|
Lecturer(s)
|
-
Ševčík Petr, Mgr.
-
Kratochvíl Jiří Jaroslav, Mgr. Ph.D.
-
Emanovský Petr, doc. RNDr. Ph.D.
-
Broušek Martin, Mgr.
-
Kurač Zbyněk, Mgr.
|
|
Course content
|
1. Polynomials in one variable over integral domains and fields. 2. Euclidean algorithm, the greatest common divisor of two polynomials. 3. Roots of polynomials, multiple roots, Horner scheme. Common roots of two polynomials. 4. Polynomials over R and C; fundamental theorem of algebra. 5. Rational roots of polynomials over Z. Relation between roots and coefficients of a polynomial. 6. Algebraic equations. Binomial equations, the group of roots of unity. Algebraic solution of quadratic and cubic equation, Cardano's formula. Trigonometric solution of a cubic equation. Solution of some particular types of equations; reciprocal equations. 7. Polynomials in multiple variables. Symmetric polynomials, elementary symmetric polynomials, fundamental theorem of symmetric polynomials and its applications.
|
|
Learning activities and teaching methods
|
|
Lecture
|
|
Learning outcomes
|
The goal is a practical ability with polynomial computing as well as the computatins of roots of alberaic eqnations.
1. Knowledge Defines polynomials over rings and study their algebraic properties.
|
|
Prerequisites
|
secondary school mathematics, ALG 1
|
|
Assessment methods and criteria
|
Oral exam, Written exam
Credit: active participation in seminars.
|
|
Recommended literature
|
-
Bican L. (2004). Lineární algebra a geometrie. Academia Praha.
-
Blažek J. (1985). Algebra a teoretická aritmetika I. SPN Praha.
-
Hort D., Rachůnek, J. (2005). Algebra I. Olomouc.
-
Kuiper, N.H. (2016). Linear Algebra and Geometry. Haerbin gong ye da xue chu ban she.
-
Poole, D. (2014). Linear Algebra: A Modern Introduction. Cengage Learning.
-
Prasolov, V. V. (2016). Polynomials. Algorithms and Computation in Mathematics. Springer.
|