Activity Resources:

Here’s the link to the actual latex code used to build the above file.

Activity Resources:

Here’s the link to the actual latex code used to build the above file.

LaTeX is a powerful document preparation system. This system is *free* and is available across many operating systems, such as Windows, Mac OS and most distributions of Linux. A successor of TeX, LaTeX was created in the 1983 by Leslie Lamport. This computer typesetting software was originally created for academic papers in STEM fields, and since has grown in popularity in other fields because of its power to create many types of paper and digital documents common in academic fields. For those who are aiming to write a long text such as a dissertation, thesis or a book, a major attraction to learning LaTeX is its ability to handle large papers and provide uniform, beautiful, and professional formatting. LaTeX handles all the mundane tasks of formatting, so you can focus on writing the content!

For some samples of what you can create with LaTeX, visit the Notes and Work section of this blog. Below are some reasons why you might be interested in using LaTeX:

- Manage large documents by using include directives, which allows for reuse or quick modification of content as well as manage large documents.
- The technique of using multiple files to represent one documents also allows for the flexibility to quickly create of many versions of an assessment.
- Automate citations, bibliographies and formatting of bibliographies. (Quickly switching from numeric style to APA when you transition from math to social sciences, for example)
- Natural to integrate into workflow if you use popular reference management software such as Zotero, Mandeley, Citavi and most others. (Check here to see if your reference manager is compatible with Bibtex.)
- Automate the creation of list of figures/tables/graphs, and the associated numbering
- Automate the creation, sorting and creation of index, acronym and glossary lists
- Typeset complex mathematical formulae, chemical equations
- Create more complicated documents like posters, slides, and double-sided flash cards
- Precise typesetting for many languages, this is especially useful for languages outside of the romantic languages family such as Arabic

There are some contrasts with WYSIWYG (What You See is What You Get) word processors like Microsoft Word or Open Office.

There are some advantages of using WYSIWYG processors:

- you wish to take advantage of the templates provided by MS Word, such as Resumes or business cards (You can create this in LaTeX also, especially if you choose Overleaf)
- if you’re creating documents that have specific syntax, such as markup language for github readmes,
- and if you’re creating very short files where formatting doesn’t matter (such as notes not meant for publication).

When common word processors attempt to handle large files, any major modifications to the file can break the table of contents, and automatic numbering of the tables/figures/lists are not reliable. Furthermore, for students working in multiple operating systems, transitioning between different operating systems using the same latex code will generate the exact same document – this precision is simply not guaranteed with most WYSIWYG processors.

With the above in mind, if you’re interested in learning about LaTeX as a beginner, I’ll be giving an introductory workshop at LSRI on November 13th, 2019.

*Coming soon: *

- Getting Started with LaTeX: Choosing a LaTeX environment
*Basic structure of a document**Links to sample latex files*

Disclaimer: Featured image source https://en.wikibooks.org/wiki/LaTeX

Curve sketching is an important application of derivatives. Here’s an example with a polynomial, with pictures to help assist understanding:

I have gathered quizzes that relate directly to the upcoming midterm, as well as included a sample midterm. Please feel free to use these for practice! If you have trouble with the material, visit this page for additional resources. Don’t forget to grab a free version of wolfram alpha pro to help you if you’re enrolled at San Francisco State University!

- 2.4: Polynomials
- Vertex of a parabola
- Determine the behavior of a polynomial near or

- 2.5: Rational Functions
- Determine the behavior of rational functions near to
- Determine the vertical and horizontal asymptotes of a rational function
- Determine the holes of a rational function, if they exist.

- 3.1: Exponential and Logarithmic Functions
- Their definitions as inverses
- Practice using #23 – #32 in
*Precalculus – Prelude to Calculus, 3rd Ed.*

- 3.2: Power Rule
- Change of Base

- 3.3: Product and Quotient Rule
- Read p.249-p.252 for applications in scientific settings

- 3.4: Exponential Growth
- Compound Interest (
*n*times per year)

- Compound Interest (
- 3.5:
*e*and the Natural Logarithm- Understanding the definition of
*e*will enhance your understanding of proofs later on. For now, we know it’s a real number that is approximately equal to 2.71, and it’s associated with Continuous growth!

- Understanding the definition of
- 3.7: Exponential Growth Revisited
- Read p.304-p.306 for an application of the approximation methods discussed in 3.6 used in financial estimations.
- Focus on Continuous Compound Interest

- 4.1: Unit Circle
- 4.2: Radians
- Make sure you can convert between degrees and radians.

- 4.3: Sine and Cosine
- Definition using unit Circle
- Domain and Range of Sine & Cosine
- If you want a challenge, try answering #45 from this section.

- Pre-Calculus
- Lesson Planning is taking a lot less time this time around, since I spent a lot of time documenting the lessons from last year. Over-planning was actually an issue last semeseter; I would never actually complete everything I planned, and that was mildly frustrating. Also, there’s an element of improvisation that happens depending on the mood of the classroom, which means that scripting every sentence is simply not possible anyway.

- Calculus II
- The first two weeks I only prepared by rereading the text on the sections that the lead professor went over, but on the second week students asked me questions that definitely stomped me because I had not seen the problem before hand. Now, I ask students to email me their questions before the TA session, so that I can prepare with care. Planning short lectures on Calculus II material has been easier after that change in preparation, especially with access to great tools.

- Algebra
- I’m really glad to be practicing with SAGE, but I’ve honed in on specific problems and end up spending significant time cleaning up code instead of doing proofs. I need to find a balance in what I’m focusing on when learning.

- Real Analysis II
- I should really be spending more time on this course. The lectures in this cource has been a blessing for preparing for Calculus II TA sessions, since it helps get me into the “mood” to do Calculus. 🙂

- Combinatorics
- Obsessing over the details in this class takes too long. I’m in a similar situation with Algebra, but there’s this one is more like I spend 4-5 hours on one proof and run out of time for the other problems.

There’s a lot of juggling, and I have to get better at this soon before the midterm season.

I have gathered quizzes that relate directly to the upcoming midterm, as well as included a sample midterm. Please feel free to use these for practice! If you have trouble with the material, visit this page for additional resources. Don’t forget to grab a free version of wolfram alpha pro to help you if you’re enrolled at San Francisco State University!

SF State has a site license for Mathematica. Under this site license, Mathematica can be installed without further cost on any computer owned by San Francisco State University, by SF State faculty, or by SF State students. This software works on Windows, Macintosh, and Unix.

Under the terms of the site license negotiated by CSU, free WolframAlpha Pro accounts are also now available to our faculty, students, and staff.

If you are an SFSU student, click here for a free WolframAlpha Pro account.

If you are a SFSU student and you want to download the *Mathematica* software to your computers, then follow the instructions below:

- Create an account
*(New users only)*:- Go to user.wolfram.com and click “Create Account”
- Fill out form using a @sfsu.edu email, and click “Create Wolfram ID”
- Check your email and click the link to validate your Wolfram ID

- Request the download and key:
- Fill out this form to request an Activation Key
- Click the “Product Summary page” link to access your license
- Click “Get Downloads” and select “Download” next to your platform
- Run the installer on your machine, and enter Activation Key at prompt

For both *Mathematica* and WolframAlpha Pro requests on the links above, **it is important that only sfsu.edu email addresses be used.** Requests from other email addresses will be rejected.

I’m wondering how group activities can be done with 40+ students; I often give short, paired activities during lecture, which (hopefully) helps with engagement, but if I want to give a longer “exploration” activity in class, there are challenges.

Checking in with each group is takes a significant amount of time, scaling linearly. I tried to keep group size to 3-4 students, but dividing students into groups of 4-5 lead to having about 8-10 groups. The down time caused some groups to finish faster than others. There must be an optimal ratio for the number of students to square foot of classroom. I currently have 40 students, but the rooms are a lot smaller than the previous semester, I must alter the group activity plans. I also had 80 minutes sessions on Tues/Thurs instead of 50 and a much larger classroom for discussions/group work in the 4th hour. My lesson plans will require more adjustments, I suspect.

Some groups had members forging ahead before everyone understood, and that’s always a challenge as well. I wonder if larger groups are a good idea, because conversations between more than 5 students often turn to a few pairs and few solo working in parallel…

This time around, when I lead the group activity I focused on the clarity of my instructions, and I’m trying a different approach this semester compared to last. Previously, I gave handouts with specific procedure, but it was confusing for some students. This time, I tried a different approach, where I verbally and visually give instructions on the board and forgo all printed handouts in order to allow for students to make their own notes instead of using data sheets. I think I might bring back the data sheet for the later activities, so that the students can know what I specifically expect from them. I should specify that students should use technology to assist in graphing and calculations.

In terms of feedback, I tried to ask questions and check for understanding, but the number of groups is high, which means I must spend less time per group, or make the group size larger. If I maintain that the groups have no more than 5 people, then I will have at least 8 groups – which can cause my feedback to the students to be less precise and more brief. Perhaps I can take a vote with my students, to see if they prefer trying larger groups, given the challenges above?

Looking back, I admire my high school teachers who managed to deal with 30 students at a time, and were able to conduct experiments in labs, with open flames, too.

When I was in my late teens to early twenties, I knew I liked math but I wanted to try everything that would require application of math: I jumped from applied math to physics to engineering. I loved the process of learning, and I took a lot of different classes, and by the time I was halfway through the second semester of Mechanical Engineering courses, I finally realized that I was only really interested in the math, and talking about the math.

Then today, I went digging through my time-capsules on the internet. I have blogs scattered across a lot of different platforms, and I found this post over on Hubpages that I wrote in 2009. I’m pretty sure this reaffirms that I’ve always wanted to teach math.

Looking back, I’m glad that I took a long, winding path. I needed to grow a lot spiritually and emotionally before I was ready to take on teaching. Hopefully I’ll maintain my capacity for growth in the upcoming years.

Teacher Evaluations are out at SFSU. 😀

From my students’ responses, I learned that I can improve in the following ways:

- Plan what I will write on the board in more detail instead of such a rough sketch,
- “Don’t let nerves cause mistakes” – definitely happened 2-3 times where I did a problem incorrectly because I tried to wing it on the board…
- More intensive examples that can tie different concepts together before the midterm (where they do see synthesized word problems),
- On Universal Design:
- Group work that involve manipulatives, geared for kinesthetic/tactile learners,
- Audio / Visual learners balance – I tend to write a conclusion and verbally say a paragraph of explanations.

- On Long Term Planning:
- More group work for inverse trig functions and beyond,
- Maybe building a story that can be used for the concept questions during class?
- Manage expectations earlier – students will need to work and figure out a lot of stuff on their own,
- Create systems that can help students organize all the information – give suggestions on how to take notes, maybe?
- Give more time to do Chapters 4-6, Trigonometry chapters of the book.

- On Class Policy:
- Attendance and participation should be recorded more in detail,
- Be better about grading and returning stuff promptly – I definitely procrastinate on handing back quizzes sometimes. (No one complained about this but I still feel bad about it.)

Looking forward to teaching next semester! I will teach one class of precalculus and TA one section of Calc II. I wonder how different TA’ing for Calculus II will feel. 🙂