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The course in basic algebra is devoted to fundamental algebraic notions that are demonstrated on basic algebraic
structures. Notions include closure systems, operations, algebras (as sets with operations), homomorphisms, congruences,
orderings and the divisibility. Lattices, monoids, groups, rings and fields are regarded as the basic structures. The course
also pays attention to modular arithmetic and finite fields.
Last update: T_KA (20.05.2009)
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There will be four homework sets, each worth 25 points. To get credit (zápočet) you need to get 64 points in total. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (16.10.2023)
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Lecture notes: https://www.karlin.mff.cuni.cz/~kompatscher/teaching/alg1_en.pdf
S. Lang, Algebra, 3rd ed. New York 2002, Springer. S. MacLane, G. Birkhoff, Algebra 3rd ed, Providence 1999, AMS Chelsea publishing company. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (16.10.2023)
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The course will be ended by a written exam followed by an oral exam based on the results of the written one. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (16.10.2023)
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1) Number theory: prime factorization, congruences, Euler's theorem and RSA, the Chinese remainder theorem 2) Polynomials: rings and integral domains, polynomial rings, irreducibility, GCD, the Chinese remainder theorem and interpolation, the construction of finite fields and applications (error-correcting codes, secret sharing,...) 3) Group theory: permutation groups, subgroups, Lagrange's theorem, group actions and Burnsides's theorem, cyclic groups, discrete logarithm and applications in cryptography
see also: https://www.logic.at/staff/kompatscher/algebra1.html Last update: Kompatscher Michael, Ph.D. (28.09.2021)
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