MATA171 Introduction to mathematical analysis 1 (5 cr)

Inequalities, functions, supremum and infimum (least upper bound and greatest lower bound), completeness of real number system, limit of a sequence and the algebraic properties of limit, monotonic sequences.

In this study-module, students practice reading and writing mathematics. They learn basics of logic and practice proving mathematical statements.

• knows the epsilon-definition for the limit of a number sequence, and can prove simple statements using that definition.
• is able to use the algebraic properties of limit to study the convergence of sequences
• knows how to apply the convergence criteria for monotonic sequences
• is familiar with the definitions of supremum and infimum, and can determine the supremum and infimum of a given set
• can use inequalities to estimate the size of a given expression
• is familiar with the basic terminology associated to functions
• can read proofs and follow their logical structure.
• can produce simple proofs 

Good command of the long mathematics curriculum of high school.

The contents of the study-module correspond to:

D. Brannan: A first course in mathematical analysis, chap. 1-2, or

P. Fitzpatrick: Advanced Calculus, chap. 1-2.