MATA171 Introduction to mathematical analysis 1 (5 cr)

Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

Description

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.

Learning outcomes

The student
  • 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 

Description of prerequisites

Good command of the long mathematics curriculum of high school.

Study materials

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.

Completion methods

Method 1

Description:
Final exam and exercises. The weekly exercises are handed in and graded. To attend the final exam, the students must receive enough bonus-points from the exercises (the exact amount is mentioned in the teaching schedule).
Evaluation criteria:
Final exam and weekly exercises.
Time of teaching:
Period 1
Select all marked parts

Method 2

Description:
Final exam.
Evaluation criteria:
Final exam score.
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish
Study methods:

Lectures (in Finnish) 36 h, exercises

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
Study materials:

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.

Teaching