The student will acquire the following skills:
1- Basic skills on mathematical reasoning including:
- Distinguish between implications and equivalence.
- Get familiar with the basic methods of mathematical proving like the method by contradiction or the method of mathematical induction.
- Learn to prove set inclusions and set identities.
2- Recognize linear and affine functions and plot them.
3- Handle and simplify polynomial equations and know the basic methods of polynomial root-finding.
4- To know the meaning of the basic trigonometric ratios.
5- To know the ratios of the remarkable angles (0º, 30º, 45º, 60º y 90º).
6- Relate the trigonometric ratios of an arbitrary angle with the ones of an angle between 0 and pi radians.
7- Relate the trigonometric ratios of complementary and supplementary angles.
8- Solve triangules.
9- Determine whether a given trigonometric identity is true or not.
10- Plot elementary trigonometric functions.
11- Identify and plot complex numbers.
12- Operate with complex numbers.
13- Obtain all different representations of a complex number (binary form, polar form, exponential form).
14- Obtain all n nth-roots of a complex number and plot them.
15- To know the Fundamental theorem of Algebra.
16- Compute the Row Reduced Echelon form of a matrix.
17- Solve linear systems using Gaussian elimination.
18- Obtain the matrix representation of a linear system.
19- Perform arithmetic operations with matrices.
20- Obtain the vector expression of a linear system.
21- Relate elementary row operations on a matrix with left products by elementary matrices.
22- Determine whether a given matrix of low size is invertible or not. In the affirmative case, compute its inverse using the algorithm related to the row reduced echelon form of the matrix.
23- Apply the recursive definition of the determinant for low-dimensional matrices.
24- Relate the determinant of a product of matrices with the determinants of each of the factors.
25- To know how the determinant changes when applying elementary row and column operations to the matrix.
26- Obtain the determinant of a matrix through an echelon form of the matrix.
27- Operate with vectors in R^n.
28- Relate the linear independence of a set of vectors with the solution of linear systems.
29- Determine whether a given small set of vectors is linearly independent or not.
30- To know the notion of spanning set and subspace spanned by a set of vectors.
31- Become familiar with the notion of basis of a subspace spanned by a set of vectors.
32- Become familiar with the notion of column space of a matrix.
33- Become familiar with the notion of null-space of a matrix and relate it with the solution of linear systems.