MATH 4321 Real Analysis, Fall 2024
Syllabus
MATH 4321 Fall 2024 Syllabus
Class meeting
Hall 219 MW 3:30pm – 4:45 pm
Office hours
Hall 314U 4:45 pm– 5:30 pm; Anytime by appointment (please email me)
Main Reference
Typed notes below
Suggested References:
- Bartle's Introduction to Real Analysis,
- Abbot’s Understanding Analysis,
- Laczkovich-Sos' Real Analysis: Foundations and Functions of One Variable,
- Pugh's Real Mathematical Analysis,
- Rudin's Principle of Mathematical Analysis
- "Survey Article: The real numbers–A survey of constructions." Rocky Mountain J. Math. 45 (3) 737 - 762, 2015. https://doi.org/10.1216/RMJ-2015-45-3-737
Typed Notes
Real Analysis: Functions of a real variable (last update: Oct. 11, 2024, 9:35 p.m.)
If(when) you find a typo please email me :)
(Raw) Notes
- Sets
- Functions
The Natural numbers and countable sets (
Exercises)
- The natural numbers
- Finite Sets
- Countable sets
- Sets Exercise Class
- Fields
- Intervals
- ** Extra credit and Group work **
Sequences and Series of Real numbers (
Exercises)
- Sequences
- Properties of sequences
Homeworks
There will be a homework each week. These assessed questions will collectively count for 20% of your overall grade.
- HW 1: Choose 5 problems of the exercises sheet for 'Sets and Functions'. Deadline: Sep 4 (Solutions .tex template I use TexShop(local) or overleaf(online) to edit latex files)***SOLUTIONS***
- HW 2: Choose 5 problems of the exercises sheet for 'The Natural numbers and countable sets'. Deadline: Sep 11 ***SOLUTIONS***
- No Homework this week due to the Exam next week.
- HW 3: 1,2,3,4,5 of 'The real numbers' exercises sheet. Deadline: Sep 30
- Extra credit 1: Choose one: Explain Dedekind's constructions of the real numbers (Dedekind cuts) or Explain Cantor's construction of real numbers (Cauchy Sequences). Deadline: Sep 30
- HW 4: 15,19,22,30,31 of 'The real numbers' exercises sheet. Deadline: Oct 14
- HW 5: 1,4,6,12,13 of 'Sequences and Series of Real number' exercises sheet. Deadline: Oct 16
Exams
Midterm I with *** Solutions ***