Mathematics: What Do You Really Study?
Structures, proofs and patterns - the precise language behind science, technology and quantitative thinking.
What Do You Study in Mathematics? Core Subjects, Year by Year
What do the degree courses cover?
Open a course to learn about its main topics and see what the work looks like in practice.
What do you learn in the course?Calculus?
The course builds a precise language to describe change and accumulation. You learn limits and continuity, derivatives and optimization, integrals and series, and practice switching between formula, graph, approximation and proof of the result.
Main topics
- Limits, continuity and basic theorems
- Derivatives, approximations and optimization
- Integrals and calculation methods
- Series, columns and convergence
What does it look like in practice?
For example, prove that a function takes on an extreme value under suitable conditions, find it and explain why the calculation alone does not replace the condition test.
What do you learn in the course?Linear algebra?
Learn to understand linear systems through vectors, matrices, spaces and copies. The course moves from solving equations to the abstract structure behind them and develops tools such as basis, dimension, determinant, eigenvalues and inner multiplication.
Main topics
- Systems of equations and matrices
- Vector spaces, basis and dimension
- Linear copies and representations
- Eigenvalues, Laxon and inner multiples
What does it look like in practice?
For example, recognize that a geometric copy is represented in a matrix, find eigendirections, and explain which directions are preserved under the operation.
What do you learn in the course?The basics of mathematics and methods of proof?
The course teaches to read, formulate and build a valid mathematical argument. Get to know logic, groups, relations and functions and practice direct proof, negation, contradiction, induction and counterexample, while paying attention to quantifiers and assumptions.
Main topics
- Logic, quantification and equivalence
- Groups, relations and functions
- Direct, contradictory and contradictory proof
- Induction and counterexamples
What does it look like in practice?
For example, you get a claim that seems true from several examples, formulate it with quantifiers and decide whether to prove it by induction or disprove it using a single case.
What do you learn in the course?Mathematical analysis?
The course examines in depth why the differential and integral calculus theorems are correct and under what conditions. Work with epsilon-delta definitions, series of functions, continuity, derivation and integration and develop proofs that handle infinite processes.
Main topics
- The actual numbers and integers
- Limits and continuity in the epsilon-delta definition
- Derivations and average value theorems
- Integration, columns and series of functions
What does it look like in practice?
For example, one proves the convergence of a series of functions and checks if it is permissible to replace a limit with an integral or a derivative, instead of assuming that the operations always alternate.
What do you learn in the course?Abstract algebra?
Learn to explore operations and structures using their common properties, without sticking to one type of numbers. The course deals with groups, circles and fields, homomorphisms, substructures and quotients and shows how symmetry and solving equations get a uniform formulation.
Main topics
- Bundles, subbundles and symmetries
- Homomorphisms, kernel and quotient
- Circles, ideals and polynomials
- Basic fields and extensions
What does it look like in practice?
For example, describe the symmetries of a polygon as a group and see how combining rotations and reflections reveals a structure independent of the particular drawing.
Frequently Asked Questions About Mathematics
Is a degree in Mathematics difficult?
There is no single answer — difficulty depends on your background, the institution, and your chosen study pace. According to this site's estimate, The degree is highly quantitative — mathematics and formal reasoning appear in nearly every course, and this is the part most students describe as challenging, and some of the reading material is in English. A good way to assess fit is to review the course map on this page: if most of the subjects interest you, the effort will usually feel worthwhile.
How long does a degree in Mathematics take?
Usually 3–4 years (Single-major or double-major). Exact duration varies by institution and depends on course load and the track you choose.
Mathematics or Statistics and Data Science — which is right for me?
The degrees most closely related to Mathematics are Statistics and Data Science, Computer Science, and Industrial Engineering and Management. Their differences are usually in emphasis rather than the overall subject, so the fastest way to decide is to compare their course maps — what you actually study in each program, year by year. You can also open the degree comparison tool to view the differences side by side.
What can you do with a math degree?
More than you'd think: algorithms and data science in high-tech, finance and actuarial work, cryptography and security, research and teaching. Employers value mathematical thinking itself, and many graduates land roles also offered to CS graduates.
How hard is a mathematics degree?
One of the most demanding: formal proofs from week one and abstract material that takes time to digest. Strong 5-unit high school math is expected. The payoff — both intellectual and in the job market — is high.
Should you combine math with a second major?
Usually yes. Math with computer science is the most popular track, combining theoretical depth with software skills; combinations with physics, statistics or economics open research and finance directions.
Where can you study this?
Mathematics is taught at all research universities — the Technion, Tel Aviv, Hebrew University, Ben-Gurion, Bar-Ilan, Haifa and the Open University. Combining it with computer science, physics or statistics is very common.