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. Abbots 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

Sets and Functions (Exercises)
- Sets
- Functions
The Natural numbers and countable sets (Exercises)
- The natural numbers
- Finite Sets
- Countable sets
- Sets Exercise Class
The real numbers (Exercises)
- Fields
- Intervals
Sequences and Series of Real numbers (Exercises)
- Sequences
- Properties of sequences
- Series
Topology of R (Exercises)
- Open sets
- Closed and compact sets
Limits (Exercises)
- Limits
Continuity (Exercises)
Derivatives (Exercises)

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 ***SOLUTIONS***
• HW 6: 17,21,23,29,30 of 'Sequences and Series of Real number' exercises sheet. Deadline: Oct 23 ***SOLUTIONS***
• No homework this week, please study for the group work we began today (namely, the exercise sheet 'Topology of R')
• HW 7: 1,4,6,7,8 of 'Continuity' exercises sheet. Deadline: Nov 11
• Derivatives Exercises ***SOLUTION IDEAS***
• Continuity Exercises ***SOLUTION***

Exam 1 with *** Solutions ***

Exam 2 with *** Solutions ***

Exam 3 with *** Solutions ***

Final Exam w/solutions