Math 31BH: Lecture 0

Welcome to Math 31BH, the second quarter of a three-quarter honors integrated linear algebra/multivariable calculus sequence for well-prepared students. Math 31BH combines vector algebra (which you learned in Math 31AH) with calculus (which you presumably already have substantial familiarity with): the two react to yield a new subject called vector calculus, which in addition to its inherent mathematical utility and appeal has many applications, especially in physics and engineering.

Vector calculus is a difficult subject, and this is especially so for the honors treatment of it offered in this course. Before saying anything else, I want to draw your attention to the following remark which accompanies the registrar’s listing for this course:

The honors calculus courses 31AH-BH-CH are unusually demanding and are intended for students with strong aptitude and deep interest in Mathematics.

– UCSD Registrar’s Office

If you’re enrolled in this class, I want you to be aware immediately: Math 31BH is an unusually demanding course. If the prospect of an intellectual challenge appeals to you, you’ve come to the right place; otherwise, this is not the course for you, and you should instead consider the Math 20 course sequence. It is not the case that the Math 31 course sequence is “better” than the Math 18/20 course sequence — but it is different. The Math 31 sequence is more theoretical and rigorous, meaning that there is a strong emphasis on precise definitions and clear logical reasoning, as opposed to an emphasis on the memorization and application of formulas. This does not mean that you are not expected to master formulas in Math 31BH — you are — rather it means that the process of translating theoretical knowledge into the ability to do concrete calculations is largely left to the student. Effectively, this means that there is a large “make your own examples” component in which you will have to unpack the course content outside of lecture.

Now let us discuss the basic parameters of the course. First of all, we will not be meeting for standard in-person lectures this quarter. The course will instead be organized as follows.

This blog will serve as the textbook for the course: the entire course content will be made available here, in the form of lecture posts. These posts will be of a quality unmatched by any textbook, and the goal is that they will be written in a way which imparts certain elements of the live lecture experience. Out of respect for your hard-earned tuition dollars, some of this content will only be available to students enrolled in Math 31BH. There will be two posts per week, each of which will contain content corresponding to what would be covered in a rather ambitious in-person lecture. Also, the posts will contain embedded links to additional material, typically background material that you should read up on. The two weekly lecture posts will be made available prior to our designated Monday and Wednesday 15:00-15:50 lecture slots.

That leaves the Friday lecture slot, which will consist of two parts. The first part will occupy the 15:00-15:50 lecture slot, and will be conducted in the style of a flipped classroom in order to cement your understanding of material you have already absorbed. This will often take the form of an interactive problem solving session: typically we will discuss the weekly problem sets and I will try to guide you through these problems so as to start you down the right path. At other times we will engage in a recap of essential material presented in the lecture posts, or a more free-form discussion of the course content intended to deepen and broaden your understanding.

The flipped classroom session will segue into an additional 70 minutes corresponding to “office hours,” which will be driven primarily by student questions (many students find it worthwhile to attend office hours even if they don’t plan to ask questions). The combined flipped classroom and office hours endeavor makes for a two hour live Zoom session every Friday, 15:00-17:00. For those of you not already aware (probably a null set), Zoom is a freely available videoconferencing platform. These Friday Zoom sessions will be recorded and made available on Canvas. I will communicate the Friday lecture Zoom link to you in a class-wide email.

In addition to the course content delivered by Professor Novak in the manner described above, the Math 31BH teaching assistant, Zhiyuan Jiang, will be running discussion sections via every Tuesday, from 17:00-17:50 for students in section A01, and from 18:00-18:50 for students in section A02. Zhiyoun will post further details concerning the discussion sections on Piazza.

Piazza is an online platform facilitating online discussion of all aspects of the course, from logistics to course content. You can sign up for the Math 31BH Piazza feed using this link. Links to the lecture posts will be made available under the “Resources” section, where you will also find a syllabus link leading back to this post. I encourage you to return to this post (via Piazza or otherwise) when you have questions about the course structure and content. Both myself and Zhiyoun will be active on Piazza. We also expect that Piazza will serve as a forum for students to discuss the course content with each other, and endeavor to answer each others questions. Please use Piazza as the default mechanism for asking questions about the course, and refrain from using email unless absolutely necessary.

Now that we have discussed how the course content will be disseminated to students, let us discuss the content to be created by students and submitted for evaluation. Students in Math 31BH will generate two types of content: solutions to weekly problem sets, and solutions to exams.

We will aim for a total of nine weekly problem sets in this course. Problem sets will be posted to Piazza on Sundays before 24:00 (with the exception of Week 1, where the problem set will be posted today), and the corresponding solutions will be due the following Sunday before 24:00. Your solutions will be both submitted by you and returned to you using Gradescope (entry code P5ZY44). This process will be managed by the teaching assistant, and any questions or concerns related to Gradescope should be directed to Zhiyoun. The problem sets are a very important part of the course, and accordingly make up 50% of the total grade. While you may submit handwritten solutions, it is recommended that you typeset your solutions using LaTeX, the professional standard for the preparation of scientific documents. Learning how to prepare scientific documents of professional quality is a valuable skill that will serve you well in your university career, and beyond. In order to help with this, the problem sets themselves will be typeset in LaTeX, and the source files will be posted along with their PDF output. Problem set solutions which have been typeset using LaTeX will receive an automatic 5% bonus.

There will be no problem set due on February 6, nor will there be a new lecture post on February 7, because this is the date of the midterm exam. The midterm exam will count for 20% of your course grade. The midterm exam will be an at-home test, submitted via Gradescope. Further details will be released as the date approaches.

The final exam for the course is set for March 16, with a scheduled time of 15:00-17:59. This date and time slot is set by the university registrar and cannot be changed; if you are unable to write the final exam at this specified day and time, you should not enroll in the course. The final exam will count for 30% of your course grade. The details of how the final exam will be written and submitted are not yet available, but will be soon, and I will keep you updated.

Our first live Zoom session will take place on January 7, 15:00-17:00. I expect you will have many questions, so this meeting will be mostly logistical, but we should still have some time for math. The schedule below indicates the expected mathematical content of future lectures. It will be filled in one week at a time (so refer back to it weekly), and is constantly subject to change.

01/03Lecture 0Course logistics
01/05Lecture 1Euclidean spaces and continuous functions
01/07Lecture 2Problem session
01/10Lecture 3
01/12Lecture 4
01/14Lecture 5
01/19Lecture 6
01/21Lecture 7
01/24Lecture 8
01/26Lecture 9
01/28Lecture 10
01/31Lecture 11
02/04Lecture 12
02/07Midterm
02/09Lecture 13
02/11Lecture 14
02/14Lecture 15
02/16Lecture 16
02/18Lecture 17
02/23Lecture 18
02/25Lecture 19
02/28Lecture 20
03/02Lecture 21
03/04Lecture 22
03/07Lecture 23
03/09Lecture 24
03/11Lecture 25
03/16Final Exam
Tentative lecture schedule, subject to change.

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