Time: MWF 12 pm
Location: David Kinley Hall 206
Instructor: Marius Junge Office hours: Thursday 5-6
URL: https://canvas.illinois.edu/enroll/NGPNLX (for self enrolment)
Gradebook RK4XjP
Tasks:
Task 1: Learn how to write proofs !!!!!
Task 2: Learn the rigorous basics of calculus!
Subtasks:
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
