Indiana University East - Bachelors of Science in Mathematics 🧮
Here you will find my notebooks, papers, code and other work towards the IUE B.S. in Mathematics. Sprinkled among these attempts at clear thinking are resources and reflections you may find helpful about mathematics, software, and philosophy.
La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si può intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezi è impossibile a intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro laberinto. Galileo, Il Saggiatore Note: Some of the projects in this repo will require some software dependencies. See here.
If you'd like to help support my studies and projects like this repo, I'd be delighted if you bought me a coffee.
Contents
- Indiana University East - Bachelors of Science in Mathematics 🧮
About
IUE - Bachelors of Science in Mathematics
In each of the sections below, as I take classes, I will include links to my work in the classes for reference.
Core Courses
The following are required courses for the program
- MATH-M 215 Calculus I (5 Credits)
- MATH-M 216 Calculus II (5 Credits)
- MATH-M 303 Linear Algebra (3 Credits)
- MATH-M 311 Calculus III (3 Credits)
- MATH-M 393 Bridge to Abstract Mathematics (3 Credits)
- MATH-M 403 Modern Algebra (3 Credits)
- MATH-M 413 Real Analysis (3 Credits)
- MATH-M 447 Mathematical Models (3 Credits)
- MATH-M 499 Senior Seminar (3 Credits)
Electives
The following are courses from which I will choose, pending discussions with academic advisors
- MATH-M 312 Calculus IV (3 Credits)
- MATH-M 313 Differential Equations (3 Credits)
- MATH-M 366 Elements of Statistical Techniques (3 Credits)
- MATH-M 371 Elementary Computational Methods (3 Credits)
- MATH-M 380 History of Mathematics (3 Credits)
- MATH-M 404 Modern Algebra II (3 Credits)
- MATH-M 405 Number Theory (3 Credits)
- MATH-M 421 Introduction to Topology I (3 Credits)
- MATH-M 448 Mathematical Models II (3 Credits)
- MATH-M 451 Mathematics of Finance (3 Credits)
- MATH-M 463 Intro to Probability Theory I (3 Credits)
- MATH-T 321 Intuitive Topology (3 Credits)
- MATH-T 336 Topics in Euclidean Geometry (3 Credits)
Tools and Resources
Articles and resources about sundry topics you may need for interacting with my repository, but that you may not be familiar with yet, depending on your background.
Environment Setup
Where possible, I will provide a containerized environment for any work that uses software, to abstract away the setup. To do this, I will primarily use Docker. Docker is a tool used frequently in software engineering for creating containers, which are similar to lightweight virtual machines, but make more efficient use of the resources of the underlying host machine.
MarkDown
This document is in Markdown!
Markdown is a text-to-HTML conversion tool for web writers. Markdown allows you to write using an easy-to-read, easy-to-write plain text format, then convert it to structurally valid XHTML (or HTML). Source: https://daringfireball.net/projects/markdown/
LaTeX
LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. LaTeX is the de facto standard for the communication and publication of scientific documents. LaTeX is available as free software. Source: https://www.latex-project.org/
Books on LaTeX
Examples
Discussions and Tutorials
- Dr. Trefor Bazett - Intro to LaTeX Part I
- Dr. Trefor Bazett - Intro to LaTeX Part II
- dspinellis/latex-advice
- Compiling LaTeX Locally on macOS with VS Code and Git
You can find a summary of my LaTeX setup here:
Citations and Bibliographies
Discussions
- Bibliographies - Stylistic conventions for bibliographies in mathematical writing
- Wikibooks - LaTeX Bibliography Management
Tools and Packages
Zotero
Zotero is a free, easy-to-use tool to help you collect, organize, cite, and share research. Source: https://www.zotero.org/
- I use Zotero to generate .bib files for myself to use in my LaTeX documents. See below on Biblatex.
biblatex and biber
The biblatex package is becoming the definitive citation management tool for LaTeX users. Biblatex provides a powerful and flexible macro interface for authors of citation styles. Biblatex's own data backend processor, biber, allows biblatex to offer [a lot of] features. Source: http://biblatex-biber.sourceforge.net/
- If you're interested, you should read this article on CICD for LaTeX, which deals with these packages.
amsrefs
amsrefs is a LATEX package for preparing bibliography or reference lists.
MathSciNet
MathSciNet is a database of known mathematics and science journals provided by the American Mathematical Society. It is available by subscription only.
Knowledge Management System ፨ 👨🏻💻 📄
I'm trying out Obsidian to manage a knowledge graph for myself with Markdown and will be storing in this repository. Running notes will be in Markdown with mathematical sketches in inline LaTeX and embedded diagrams generated from other tools. Since Markdown is plain-text, this knowledge graph will be maintainable through git, like the rest of the project. It will be consumable through Obsidian or Foam (one of its VSCode-plugin competitors).
Visualizations and Math Tools
Jupyter
Jupyter provides interactive coding notebooks that make it easy to prototype, create visualizations and interactive presentations, and to make the software used in research more transparent. Jupyter notebooks are used widely both in industry and in academia. I will use Python-based Jupyter notebooks primarily, but other programming languages are supported. You can find out more about the project here.
I have defined a docker image that builds on the Docker Stacks that are maintained by the Jupyter Team. That image can be found in Docker Hub under jllovet/math-notebook, and the definition can be found in this repository under 000-setup/jupyter, where you can also find usage instructions.
Python Packages
Standalone Tools
Software Engineering
Math Resources
Tools, Calculators, and Interactive Courses
Channels
- 3b1b
- Khan Academy
- The Organic Chemistry Tutor
- The Bright Side of Mathematics
- Numberphile
- Prof. Redden
- Cowan Academy
Fields of Mathematics and Self-Study Roadmaps
Chapters, Papers, etc
Geometry
Algebra
Precalculus
- Precalculus Course
- Precalculus Introduction, Basic Overview, Graphing Parent Functions, Transformations, Domain & Range