Portal:Mathematics
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Welcome to the Mathematics Portal! This page connects visitors to the learning resources that have been developed by various Wikiversity content development projects. Wikiversity participants who are interested in mathematics are invited to create and develop learning projects and learning resources and help organize them by developing this portal.
Linear algebra (Osnabrück 2024-2025)/Part I
Linear algebra is a fundamental course in mathematics. It deals with "linear structures“: linear systems of equations, vectors and their representation, bases and base change, linear mappings and matrices, determinants, eigenvalues and eigenvectors, optimal descriptions of linear mappings, affine mappings, normed vector spaces, lengths and angles, analytic geometry, isometries and symmetries, bilinear forms, more general algebraic structures like equivalence relations, groups, residue class construction, and multilinear algebra.
One could learn the following topics in the following order, although it is also possible to skip certain courses according to one's interests.
These courses are also the most commonly found courses in a mathematics undergraduate concentration in English-speaking universities. However, universities will differ in their course titles and content.
At many universities, a minimal sequence of courses to earn a degree in mathematics could include: Calculus 1 through 3, linear algebra, discrete mathematics, differential equations, real analysis 1 and 2, abstract algebra 1 and 2. Studying these courses would nearly approximate a four-year mathematics degree. However, note that most students with a four-year degree also take "elective" mathematics courses beyond the minimum requirement.
- Arithmetic (no prerequisites)
- Algebra and Geometry (requires arithmetic)
- Discrete Mathematics (requires algebra)
- Introductory Statistics (requires algebra)
- Calculus 1 (requires algebra and geometry)
- Linear Algebra (requires algebra and geometry)
- Calculus 2 (requires calculus 1)
- Differential Equations (requires calculus 2 and linear algebra)
- Calculus 3 (requires calculus 2 and linear algebra)
- Mathematical Statistics (requires calculus 3)
- Mathematical Logic (requires discrete math)
- Modern Analysis (requires calculus 1 and linear algebra)
- Modern Algebra (requires discrete mathematics)
- Set Theory (requires discrete mathematics)
- Number Theory (requires discrete mathematics)
- Complex Analysis (requires modern analysis)
- General Topology (requires modern analysis)
- Combinatorics (requires discrete mathematics)
- Differential Geometry
- Partial Differential Equations
- Measure and Integration Theory (requires modern analysis)
- Functional Analysis (requires measure and integration theory)
- Probability Theory (requires modern analysis and mathematical statistics)
- Algebraic Topology
Many mathematics-related learning resources are for specific scientific sub-disciplines and can be found with the aid of other Wikiversity portals: Engineering and Technology - Life Sciences - Physical Sciences - Social Sciences - - General Science Portal
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