Problems

Exercises

Exercises from [Foll13]:

• Chapter 1:

  • Exercises 3 (with the sets in 3(a) nonempty), 7, 10, 12, 14

  • Exercises 15, 17, 18, 19, 22(a), 24, 28

  • Exercises 26, 30, 31

• Chapter 2:

  • Exercises 2, 3, 7, 9 (in 9(c), Exercise 1.29 may be used without proof)

  • Exercises 10, 12, 13, 14, 16, 19

  • Exercises 24, 25, 28(a,b), 33, 34, 35, 38, 41; Exercise 24 shows that upper sums are not needed in the definition of the integral

  • Exercises 40, 44, 47, 49, 50, 51, 52, 54, 56, 58, 59

• Chapter 3: Exercises 3(b,c), 5, 6, 9, 12, 13, 14, 16, 20, 21, 22

• Folland exercises, clipped

Problem collections and exam archives

• List of real analysis problems

• Measure theory qualifying exam problems

• LSU analysis test bank (2009)

• UCLA basic exam problems: analysis

• Analysis qual problem collection

• Math 4100/6100 Sequences and Series / real-analysis assignments (Fall 2020) – nine assignments spanning sequences and series, limsup/liminf, cardinality, topology of the real line, continuity, differentiation, and uniform convergence, with 67 regular, bonus, and challenge problems.

• Analysis exam, January 2014

• Analysis exams, 2008–2013

• Analysis exams, 2014–2016

• Analysis exams, 2003–2007

• Mark Coleman’s MATH341 problem sheets (Manchester)

• UC Riverside historical real analysis qualifying exams

• Johns Hopkins analysis graduate exams

Qualifying exam workshop

UNL real-analysis workshop is the UNL real analysis workshop packet, organized by day, with links to the source PDFs; Days 1, 9, and 10 are the corresponding qualifying exam collections.