The student who successfully completes this course will have the following skills:

-Knowledge and ability to understand:

to use the rules of logic to study the way in which mathematical arguments are constructed

to use the structure of topological space

to analyze the structure of mathematical proofs and illustrate proof techniques by means of examples

to define the limit of a function and continuity of a function

to prove and to work with theorems relating to continuous functions beyond those found in elementary calculus

to define the derivative of a function andto establish properties of differentiable functions

to define the Riemann integral and to establish properties of integrable functions

-autonomy of judgment

to analyse new problems and to solve them

-communication skills

to use the mathematical language to describe and to solve problems