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Studies & Degrees in Probability Theory

Probability theory is the branch of mathematics that studies chance. It gives precise rules for measuring how likely an event is and for working with quantities whose values are uncertain. Its results are the basis of statistics, and they are used wherever uncertainty has to be modelled: insurance, finance, physics, biology, engineering and data science.

A first university course shows what students learn. Introduction to Probability at the University of California San Diego (UC San Diego) covers probability spaces, random variables, independence, conditional probability, distributions, expectation, variance, joint distributions and the central limit theorem. Later courses turn to stochastic processes, which describe random systems that change over time: Markov chains, random walks and Brownian motion.

Qualifications and levels

Probability theory is rarely a degree in its own right. It is studied inside degrees in mathematics, statistics or data science, and students specialise step by step.

  • Bachelor's level. Mathematics and statistics degrees include one or more probability courses. Some offer a named track. The University of Colorado Denver, for example, lets mathematics students choose among four areas of emphasis, one of which is probability and statistics. Its BS in Mathematics with the Probability and Statistics Option requires 54 credit hours in the major, at least 42 of them in mathematics, with courses such as Introduction to Probability and Probabilistic Modeling.
  • Master's level. In France, the Master Mathématiques et applications of Sorbonne Université has a common first year and eight specialised tracks in the second year, among them Probabilités et Finance and Probabilités et Modèles Aléatoires. In Austria, the master's programme Technical Mathematics at TU Wien takes 4 semesters, has 120 ECTS credits and is taught in German.
  • Doctoral level. Research training starts with measure-theoretic probability. At UC San Diego the graduate sequence Probability Theory I to III covers the measure-theoretic foundations, the law of large numbers, the central limit theorem, conditional expectation, martingales, Markov processes and Brownian motion.

Calculus comes first. Introductory probability courses for science students are calculus-based, and UC San Diego strongly recommends a completed course in real analysis before its graduate sequence.

Where to study probability theory

SpainExchange lists five active schools for probability theory: two in the United States and one each in Austria, the United Kingdom and France. They are UC San Diego and the University of Colorado Denver, TU Wien in Vienna, The University of Sheffield and Sorbonne Université in Paris.

Because the subject sits inside wider degrees, the directory only shows schools that name it as a study area. Almost every university with a mathematics or statistics department teaches probability, so it is worth looking at the course lists of mathematics degrees as well. The language of instruction follows the country and the programme: the TU Wien master's is taught in German, for example. Check the language of each programme before applying.

Careers

Probability is a tool more than a job title. Graduates who specialise in it work as statisticians, actuaries, quantitative analysts in finance, data scientists and researchers.

  • Mathematicians and statisticians. The US Bureau of Labor Statistics (BLS) counted 33,500 jobs in 2025 and projects employment to grow 10 percent from 2025 to 2035. It states that these occupations typically need at least a master's degree, although some positions are open to those with a bachelor's degree.
  • Actuaries. According to the BLS, actuaries use mathematics, statistics and financial theory to analyse the economic costs of risk and uncertainty. They typically need a bachelor's degree and must pass a series of exams to become certified. Employment is projected to grow 9 percent from 2025 to 2035.
  • Finance. Pricing and risk models rest on probability. A course on the mathematics of finance at UC San Diego, for instance, covers conditional expectation, martingales, optimal stopping, arbitrage pricing and hedging.

Frequently asked questions

Can I take a degree only in probability theory?

Usually not at bachelor's level. Probability is a set of courses or a track inside a mathematics or statistics degree, such as the Probability and Statistics Option at the University of Colorado Denver. Specialised tracks appear at master's level, for example the two probability tracks of the mathematics master's at Sorbonne Université.

What mathematics do I need before studying probability?

Calculus for a first course, and linear algebra soon after. Graduate courses also require real analysis: UC San Diego strongly recommends it before its Probability Theory sequence.

Is probability the same as statistics?

No. Probability builds mathematical models of chance. Statistics uses those models to draw conclusions from data. The two are taught together in many degrees because each needs the other.

What jobs use probability theory?

Statistician, actuary, quantitative analyst, data scientist and academic researcher are the most common. The BLS projects growth of 10 percent for mathematicians and statisticians and 9 percent for actuaries in the United States from 2025 to 2035.