Foundations of analysis

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Foundations of analysis

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
3 + 2	3 + 2	exam + term grade	all	mm1c1ap2 mm1c2ap2	2	alternative

Course coordinator

Strong	Weak	Prerequisites
Practice class
Practice class		Strong: Calculus1L (mm1c1ka1)
Lecture
		Weak: practice class
		Weak: Calculus2L (mm1c1ka2)

Remarks

You have to take exactly one of the following two equivalent sets of courses: {Analysis 1, Analysis 2} or {Calculus 1, Calculus 2, Foundations of analysis}.

Syllabus designed by:

Course objectives

Fill the gap between the analysis and calculus courses.

Syllabus

Real numbers, frequently used inequalities, boundedness, upper and lower bounds, powers.
Finite and infinite limit of real sequences, operations, inequalities for limits, monotonicity.
Limit and continuity of functions, operations and inequalities for function limits.
Mean value theorems for derivatives, Taylor formula.
Riemann integral and integrability, Newton--Leibniz formula.
Applications: Stirling's and Wallis' formula.