University of California, Berkeley

Spring 2009

This is an introductory course on analysis.

The official prerequisites for taking this course are Math 53: Multivariable Calculus and Math 54: Linear Algebra and Differential Equations.

- 05/12/09: Solutions to Problem Set 10 posted.
- 05/10/09: Extra office hours this week: 2–3 on Mon, Wed, 1–3 on Fri.
- 05/10/09: Final exam to be held 5–8, Mon, May 18, in 150 GSSP.
- 05/09/09: Problem Set 10 posted.
- 05/09/09: Revision lecture, 3–4:15pm, Mon, May 11.
- 05/08/09: Solutions to Problem Set 9 posted.
- 05/07/09: Solutions to Problem Set 8 posted.
- 05/02/09: Problem Set 9 posted.
- 04/30/09: Solutions to Problem Set 7 posted.
- 04/27/09: Solutions to Problem Set 6 posted.
- 04/26/09: Solutions to Problem Set 5 posted.
- 04/25/09: Problem Set 8 posted.
- 04/25/09: Make-up lecture 4–5pm, Fri, May 08.
- 04/17/09: Problem Set 7 posted.
- 04/17/09: Prof. Shamgar Gurevich will be holding office hours on my behalf next week. Venue: Evans 869. Time: 1:30–2:30. Dates: Mon, Apr 20 & Wed, Apr 22.
- 04/09/09: Problem Set 6 posted.
- 03/31/09: Problem Set 5 posted.
- 03/21/09: Solutions to Problem Set 4 posted.
- 03/14/09: Fri office hours next week moved to Wed 1:30–3.
- 03/14/09: Problem Set 4 posted.
- 03/04/09: Solutions to Problem Set 3 posted.
- 02/28/09: Solutions to Problem Sets 1 & 2 posted.
- 02/28/09: Midterm exam to be held 3–4, Fri, Mar 06.
- 02/26/09: Problem Set 3 posted.
- 02/17/09: Problem Set 2 posted.
- 02/12/09: Office hours next week: 1:30–3, Wed, Feb 18.
- 02/12/09: No lecture next Fri, Feb 20.
- 02/05/09: Problem Set 1 posted.
- 01/14/09: Check this page regularly for announcements.

**Location:** Evans Hall,
Room 71

**Times:** 3:00 PM–4:00 PM on Mon/Wed/Fri

**Instructor:** Lek-Heng
Lim

Evans Hall, Room 873

`lekheng(at)math.berkeley.edu`

(510) 642-8576

**Office hours:** 1:30–3:00 PM, Mon and 1:00–2:30 PM, Fri

- Real number system
- Sequences
- Limits
- Continuous functions on
**R**and**R**^{n} - Metric space
- Uniform convergence
- Interchange of limit operations
- Infinite series
- Differentiable functions on
**R**and**R**^{n} - Mean value theorem
- Riemann integral

Homework will be assigned once a week and will be due the following week (except possibly in the weeks when there is a midterm). Collaborations are permitted but you will need to write up your own solutions.

- Problem Set 10: PDF (posted: May 09; due: May 15); Solutions: PDF (posted: May 12)
- Problem Set 9: PDF (posted: May 02; due: May 08); Solutions: PDF (posted: May 08)
- Problem Set 8: PDF (posted: Apr 25; due: May 01); Solutions: PDF (posted: May 07)
- Problem Set 7: PDF (posted: Apr 17; due: Apr 24); Solutions: PDF (posted: Apr 30)
- Problem Set 6: PDF (posted: Apr 09; due: Apr 17); Solutions: PDF (posted: Apr 27)
- Problem Set 5: PDF (posted: Mar 31; due: Apr 08); Solutions: PDF (posted: Apr 26)
- Problem Set 4: PDF (posted: Mar 14; due: Mar 20); Solutions: PDF (posted: Mar 21)
- Problem Set 3: PDF (posted: Feb 26; due: Mar 04); Solutions: PDF (posted: Mar 04)
- Problem Set 2: PDF (posted: Feb 17; due: Feb 25); Solutions: PDF (posted: Feb 28)
- Problem Set 1: PDF (posted: Feb 05; due: Feb 11); Solutions: PDF (posted: Feb 28)

**Bug report** on the problem sets or the solutions:
`lekheng(at)math.berkeley.edu`

**Grade composition:** 40% Homework, 20% Midterm, 40% Final

- Kenneth Ross,
*Elementary Analysis: The Theory of Calculus*, Springer, 2003.

- W. Rudin,
*Principles of Mathematical Analysis*, 3rd Ed., McGraw Hill, 1973.

- Tom Körner's notes: 2001, 2007; Martin Hyland's notes

- Richard Earl's notes I: Sequences and Series, Brian Stewart's notes II: Continuity and Differentiability, Terry Lyons's notes III: Integration