MATH 444- Introduction to Real Analysis

Time:  MWF 10:00-1:50pm

Location:  Altgeld Hall  242 

Instructor: Marius Junge    

Grader:  TBA

Office hours:  Thursday 5-6

Course description

Introduction to real analysis is a gateway. The idea is to find  balance between rigorous proofs and real understanding - this principle is the core of mathematics at all levels.

Be prepared to learn to write proofs.

I: Real Numbers 

What are real numbers?; sets, maps, functions, cardinality; Natural numbers, equivalence relations, integers, rational numbers, fields, ordered fields; complete ordered fields.  


II: Sequences

Limits, monotone sequences, subsequences, Bolzano-Weierstrass, limsup and liminf, series.

III: Continuous Functions

Definition and permanence properties,  uniform continuity, removing singularities, monotonicity, inverse function and intermediate alue theorem 

IV: Differentiation 

Basic rules, mean value theorem and taylor

IV: Integration 

Different definition and Fundamental Theorems. Applications. 

V: Power Series 

Interchanging limits, examples. 

VI: Misselinia


Elementary Analysis: The Theory of Calculus by Kenneth Ross, 2 edition, Springer

Homework   (40)

Midterm1   September 27 
Midterm2   October  24
Midterm2   November  15 (if necessary-probably take home)

Final:  see uncombined schedule

Homework: See folder in Box, contact me if not invited

Additional Material: See Box

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