SNS - Math 275A

The format of this course will be Inquiry Based Learning (IBL). I will provide weekly assignments consisting of a list of theorems and exercises from the textbook. Your goal will be to do the assignments (prove all the theorems and solve all the exercises) by yourselves in a guided discovery process, with collaboration of classmates and guidance from me. You will take turns presenting proofs of theorems in class, while other students will determine if they are correct. I will provide perspective on the material and motivating examples.

No outside sources

As is customary in any IBL course, you are not allowed to consult any outside sources, including textbooks or the internet, to solve these problems. (The exceptions are sources that you are required to use for other courses.)

Notebook

You should acquire a loose-leaf binder, in which you will save all course notes. As you prove theorems in this course (or see them proved in class), you will write up these proofs and add them to your Notebook. In a sense, you are writing your own book on the subject, filled with your own proofs. As part of your grade for the course, these Notebooks will be evaluated.

Homework

You will be asked to write up selected theorems to be handed in weekly. Thus it is important to pay attention to proofs of theorems presented in class, since you will write these up for credit.

Homework will be due on Wednesdays.

(HW1) Reading for the week of 1/27: Sections 1.1, 1.2 and 1.3. Sections 1.4 and 1.5 are recommended but optional.

Homework due 1/29: Exercise 1.3, Theorems 1.12, 1.13, and 1.16.

Target for 1/29: be prepared to present Theorems 1.12, 1.13, and 1.16.

(HW 2) Go over the following theorems and exercises (referred to only by their number):

1.20 and 1.22 (from section 1.3);

2.3-2.6 (from section 2.2);

2.8-2.20, 2.22, and 2.24 (from section 2.3).

Target for Monday, February 3: up to 2.6. Be prepared to present 1.20, 1.22, and 2.3-2.6.

Target for Wednesday, February 5: 2.8-2.20, 2.22, and 2.24. Be prepared to present 2.13, 2.14, 2.16, 2.20, and 2.22.

Carefully write up all the theorems/exercises in bold and turn your proofs/solutions on Monday, February 10.

(HW 3) To prepare for next week, go over the following theorems and exercises (referred to only by their number):

2.16-2.24 (from section 2.3);

2.26-2.29 (from section 2.4);

2.30-2.33 (from section 2.5).

Note that some of these had been assigned for this week, but since we didn't have time to cover them, we are moving them to next week.

Target for Monday, February 10: up to 2.24. Be prepared to present 2.16, 2.20, 2.22, 2.24.

Target for Wednesday, February 12: the rest. Be prepared to present 2.26, 2.28, 2.30, 2.31, and 2.32.

Carefully write up all the theorems/exercises in bold and turn your proofs/solutions on Monday, February 17.

(HW 4) To prepare for next week, go over the following theorems and exercises (referred to only by their number):

Section 3.1: 3.1, 3.2, 3.3, 3.6, 3.8.

Section 3.2: 3.14

Section 3.3: 3.20.

Section 3.4: 3.25, 3.26, 3.28.

Target for Monday, February 17: up to 3.8. Be prepared to present 3.1, 3.2, 3.3, 3.6, 3.8.

Target for Wednesday, February 19: the rest. Be prepared to present 3.14, 3.20, 3.25, 3.26, 3.28.

Carefully write up all the theorems/exercises in bold and turn your proofs/solutions on Monday, February 24.

(HW 5) To prepare for next week, read sections 3.5 (Product Spaces) and 4.1 (Hausdorff, Regular, and Normal Spaces).

Target for Monday, February 24: be prepared to present 3.34, 3.35, 4.1, 4.2.

Target for Wednesday, February 26: be prepared to present 4.6, 4.7, 4.8, 4.9.

Carefully write up all the target theorems/exercises and turn your proofs/solutions on Monday, March 2.

(HW 6) To prepare for next week, read sections 4.2 and 4.3.

Target for Monday, March 2: be prepared to present 4.13 (1-8 and 12), 4.16, 4.17.

Target for Wednesday, March 4: be prepared to present 4.19, 4.20, 4.23.

Carefully write up all the target theorems/exercises and turn your proofs/solutions on Monday, March 9.

(HW 7) To prepare for next week, please read Chapter 5.

Target for Monday, March 9: be prepared to present 5.1, 5.2, 5.5, 5.9.

Target for Wednesday, March 11: be prepared to present 5.10 (1) & (2), 5.11, 5.13, 5.21.

Carefully write up all the target theorems/exercises and turn your proofs/solutions on Monday, March 16.

(HW 8) To prepare for next week, please read Sections 6.1 and 6.2.

Target for Monday, March 16: be prepared to present Theorems 6.1, 6.2, 6.3, 6.5

Target for Wednesday, March 18: be prepared to present Theorems 6.6, 6.8, 6.9, 6.12.

Carefully write up the proofs of the target theorems and submit your assignment via a private note on Piazza next week (no strict deadline).

(HW 9) To prepare for next week, please read Sections 6.2 and 6.3.

Target for Monday, March 23: be prepared to present Theorems 6.9, 6.12, 6.14, 6.15

Target for Wednesday, March 25: be prepared to present/participate in a discussion of Theorems 6.18, 6.19, 6.20.

Carefully write up the proofs of the target theorems and submit your assignment via a private note on Piazza the week after (no strict deadline).

(HW 10) To prepare for next week, please read Section 7.1.

Target for Monday, April 6: be prepared to present Theorems 7.1, 7.2, 7.3, 7.5.

Target for Wednesday, April 8: be prepared to present/participate in a discussion of Theorems 7.6, 7.7, 7.9, 7.10.

Carefully write up the proofs of the target theorems and submit your assignment via a private note on Piazza the week after (no strict deadline).

(HW 11) To prepare for next week, please read Sections 7.2 and 7.3.

Target for Monday, April 13: be prepared to present 7.15, 7.18, 7.20, 7.21.

Target for Wednesday, April 8: be prepared to present/participate in a discussion of 7.24, 7.27, 7.28, 7.29.

Carefully write up the proofs and solutions of the target theorems and exercises, and submit your assignment via a private note on Piazza the week after (no strict deadline).

(HW 12) To prepare for next week, please read Sections 7.4 and 7.5.

Target for Monday, April 20: be prepared to present 7.32, 7.36, 7.44, 7.45

Target for Wednesday, April 22: be prepared to present/participate in a discussion of 7.47, 7.48, 7.49, 7.53.

Carefully write up the proofs and solutions of the target theorems and exercises, and submit your assignment via a private note on Piazza the week after (no strict deadline).

(HW 13) To prepare for next week, please read Section 8.1.

Target for Monday, April 27: be prepared to present 8.1, 8.2, 8.3, 8.6.

Target for Wednesday, April 29: be prepared to present 8.7, 8.9, 8.10, 8.11.

Carefully write up the proofs and solutions of the target theorems and exercises, and submit your assignment via a private note on Piazza the week after (no strict deadline).

(HW 14) To prepare for next (and last full) week, please read the beginning of Section 8.3, then Sections 8.4 and 9.1.

Target for Monday, May 4: be prepared to present 8.18, 8.35, 8.37, 8.38.

Target for Wednesday, May 6: be prepared to present 9.1, 9.2, 9.4, 9.8.

Carefully write up the proofs and solutions of the target theorems and exercises, and submit your assignment via a private note on Piazza the week after (no strict deadline).

Honor code

Cooperation is encouraged, but solutions should be written up individually. You may not consult outside mathematical sources without my permission, unless required for some other course.

Exams

None

Expository paper

Each student will be required to write a short expository paper on a topic related to the course. A list of potential topics will be posted later. Papers need to be typeset in LaTeX.

Presentation

Each student will be required to present her/his expository paper at the end of the semester. Presentations will be 10-15 minutes long with a few minutes for questions.

Grading policy

Homework 20%, notebook 20%, participation 20%, expository paper 30%, presentation 10%

Piazza

To handle questions posed outside of class, we will be using Piazza. Piazza is a free online gathering place where students can ask, answer, and explore 24/7, under the guidance of their instructors. On the class dashboard, students can post questions and collaborate Wikipedia-style to edit responses to these questions. I as an instructor can also answer questions, endorse student answers, and edit or delete any posted content.

Instead of emailing me math questions, I encourage you to post them on Piazza.

Each student will be invited to join Piazza by email. Please join it as soon as you can, as I plan to use Piazza extensively.

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