Real Analysis Qual Prep

Meeting times: Please refer to email sent.

Official Qualifying Exam Date and Time: Monday, September 21 at 1pm

Please feel free to contact me for any reason at nchie005@ucr.edu

Approximate weekly outline:

1. Undergraduate

   • Continuity 

   • Convergence

   • Derivatives

   • Integration

2. Real A

   • Convergence Theorems

   • Measures

   • Measurable sets and functions

   • Limits

   • Fubini-Tonelli

3. Real B

4. Real C

5. Mock Qual

6. Reflection of Mock Qual

7. Mock Qual

Week 1 

• Day 1 (July 28): Continuity and convergence worksheet 

  • 1. Link to wiki for Thomae's Popcorn Function, which can be used for problem 7 on continuity and convergence. If a solution is needed for a reference please email me.

    2. Keep in mind common examples like x and x^2.

• Day 2 (July 29): Derivatives and Integration worksheet 

  • 1. Present solutions for at least one problem from continuity and convergence worksheet.

    2. TYPO in Q1, should say assume f(x) has continuous... instead of show f(x)...

    3. Important to know how to run the partition arguments for integration.

Week 2: Real A worksheet 

1. Please ensure to do all the convergence problems.

2. Typo in Q3 from measures section, the right hand integral should state d\mu.

Week 3: Real B Worksheet 

I recommend doing the second problem for LRN, as this problem personally helped me truly understand the theorem. 

Week 4: Real C Worksheet  

Please do all the "recommended problems".

Topology: Nets, Tietze, Urysohn

Week 5: Practice qual

Week 6:

Week 7: