The Discrete Algebra and Geometry (DAG) group at the TU/e develops the mathematics needed for such a description. This unit introduces students to several related areas of discrete mathematics, which serve their interests. While the latter are typically modelled using real numbers, differential equations, and numerical computations, describing the discrete-algebraic aspects involves objects like nite elds, graphs, polynomials, groups, algebras, and symbolic computations. MATH2069: Discrete Mathematics and Graph Theory. Phenomena throughout mathematics and the natural sciences have discrete algebraic aspects, often along with analytical counterparts. The third main area in DM covers discrete algebra and geometry including ,enumerative and algebraic combinatorics. For a simple graph with no self-loops, the adjacency matrix must have 0s on the diagonal. Work in the groups in DM covers coding theory, optimization for data storage and recovery, network coding, quantum error correction, and links with cryptography in code-based cryptography, an area of post-quantum cryptography. The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in position (vi,vj) according to whether vi and vj are adjacent or not. Mathematical communication theory enables reliably communicating data over a possibly noisy channel, efficiently storing and retrieving them, and guaranteeing their integrity. To ensure correctness of security proofs, groups also work on applying tools from formal verification to verify proofs. Moreover, different groups work on analyzing the security of cryptographic schemes using cryptanalysis techniques (analyzing the underlying mathematical problems) and security proofs (relating the security of schemes and protocols to the security of used building blocks). A graph is a collection of points, called vertices, and lines between those points, called edges. Work in the groups in DM covers the design of systerms as well as building larger constructions and protocols, including multi-party computation. In discrete mathematics, we call this map that Mary created a graph. Cryptology is the mathematical theory of protecting information against unauthorized access (confidentiality), ensuring that a message has not been altered by a third party (integrity) and really originated from the person who is claimed to be the sender (authenticity).
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