Instructor:
Wee Teck Gan
wgan@math.ucsd.edu
Lectures: MWF 11 am-11:50am in U413, Room 2
Office Hours: Mon 3-4pm and Wed 2-3pm in AP&M 7240
Teaching Assistant: Ben Wilson
bewilson@math.ucsd.edu.
Section: A01: W 4-4:50 pm, and A02: W 5-5:50 pm in CENTER 201
TA Office Hours:
T 1:30-2:30 pm, Th 1-2 pm, F 10-11 am or by appointment, in AP&M
6452.
Text: "Principles of Mathematical Analysis" (third edition) by Walter Rudin, McGraw-Hill.
Syllabus: 140ABC is a rigorous introduction to mathematical
analysis. In particular, it gives rigorous development of the
foundations necessary for calculus.
Most of what we will cover in 140A is in
chapters 1-4 of Rudin. The topics are the real and complex
number systems, cardinalities, topology of Euclidean space, the notion of metrics and metric spaces, limits,
connectedness, completeness and compactness, continuous functions, sequences and series. A less rigorous
treatment is given in Math 142AB, but credit cannot be obtained for both
140AB and 142AB.
Prerequisites: MATH 109.
Homework: Homework is due on Fridays, 3pm, in the TA's dropbox (in AP&M, 6th floor). Late homeworks will not be accepted.
It is OK, even encouraged, to discuss homework problems with your classmates, but you are required to write up your own solutions. Please write legibly and in coherent sentences.
Each week, 3 of the hoemwork problems will be selected for grading, one of which is the one marked with a * below. The problem marked with a *
will not be discussed in sections or during office hours..
HW 1 (Due 10/3): Chap. 1, # 1, 2*, 3, 4, 5
HW 2 (Due 10/10): Chap 1, # 6, 7, 8*, 9, 10, 12, 13, 16, 17, 18, 19
HW 3 (Due 10/17): Chap. 2, # 2, 3, 4, 5*, 6, 7, 8 9
HW 4 (Due 10/24): Chap. 2, # 11, 19, 20*, 22, 23, 24
HW 5 (Due 10/31): Chap. 2, # 12, 13, 15, 16, 25*, 26, 29
HW 6 (Due 11/7): Chap. 2, # 27, 28; Chap 3: # 1, 3, 20*, 23
HW 7 (Due 11/14): Chap. 3, # 4, 5*, 24, 25
HW 8 (Due 11/21): Chap. 3, # 6, 7, 8, 9, 10, 11, 12*
HW 9 (Due 12/5): Chap. 3, # 13, 16; Chap. 4: # 1, 2, 4, 6*, 8, 11, 20, 21
Exams:
Midterm 1: Fri, Oct 17 in class.
Sample Midterm 1
Midterm 2: Fri, Nov 14 in class.
Sample Midterm 2
Final: Tues, Dec 9.
Sample Final
Grading:
Homework: 20%,
2 midterm exams: 15% each, final exam: 50%.
(The lowest homework score will not be counted. Missed exams will
count zero.)
Approximate Lecture Schedule (may be updated during the course):
wk | date | Monday | Wednesday | Friday |
0 | 9/22 | Rational Numbers, Incompleteness | ||
1 | 9/29 | Ordered Sets and fields | The Real Numbers | Dedekind Cuts |
2 | 10/6 | Complex Numbers and Euclidean Spaces | Infinity: Countable and Uncountable | Metric Spaces |
3 | 10/13 | Metric Spaces | Open/Closed Sets | Exam |
4 | 10/20 | Open/Closed sets | Connected sets | Compact Sets |
5 | 10/27 | Compact Sets | Heine-Borel and Bolzano-Weierstrass | Cantor Set |
6 | 11/3 | Convergent and Divergent sequences | Cauchy sequences and completeness | Upper and lower limits |
7 | 11/10 | Series | e | Exam |
8 | 11/17 | Tests | Power Series | Absolute Convergence and Rearrangements |
9 | 11/24 | Continuity | Uniform Continuity | Holiday |
10 | 12/1 | Continuity and Compactness | Continuity and Connectedness | Review |
11 | 11/9 | 11/9 Exam |