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Studies & Degrees in Geometry

Geometry is the branch of mathematics that studies shape, size, position and the properties of space. It starts with points, lines, angles, triangles and circles and extends to curved surfaces and spaces of many dimensions. It is also a training in reasoning: geometry is where most students first meet formal proof, deriving a result step by step from definitions and axioms.

The subject has practical uses well beyond the classroom. The US Common Core State Standards give as examples interpreting a schematic drawing, estimating the wood needed to frame a sloping roof, rendering computer graphics and laying out a sewing pattern efficiently. Architecture, engineering design, surveying, robotics and computer animation all rely on geometric methods.

What students learn

At school, according to the Common Core standards, mathematics is devoted mainly to plane Euclidean geometry, studied both without coordinates (synthetic geometry) and with them (analytic geometry). A high school geometry course typically covers:

  • Congruence, similarity and symmetry, understood through transformations such as translations, rotations and reflections
  • Proofs about triangles, quadrilaterals and circles, with precise definitions
  • Right triangles and trigonometry: sine, cosine and tangent
  • Analytic geometry, which connects algebra and geometry through coordinates and equations
  • Measurement of length, area and volume, and modelling with shapes

At university, geometry branches out. Students may build Euclidean and other geometries from a small set of axioms, and go on to differential geometry (curves and surfaces studied with calculus), convex and discrete geometry, geometric analysis and applied or computational geometry. These are, for example, the names of the geometry research units at the Institute of Discrete Mathematics and Geometry of TU Wien.

Qualifications and levels

  • Secondary school. In the United States, geometry is a year-long course within the high school diploma, and college preparatory schools include it in their mathematics sequence. Online schools offer it as a separate course as well.
  • Bachelor's degree. Geometry is not usually a degree in its own right; it is a set of courses within a mathematics degree. At TU Wien (Vienna University of Technology), the bachelor's programme in Technical Mathematics takes six semesters and 180 ECTS credits and is taught in German. In Spain, official bachelor's degrees (grados) have 240 ECTS credits.
  • Master's degree. Specialisation comes at this level. TU Wien's master's programme in Technical Mathematics takes four semesters and 120 ECTS credits, is taught in German, and offers a specialisation in Analysis and Geometry with in-depth theoretical training in both areas. Official master's degrees in Spain have 60, 90 or 120 ECTS credits.
  • Doctorate. Research in geometry is done in doctoral programmes within mathematics departments.
  • Teacher education. Geometry is part of the training of mathematics teachers, and descriptive geometry is taught to future architects and engineers.

Where to study it

SpainExchange lists four active schools for geometry: two in the United States, one in Austria and one in Zimbabwe. They are of very different kinds, so check the level before comparing them.

  • Vienna University of Technology (TU Wien) teaches geometry at university level; its geometry groups invite students to consult their information on studying geometry and on the curricula.
  • Midlands State University in Gweru, Zimbabwe, has a department of Applied Mathematics and Statistics in its Faculty of Science and Technology, which offers programmes at undergraduate and postgraduate levels to local and international students.
  • Forest Trail Academy, based in West Palm Beach, Florida, is an accredited online school for kindergarten to grade 12.
  • Grand River Academy, in Austinburg, Ohio, is a college preparatory boarding and day school for boys.

Teaching at the two US schools and at Midlands State University is in English; at TU Wien the mathematics programmes named here are in German.

Careers

Few jobs carry the title "geometer". Geometry is a skill that mathematicians, engineers, architects, surveyors, computer graphics developers and teachers use. People who specialise in it at university usually follow the career paths of mathematics graduates: research, teaching, software and data work, and engineering.

According to the US Bureau of Labor Statistics, mathematicians and statisticians held 33,500 jobs in the United States in 2025 and typically need at least a master's degree, although some positions are open to people with a bachelor's degree. Their employment is projected to grow 10 percent from 2025 to 2035.

Frequently asked questions

Can I take a degree in geometry?

Not usually as a named bachelor's degree. You study mathematics and choose geometry courses, and you can specialise at master's or doctoral level, as in the Analysis and Geometry specialisation at TU Wien.

What is the difference between school geometry and university geometry?

School geometry is mostly plane Euclidean geometry with proofs, trigonometry and coordinates. University geometry is more abstract: it builds geometries from axioms and studies curved spaces with the tools of calculus and algebra.

What do I need to know before starting geometry?

For a high school course, basic algebra. For university geometry, calculus and linear algebra, which are taught in the first years of a mathematics degree.

In which language can I study it?

That depends on the school. The US schools listed teach in English, and TU Wien's Technical Mathematics programmes are taught in German.