Math 104. Introduction to Analysis
Department of Mathematics
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.
Announcements
- 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.
Lectures
Location: Evans Hall,
Room 71
Times: 3:00 PM–4:00 PM on Mon/Wed/Fri
Course staff
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
Syllabus
- Real number system
- Sequences
- Limits
- Continuous functions on R and Rn
- Metric space
- Uniform convergence
- Interchange of limit operations
- Infinite series
- Differentiable functions on R and Rn
- 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
Supplementary materials
Grades
Grade composition: 40% Homework, 20% Midterm, 40% Final
Textbooks
- Kenneth Ross, Elementary Analysis: The Theory of Calculus,
Springer, 2003.
- W. Rudin, Principles of Mathematical Analysis, 3rd Ed., McGraw
Hill, 1973.