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| NMAA11 | Algebra, 5 p (sw) /ALGEBRA/ Advancement level: A | |
| Aim: To familiarize students with the concepts introduced in the course so that they may use them with confidence in courses at a higher level.Prerequisites: Admission to the course requires, as well as general university entrance requirements, secondary school matematics E (or equivalent). Course organization: The course is taught in lectures, and problem classes.Course content: Elementary logic. Set theory. The integers: induction, divisibility properties, prime numbers, Euclid's algorithm, diophantine equations, position system. Combinatorics: the multiplication principle, permutations and combinations, binomial theorem. Real numbers: rules of calculation and logical structure of the natural, rational and real numbers. Complex numbers: rules of calculation and elementary concepts, triangle inequality, polar form, the exponential function, binomial equations, quadratic equations. Polynomials and algebraic equations: divisibility properties, roots and zeroes, the factor theorem, multiplicity, the fundamental theorem of algebra, connection between roots and coefficients. Analytic geometry: vectors, basis vectors, coordinates, coordinate systems, scalar products, orthogonality, lines and planes, vector product. Course literature: Vretblad, A: Algebra och geometri. Compendium published by the Department of Mathematics. | ||
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