Mathematics is a broad school that encompasses far more than simple arithmetic. Anyone who pursues maths to a degree level will find that it’s exceptionally varied, with lots of different branches ready to be pursued. Which route you follow depends on where your passion lies, but it’s always worth considering the type of career you want at the end of your studies.
Calculus is one of the first things that comes to mind when people think about mathematics. It’s exceptionally varied but can broadly be classified as the study of “continuous change,” although even this is divided into two schools. Infinitesimal calculus is the older of the two, while differential calculus is more modern.
Calculus is viewed by many as the foundation of all maths. As a result, you’ll find that it’s a prerequisite for a large number of careers, including aerospace engineer, software designer, and even economist. Calculus is so important, in fact, that you’ll struggle to avoid it. Any bachelors (or higher) degree in mathematics will come with at least some calculus modules, but if you want to pursue any of the above-listed careers, it’s worth taking an even deeper dive. Many students choose to supplement their learning with an online course like the one at https://www.straighterline.com/online-college-courses/mathematics/general-calculus-i/. This gives them a better knowledge of the area, which doesn’t just help with their future careers but boosts their prospects across other modules.
2 Probability and statistics
Moving away from the objective truths of calculus, probability and statistics is a more abstract area. Students will use data to predict how and when events will occur, analyze trends and interpret numbers to reach nuanced conclusions. Probability and statistics cover a big area, and specialized degrees are much sought by employers. A business analyst is one of the main career paths associated with this branch, but it’s far from the only one. Data analysts, economists, and market researchers all make use of probability and statistics to forecast events. There’s even ample room within the world of politics for this kind of skill set.
Probability is often favored by those who prefer more “tangible” mathematics. It doesn’t make heavy use of mathematical theory and, since this area is quite new, students won’t have to worry about the history of the subject. It’s focused on real-world results and applications, so it is the preferred area for more practically minded students.
Everybody will be familiar with this branch of mathematics from school, but advanced degrees are about much more than measuring angles. Geometry is one of the more practical branches of mathematics, and jobs are accordingly “hands-on.” Creative career paths including animator, interior designer, and even architect all make use of geometry. It’s an important specialization for surveyors too, and CAD engineers need in-depth knowledge. Generally speaking, if you pursue this branch of mathematics, you’ll be able to find a home in the engineering or architecture sectors without any trouble.
The beauty of geometry lies in its links with the arts. This is the area that’s most routinely pursued by students with an artistic bent, opening the way as it does for a design-focused career. While the other areas on this list have firmer links to the sciences, geometry represents the meeting point between maths and art. It allows students to use numbers to create and shape the world around them.
4 Number theory
Number theory is one of the oldest branches of mathematics and, as such, has somewhat of a fearsome reputation. It is pure mathematics and focuses solely on integers. Careers in this area are mostly academically based, so if you are hoping to become a researcher or mathematics professor at a college, number theory is the way to go. Number theory is linked to the wider sciences, and it is a good branch to pursue if you want to move into physics, even venturing towards areas like quantum physics. Some computer science careers (especially those concerned with AI or algorithmic learning) increasingly utilize number theory too.
It certainly isn’t the most accessible area on the list, and not many students go into number theory without a solid grounding elsewhere. This might be considered the most advanced area, and as such, it’s usually reserved for those seeking academic careers or simply mathematicians with a passion for their subject.
All of these routes are ripe with potential, both for personal development and in terms of career options. Mathematics is widely applicable across nearly all other academic areas, including the sciences and humanities. Whatever you choose, mathematics demands research, practical and analytic skills, which are widely transferable across other subjects. Any area will boost your career prospects and help you along the path of further education.