math104-s22:start

Instructor: Peng Zhou

Email: pzhou.math@berkeley.edu

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

- Online Lecture Zoom
- Online Discussion Discord
- Virtual Group Discussion SpatialChat
- Gradescope: homework submission, entry code GEDJP3

GSI: Jacobo, Evans 747. zoom office.

- M 2-5pm; T: 12-2; W: 12-3pm (remote); F: 2-4pm
- First two weeks all above slots are for remote access.

** What do we cover in this class? ** It will consist of three parts

- Sequence and Limits
- Metric space Topology
- Differentiation and Riemann Integral

**How to learn this course?** One should

- read the textbook and then come to lecture. In lecture, I will focus on motivations and examples, and key steps in the proofs, but I will leave many details as exercises for you to fill in.
- participate in in-class group discussion. Since we don't have a discussion session, this is the chance for you to know your classmates. We will have 2-3 person small groups, and have discussion 20-30 minutes. For the first two weeks, we will use spatialchat.
- participate in discord discussion. You can ask question about lecture and homeworks, and post your homework solutions here for others to comment.
**[NEW]**Student homepage. Our course has an area where you can create your own homepage. In your homepage, you can share your class notes, homework solutions, and whatever you think is relevant for this course.

** 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

- ask and answer at least one question on discord.
- post your homework solution to to discord
- in discord, comment at least two other student's homework posting.
- You will also submit the homework to gradescope, where the grader or myself will give you comments.
- make correction to the homework, and upload to your student homepage.

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

- Rudin: Principles of Mathematical Analysis
- Ross: Elementary Analysis
- Tao: Analysis I and Analysis II

Some other lecture notes might be useful

- my own lecture note in 2021 spring
- Harrison Chen's course website
- Pugh: Real Mathematical Analysis, colloqial, to-the-point, with many pictures.

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 |

math104-s22/start.txt · Last modified: 2022/05/02 14:24 by pzhou