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.  

Notes

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

 

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





Grading:
Homework   (40)

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



Final:  see uncombined schedule




Homework1:
Homework: See folder in Box, contact me if not invited

Additional Material: See Box
   

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