might be able to point you towards some other people who would be better suited to help, or resources and references that might help you get started on your own.

 

Is it possible to get a minor in math while still in high school? I’ll have enough credits from dual enrollment. 

 

Technically, no, you can’t get a minor in math while still in high school; you could satisfy the requirements and then graduate with a minor in math later, but it really, that also depends on the college that you go to. Most top colleges don’t take that much transfer credit; for example, at Harvard, they don’t take any transfer credit, and only take one credit from an AP exam. 

 

Do mathematical areas use concepts from one area of math in another? 

 

This happens all the time and is a recurrent theme in math. What is both amazing but also daunting about math is how interconnected everything is. Once you get to a certain point, in order to learn more things about one subject, you need to learn more things about another.

 

At a certain point, when you get to graduate-level classes, you’ll need to know abstract algebra and topology and analysis all at the same time to give you a really good foundation to build on top of. Graduate students generally have to pass qualifying exams in a lot of different areas.

 

What are the top liberal arts colleges for math? 

 

Williams College, Harvey Mudd College, and Pomona College have very strong math programs. Smith and Wellesley are women’s liberal arts colleges with strong math programs. 

 

What research projects for computer science can high schoolers do? 

 

Data science projects and data analytics can look very impressive on your college application and also be something that’s really interesting and fun for you to try. There are also other theoretical computer science projects you can find online and complete.

 

Should I minor in math? 

 

If you are more interested in some of the applied fields like computer science, physics, and engineering, it may be more helpful for you to minor in math, and a little bit less overwhelming or overburdening than necessarily doing a double degree. At schools with really strong engineering programs, the engineering degree is intense, and picking up a second major is maybe a little bit too much. Therefore, if you’re really interested in math, but there’s something else that you are even more interested in, a math minor could be the way to go. 


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