Here’s the link to the actual latex code used to build the above file.
There are many benefits to using LaTeX as an academic. This post aims to giving you resources on how to setup your coding environment. The aim is not a comprehensive review of LaTeX editors, but to give a starting point for novices, so apologies if your favorite editor is not included here.
There are many ways to setup your environment, and here I’ll layout the two major ways – desktop and cloud. and their pros and cons:
|Cloud||+ Does not require disk space or significant time to setup|
+ Easily access your files from multiple operating systems with any reasonably modern browser
+ Many templates exists
+ Great for novices to get a feel for LaTeX
+ Great for creating simpler documents or singular images
+ Some blend features of WYSIWYG document creators, which is a nice scaffold for novices.
|– Requires internet access for the entire duration of editing|
– Sharing editing power with others requires a paid account, on a subscription basis.
– On the very rare occasions when the servers are down, you will not have access to your files
– Handling and breaking your document into multiple files can be a bit messy
– Privacy: Trusting sometimes sensitive text to be handled by a server not owned by you.
– Code version control: compiling offline allows for you to update distributions of each component yourself, whereas the server sometimes gives minor bugs due to distribution bugs.
|Desktop||+ Entirely free and full control over your own files|
+ Does not require internet access to create files unless you use a new package that requires download. (Likely by citing a new package you were looking on the internet and found out about it anyway.)
+ Custom libraries and style files “easy” to manage
+ Can set up your files on a cloud, and have full control over your backups
+ Can handle as many subfiles as you need to.
|– Steeper learning curve in setup.|
– Compiling time depends on the power of your machine. However, unless you’re running unix on a toaster, there’s not really an issue with modern machines now.
– Working with multiple editors will likely require GitHub, unless there’s one person who is in charge of translating more basic document files into LaTeX.
– Unforgiving in syntax during compile time
Based on what you’re building, you’d likely switch between cloud and desktop environments. Thus, I’ll recommend some specific ones below.
First, depending on your operating system, you should install a LaTeX compiler:
Then, choose a LaTeX editor. I’ve only included dependable editors that are usable across Windows, Mac as well as Linux, as that is important to me personally because I switch between Ubuntu and Windows depending on the task often.
For a more comprehensive breakdown of editors, visit this wikipedia page.
Next in the series we will cover the basic structure of a latex document, and common resources to help you as you build your code.
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:
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:
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.
Disclaimer: Featured image source https://en.wikibooks.org/wiki/LaTeX
To pay homage to mathematician peers and mentors, these notes will maintain the same familiar formatting structure of definitions, theorems, and corollaries similar to mathematical text. These notes contain a few original ideas in the form of conjectures and remarks. Outside of these comments, the words arranged below and in subsequent posts are summaries of readings from the STEM education journal club at LSRI.
The very most recent news is that I have decided to join University of Illinois at Chicago to work on a PhD in Learning Sciences, with a focus on Mathematics Education. I’m very excited to join the Learning Sciences Research Institute (LSRI) in continuing my research!
I’m moving this July, and this site will see significantly more activity; especially WRT notes on math education! I’ll be compiling notes and some definitions here as a resource
Some Highlights of 2018-2019:
I defended my thesis, “Computational Verification of the Cone Conjecture”, in December 2018, and submitted all final edits in May 2019.
My advising committee:
The set of polyhedral pointed rational cones form a partially ordered set with respect to elementary additive extensions of certain type. This poset captures a global picture of the interaction of all possible rational cones with the integer lattice and, also, provides an alternative approach to another important poset, the poset of normal polytopes. One of the central conjectures in the field is the so called Cone Conjecture: the order on cones is the inclusion order. The conjecture has been proved only in dimensions up to 3. In this work we develop an algorithmic approach to the conjecture in higher dimensions. Namely, we study how often two specific types of cone extensions generate the chains of cones in dimensions 4 and 5, whose existence follows from the Cone Conjecture.
A naive expectation, explicitly expressed in a recently published paper by Dr. Gubeldaze, is that these special extensions suffice to generate the desired chains. This would prove the conjecture in general and was the basis of the proof of the 3-dimesional case. Our extensive computational experiments show that in many cases the desired chains are in fact generated, but there are cases when the chain generation process does not terminate in reasonable time. Moreover, the fast generation of the desired chains fails in an interesting way—the complexity of the involved cones, measured by the size of their Hilbert bases, grows roughly linearly in time, making it less and less likely that we have a terminating process. This phenomenon is not observed in dimension 3. Our computations can be done in arbitrary high dimensions. We make a heavy use of SAGE, an open-source mathematics software system, and Normaliz, a C++ package designed to compute the Hilbert bases of cones.
Full Text is below:
The actual latex code is hosted on github.
Finally set up a github to house all the custom LaTeX files that I’ve created!
Will be updating this over time – this particular github is mostly meant for personal use, though I’m happy to share what I have and continue to update this github.
As I continue to create new tools, I’ll be hosting them here.
You’ll see currently the following repositories:
April 5th, 2018
April 6th, 2018
April 8th, 2018
Curve sketching is an important application of derivatives. Here’s an example with a polynomial, with pictures to help assist understanding:
I took Real Analysis I & II with Professor Alex Schuster in 2016-2017. These comprehensive notes were compiled using lecture notes and the textbook, An Introduction to Analysis (Fourth Edition), by William Wade.
Please feel free to download and print these notes for your convenience.
Disclaimer: my notes are meant to be a toolbox while doing proofs and studying/practicing the course in general. There may contain typos or mistakes. Please feel free to let me know if you find any errors!