Math 444-E13-Inroduction to real analysis

Time:  MWF 12 pm

Location: David Kinley Hall 206

Instructor: Marius Junge      Office hours: Thursday 5-6

URL:    (for self enrolment)

Gradebook RK4XjP

Book: Introduction to Real Analysis by Bartel and Sherbert


Task 1:  Learn how to write proofs !!!!!

Task 2:  Learn the rigorous basics of calculus!


        Foundation:   Sets, Natural Numbers, Rationals and Real Numbers, Completeness and cardinality    

        Sequences:   Monotone, convergent, limits and limit rules, the set of limits, Bolzano Weierstrass, first                                           applications to continuous functions. 

        Topology: What are open, closed and compact sets? 

        Continous functions: Elementary properties, uniform continuity, invertibility.

        Differentiation: Basics, Mean Value, de l’Hopital and Taylor’s theorem. (can we prove what we promised?)

        Integration: Riemann and Darboux inegral, Integrability criteria, Fundamental Theorem 

        Everything else: Just for fun             



Grading: 30% HW (submission in pairs), 30 % midterm, 30% final, 10 % participation in other activities