MATH 4321 Fall 2024 Syllabus

Hall 219 MW 3:30pm – 4:45 pm

Hall 314U 4:45 pm– 5:30 pm; Anytime by appointment (please email me)

Typed notes below

1. Bartle's Introduction to Real Analysis,
2. Abbot’s Understanding Analysis,
3. Laczkovich-Sos' Real Analysis: Foundations and Functions of One Variable,
4. Pugh's Real Mathematical Analysis,
5. Rudin's Principle of Mathematical Analysis
6. "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

Real Analysis: Functions of a real variable (last update: Oct. 12, 2024, 6:45 p.m.)

If(when) you find a typo please email me :)

- Sets
- Functions
- The natural numbers
- Finite Sets
- Countable sets
- Sets Exercise Class
- Fields
- Intervals
- ** Extra credit and Group work **
- Sequences
- Properties of sequences
- Series

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 21

Midterm I with *** Solutions ***