Instructor: Peng Zhou
Office: Evans 931, zoom office
Office Hour: TuTh, 11:10 - 12:30, Friday 4-4:50 (zoom, by appointment. send me a message on discord to let me know)
Lecture: TuTh 9:30A-10:59A at Evans 3
Final : Wed, May 11, 11:30A - 2:30P • Evans 3
GSI: Jacobo, Evans 747. zoom office.
What do we cover in this class? It will consist of three parts
How to learn this course? One should
How do we grade? Our grade will consist of
participation (20%) + midterms (30%) + final (50%).
Weekly homework is part of participation, and is not graded based on correctness.
It is hard to quantify participation, and I don't want to assign grade based on how many sentence you say. If one has to set a criterion, let's say, each week, you should
We will have two in-class midterms, and the one with the lower grade will be dropped.
The final is accumulative, 3-hour in class.
We will be using three textbooks
Some other lecture notes might be useful
We will first cover sequence and limits, mainly following Ross and Tao-I
Then, we will cover metric space topology and continuous functions, where we will follow Rudin and Tao-II.
Finally, we will cover integration and differentiation, following Rudin.
|Lecture||Date Day||Content||Reading||Notes and Videos|
|Lecture 1||Jan 18 Tue||Number system $\R$||Ross §1 - §4||note, video|
|Lecture 2||Jan 20 Thu||Completeness Axioms and Sequence||Ross §4, §7||note, video, HW1|
|Lecture 3||Jan 25 Tue||Basic properties and examples of limits||Ross §9||note, video|
|Lecture 4||Jan 27 Thu||monotone seq, limsup, liminf||Ross §10||note, video,HW2|
|Lecture 5||Feb 1 Tue||Cauchy Seq, Subseq||Ross §10, §11||video|
|Lecture 6||Feb 3 Thu||Subseq, limsup liminf||Ross §11, §12||video,HW 3|
|Lecture 7||Feb 8 Tue||more on limsup/liminf , Series||Ross 12, 14||video|
|Lecture 8||Feb 10 Thu||More on series. Rearrangements||Rudin, Ch 3||video , HW4|
|Lecture 9||Feb 15 Tue||review|
|Lecture 10||Feb 17 Thu||midterm 1,stat (no Office Hour today)||2021-spring||No HW|
|Lecture 11||Feb 22 Tue||Exam review. Begin metric space.|
|Lecture 12||Feb 24 Thu||closure, limit points||Ross 13||video HW 5|
|Lecture 13||Mar 1 Tue||More metric spaces. Continuous function||Pugh Ch 2||video|
|Lecture 14||Mar 3 Thu||Compactness||video HW6|
|Lecture 15||Mar 8 Tue||Theorems about Compactness. Connectedness.||Rudin 2.41, 2.45-2.47||video|
|Lecture 16||Mar 10 Thu||Connectedness.||Rudin 4.13 - 4.27||video , HW 7|
|Lecture 17||Mar 15 Tue||Discontinuity. Uniform Continuity||Rudin Ch 4||video|
|Lecture 18||Mar 17 Thu||Sequence and Convergence of functions||Rudin Ch 7.1, 7.2||video HW 8|
|Spring Recess||Mar 22 Tue|
|Spring Recess||Mar 24 Thu|
|Lecture 19||Mar 29 Tue||Differentiation. Mean Value Theorem||video(partially recorded)|
|Lecture 20||Mar 31 Thu||L'hopital rule.||video No HW|
|Lecture 21||Apr 5 Tue||Midterm 2||solution|
|Lecture 22||Apr 7 Thu||Review of Midterm 2. Taylor Theorem||video , HW 9|
|Lecture 23||Apr 12 Tue||Power Series. Riemann integral||Ross 32||video|
|Lecture 24||Apr 14 Thu||Riemann integral, weight function||Ross 33, 35||no video, HW 10|
|Lecture 25||Apr 19 Tue||More on integrability||Rudin Ch 6||video, note|
|Lecture 26||Apr 21 Thu||Integration and Differentiation||Rudin Ch 6||video note, HW 11|
|Lecture 27||Apr 26 Tue||uniform convergence and $\int, d/dx$||Rudin Ch 7, p151-153||video, note|
|Lecture 28||Apr 28 Thu||review of 2021sp final||video|
|RRR||May 3 Tue|
|RRR||May 5 Thu|