Math 405: Introduction to Real Analysis
This is an introduction to real analysis. Topics covered in the course will include, The Logic of Mathematical Proofs, Construction and Topology of the Real Line, Continuous Functions, Differential Calculus, Integral Calculus, Sequences and Series of Functions. There will be 10 problem sets (20% of final grade), two in class midterm exams (20% each) and one final exam (40%).
Lectures are Monday and Wednesday 1:30-2:45 in Krieger 300. Section meets Friday 1:30-2:20 in Krieger 300.
Problem sets will be due in class on Wednesdays (see below for dates). No late homework will be accepted. The lowest grade will be dropped.
Lecturer office hours: Tuesday, 3-5pm or by appointment in Krieger 408.
TA office hours: Thursday, 4-5pm in Krieger 211.
The syllabus is here.
ReferencesThe course text is
ExamsThere will be three exams. Two in class midterms and a final.
Week 1 (1/26 & 1/28) : Logic of Mathematical Proofs
Week 2 (2/2 & 2/4): Construction of the Real Numbers
Week 3 (2/9 & 2/11): Construction of the Real Numbers (cont.); Topology of the Real Number Line
Week 4 (2/16 & 2/18): Topology of the Real Number Line (cont.)
Week 5 (2/23 & 2/25): First Midterm; Continuous Functions
Week 6 (3/2 & 3/4): Continuous Functions (cont.)
Week 7 (3/9 & 3/11): Differential Calculus
Week 8: Spring Break
Week 9 (3/23 & 3/25): Differential Calculus (cont.); Integral Calculus
Week 10 (3/30 & 4/1): Integral Calculus (cont.);
Week 11 (4/6 & 4/8): Second Midterm; Integral Calculus (cont.);
Week 12 (4/13 & 4/15): Sequences and Series of Functions
Week 13 (4/20 & 4/22): Sequences and Series of Functions (cont.)
Week 14 (4/27 & 4/29): Picard iteration and the existence theory for ODEs.