math104:start

$$\gdef\Q{\mathbb{Q}}$$

Instructor: Peng Zhou

Email: pzhou.math@berkeley.edu

Office: Evans 931

Office Hour: Monday 12:10-1pm, Tuesday 11:10-12. Friday 10-11pm

Lecture: MWF, 11:10am - 12:00. Etcheverry 3107.

GSI: James Dix. Mondays 9am-6pm, Wednesday 12-2pm in Evans 1049.

Online Help:

- Zoom chat channel: search for “Math 104 with Peng Zhou”, then you will find the channel. I will answer question there.
- My zoom office: https://berkeley.zoom.us/j/97935304012 time by appointment.

- Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross. springer link (UC login required).
- Principles of Mathematical Analysis, by Walter Rudin
- Introduction to analysis, by Terry Tao. ( springer link )

20% homework; 2 midterms 20% + 20%; and final 40%. If you didn't do well in one of the midterm, you have the option to drop it, and final will have a 60% weight. The lowest homework grades will be dropped.

Midterm date: 9/22 (Wed), 11/3 (Wed). There will be no make-up midterms.

Homework will be submitted via gradescope. Entry Code:YVZRDZ

part 1: number system, sequence and limit, series.

part 2: metric space and topology. continuity.

part 3: differentiation and integration.

- Aug 25: introduction. counter-examples. Tao, Ch 1.
- Aug 27: Peano Axioms for natural numbers. (Tao Ch2). Inadequacy of $\Q$. Least upper bound (Rudin Ch 1, section 1)
- Reading homework; Tao Ch 1 and 2. Rudin Ch 1.
- HW 1 (with solution): due next Tuesday (Aug 31) 6pm

- Aug 30: More about sup. Definition of field.
- Sep 1: Cauchy sequence of rational numbers.(Tao 5.2)
- Sep 3: Equivalent Cauchy sequences of rational numbers as real numbers. Operation and properties of real numbers. (Tao 5.3)
- HW 2 (with Solution): Due next
**Thursday**6pm. (Due date changed)

Tao 5.3-5.5

- Sep 8: arithmetic operation on $\R$.
- Sep 10: order on $\R$, and least upper bound property of $\R$.
- HW 3: due next Tuesday (Sep 14) 6pm

Tao Ch 6. Ross Ch 2.1 - 2.7.

- Sep 13: Sequences in $\R$. Convergent implies Cauchy. Arithmetic operation commute with limit. Bounded monotone sequences are convergent. limsup.
- Sep 15: $\pm \infty$. Tao 6.4. Cauchy sequences are convergent.
- Sep 17: Finish Cauchy sequence is convergent. Limit points and subsequence.
- HW 4 Due next Tuesday 6pm

- Sep 20
- Sep 22 (Midterm 1)
- Sep 24

- Sep 27
- Sep 29
- Oct 1

math104/start.txt · Last modified: 2021/09/16 10:47 by pzhou