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 302. Section meets Friday 1:30-2:20 in Krieger 302.
Problem sets will be due in section on Fridays (see below for dates). No late homework will be accepted. The lowest grade will be dropped.
Office hours: W 3-5pm.
The syllabus is here.
ReferencesThe course text is
ExamsThere will be three exams. Two in class midterms and a final.
Week 1 (1/27 & 1/29) : Logic of Mathematical Proofs
Week 2 (2/3 & 2/5): Construction of the Real Numbers
Week 3 (2/10 & 2/12): Construction of the Real Numbers (cont.); Topology of the Real Number Line
Week 4 (2/17 & 2/19): Topology of the Real Number Line (cont.)
Week 5 (2/24 & 2/26): Continuous Functions
Week 6 (3/3 & 3/5): Continuous Functions (cont.); First Midterm
Week 7 (3/10 & 3/12): Differential Calculus
Week 8: Spring Break
Week 9 (3/24 & 3/26): Differential Calculus (cont.)
Week 10 (3/31 & 4/2): Integral Calculus
Week 11 (4/7 & 4/9): Integral Calculus (cont.); Second Midterm
Week 12 (4/14 & 4/16): Sequences and Series of Functions
Week 13 (4/21 & 4/23): Sequences and Series of Functions (cont.)
Week 14 (4/28 & 4/30): Sequences and Series of Functions (cont.)