Numerical Analysis

Foundations and Exercises

TANAKA, Kazuaki (田中 一成)
k.tanaka@aoni.waseda.jp

Institute for Mathematical Science, Waseda University

Attention!

⚠️

The 2nd period “Foundations of Numerical Analysis” and 3rd period “Exercises in Numerical Analysis” are designed to be taken together.

It is possible to take only the 2nd period class, but it is very cost-ineffective.

Schedule

  • Schedule may change depending on the situation

Week Topic
1st Orientation and Guidance
2nd-3rd Errors in Numerical Computation / Floating-Point Numbers
4th Vector Norms and Matrix Norms
5th-6th System of Linear Equations
7th-8th Nonlinear Equations
9th Midterm Examination (June 12th)
10th Review and Feedback
11th-14th Numerical Integration / Discussion for final presentation

Grade Evaluation

Evaluation Items Foundations Exercises
Exercises (including Homework) 20% 40%
Midterm Examination 40% 20%
Group Project & Presentation or Alternative Assignment 40% 40%
Total (Base points) 100% 100%

Note: Some extra points or deductions will be applied.

What is Numerical Analysis?

∫ Σ ∂
A Branch of Mathematics
Algorithms for solving mathematical problems
that cannot be solved analytically
🏛️
Deep Historical Roots
Dating back to 1800 BCE, with significant contributions from renowned mathematicians throughout history
🌍
Wide Applications
Across natural sciences, engineering, and even humanities & social sciences
💻
Computer-Driven
Modern numerical analysis relies on computer technology for practical computation

Process of Numerical Analysis

Support & Tools

👥
Teaching Assistants
Chenjian XU (M2)
Audrey CHEN (M1)
💬
Mattermost
For questions, discussions, and direct messages
🤖
LLMs & AI Agents
For coding assistance, debugging, and learning support
GitHub Classroom
For programming assignments and submission

AI Tools

💬 Chat-Based Generative AI
ChatGPT (OpenAI)
Gemini (Google)
Claude (Anthropic)
Perplexity (Perplexity AI)
Copilot (Microsoft)
and more...
💻 Editor-Based AI Agents
Cursor
AI code editor (fork of VS Code)
Antigravity (Google)
AI-powered dev environment (very similar to Cursor)
Free for Students
VS Code + GitHub Copilot
AI assistant as an extension

Using AI: Key Cautions

AI is extremely powerful and useful, but keep these in mind.

🎯
1. Think Based on Purpose
Is this AI usage truly optimal for your objective?
🕵️
2. Don't Trust the Output (Always Verify)
AI frequently states things that are contrary to facts; always cross-check with primary sources.
⚠️
3. Recognize the Risks
Personal data leakage, plagiarism, intellectual laziness.

Mission 1 — Mattermost

  1. Open Mattermost and sign in with your Waseda email address
    Apps: mattermost.com/apps — Settings:
    　Server URL: https://class.s-top.dev/
    　Server Name: anything you like (e.g. Numerical Analysis 2026)
  2. Find TANAKA, Kazuaki in the member list (use the search bar if needed)
  3. Send a direct message containing:
    • Your Name
    • First Name in HIRAGANA or KATAKANA (if possible)
    • Student ID
    • Any other comments (optional)

What is GitHub?

Git — A version control system that tracks every change to your files
GitHub — A cloud platform to store, share, and collaborate on Git repositories
Key actions: clone (download) → edit → commit (save) → push (upload)
💻
Your PC
Local Repository
push →
← pull / clone
☁️
GitHub
Remote Repository
pull / clone →
← push
👥
Teammates
Their Local Repos
🌐 Public — Anyone can view 🔒 Private — Only you and invited members

Mission 2 — GitHub Account

  1. Go to github.com and click Sign up
  2. Register with your email address and choose a professional username
  3. After sign-up, go to github.com/settings/copilot
  4. Enable GitHub Copilot Free (no payment is required)

Mission 3 — GitHub Student Developer Pack

  1. Go to education.github.com/pack
  2. Click Sign up for Student Developer Pack
  3. Verify your student status (Waseda email or student ID card)
  4. Once approved, Copilot Pro and many other premium tools become free!
⚠️
This process can be tricky! Feel free to ask AI or TAs for help.
(Approval may take a few days — proceed with the other missions in the meantime)

Mission 4 — VS Code + GitHub Copilot

  1. Download VS Code from code.visualstudio.com and install it
  2. Launch VS Code and open the Extensions panel (Cmd+Shift+X / Ctrl+Shift+X)
  3. Search for GitHub Copilot and install it
  4. Click Sign in to GitHub when prompted — authorize with your GitHub account
  5. Copilot is now ready — try typing some code and see suggestions appear!
💡
With this setup, AI can assist you with many tasks, including environment setup and debugging.

Mission 5 — Clone the Course Materials

Repository: github.com/waseda-num-analysis-2026/materials

  1. Try asking GitHub Copilot to do it for you! (e.g., “How do I clone this repository in VS Code?”)
  2. Follow the AI’s instructions to clone the repository to a folder on your PC
  3. After it’s done, ask Copilot to explain what it did step by step — so you can do it yourself next time.

Exercise 1.1 — Hello GitHub

Assignment Link: Ex 1.1 — GitHub Classroom   |   Deadline: Apr 17, 23:59

  1. Access the assignment link above to accept the task
  2. Clone the repository to your local machine
  3. Edit README.md (add your Student ID and Name)
  4. Commit & push your changes
  5. Confirm your changes appear on GitHub

Exercise 1.2 — Summarize How to Use GitHub

Assignment Link: Ex 1.2 — GitHub Classroom   |   Deadline: Apr 23, 23:59

  1. Create your own reference document on how to use GitHub (clone, commit, push, pull, etc.)
  2. Ensure it meets the Requirements:
    • AI-friendly file format — OK: tex & pdf, md, qmd, html / NG: docx, xlsx, pptx
    • The best explanation for yourself — maximally clear and useful for you
  3. Submit via GitHub Classroom (commit & push to your assignment repository)
💡
Tips: Use AI aggressively! (ChatGPT, Gemini, GitHub Copilot, etc.)
⚠️ Always cross-check with multiple AIs and verify with primary sources.

Exercise 1.2 — Suggested Workflow

Step 1. Ask a browser-based AI to draft a summary

Prompt example:
“Explain how to use Git and GitHub step by step: clone, commit, push, pull. Write it as a beginner-friendly guide.”

Step 2. Save the output as a local file (e.g. draft.txt or draft.md)

Step 3. Open it in VS Code and ask GitHub Copilot to enhance it with diagrams

Prompt examples:

  • “Create an SVG diagram showing the Git workflow: working directory → staging area → local repo → remote repo.”
  • “Embed this SVG into a Markdown file and reorganize my draft into a well-structured github-beginners-guide.md with sections and the diagram.”

(An example I ran is in ex1.2-sample/ in this repository.)