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[4] [5] If used as part of a summative assessment they are usually given a low weight, [6] between 10% and 25% of the total mark of the course for all problem sets put together, [3] [5] and sometimes will count for nothing if the student receives a better grade on the exam. Alternatively, problem sets may be used purely for formative assessment ...
6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
The problem asks, given an undirected graph, how many maximal independent sets it contains. This problem is #P-hard already when the input is restricted to be a bipartite graph. [15] The problem is however tractable on some specific classes of graphs, for instance it is tractable on cographs. [16]
Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A connected dominating set is a dominating set that is also connected.If S is a connected dominating set, one can form a spanning tree of G in which S forms the set of non-leaf vertices of the tree; conversely, if T is any spanning tree in a graph with more than two vertices, the non-leaf vertices of T form a connected dominating set.
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. [1] In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching.
The main problems identified in the audit included: a fall in the level of employment, low rates of completion of works (only 30.3 per cent of planned works had been completed), poor planning (in one-third of Gram Panchayats, the planning process mandated by the act had not been followed), lack of public awareness partly due to poor information ...