Instructor Guide: Week-by-Week Curriculum

This comprehensive guide helps instructors deliver the Course Project effectively to mathematics students (CSMI program). The curriculum is designed for a 12-week semester with flexible pacing based on student backgrounds.

Course Overview for Mathematics Students

Key Teaching Principles for Mathematics Students:

  1. Start with "Why" - Always explain the mathematical relevance before diving into technical details

  2. Use Mathematical Examples - Replace generic programming examples with numerical analysis, LaTeX, data analysis

  3. Build Confidence Gradually - Many students may feel intimidated by command-line interfaces

  4. Connect to Research - Show how tools apply to mathematical research and collaboration

Pre-Course Preparation (Week 0)

Instructor Tasks

Before the semester begins:

Setup and Assessment

  • Send prerequisites assessment to all students 2 weeks before class

  • Prepare 3 different lesson plans based on student skill levels (Beginner/Intermediate/Advanced)

  • Set up course Slack workspace for Q&A and peer support

  • Prepare virtual machines or lab access for students without Linux systems

  • Create mathematical example datasets and code repositories

Student Grouping Strategy

  • Group students by skill level based on assessment results

  • Assign peer mentors (advanced students help beginners)

  • Prepare differentiated assignments for mixed-level classes

Sample Pre-Course Email:

Subject: Course Project - Pre-Assessment & Preparation

Dear CSMI Students,

Welcome to Course Project! This course will teach you essential computational tools for mathematical research. Please complete the self-assessment at [link] by [date].

Based on your responses, we'll customize the first few weeks to match your background. Don't worry if you have no programming experience - the course is designed for mathematicians!

Best regards,
[Instructor Name]

🟢 LEVEL 1: FOUNDATIONAL TRACK (Weeks 1-8)

For students with minimal computational experience

Week 1: Introduction and Environment Setup

Learning Objectives

  • Understand why computational tools matter in mathematics

  • Complete environment setup (Linux/WSL, basic software)

  • Navigate the course structure and assessment approach

Monday: Course Introduction (90 minutes)

Opening (15 min)

  • Course overview and mathematical relevance

  • Student introductions and background sharing

  • Review self-assessment results

Why These Tools Matter for Mathematics (30 min)

  • Case study: Collaborative paper writing with LaTeX and Git

  • Demo: Managing mathematical datasets and simulations

  • Show: How mathematical software benefits from version control

Environment Setup Workshop (45 min)

  • Install Linux/WSL for Windows users

  • Basic system verification

  • Install essential tools (text editor, terminal)

Wednesday: Linux Foundations (90 minutes)

Mathematical Context Introduction (20 min)

  • Show real mathematical workflows that use command line

  • Demonstrate: File management for research projects

  • Examples: Organizing mathematical papers, datasets, simulation results

Hands-on Linux Basics (70 min)

  • File system navigation (cd, ls, pwd)

  • Creating and managing directories for research projects

  • File operations for mathematical work

  • Mathematical Exercise: Organize a sample research project structure

Friday: Linux Practice & Problem Solving (90 minutes)

Advanced File Operations (45 min)

  • Text processing for mathematical data

  • File permissions and sharing

  • Remote access basics (SSH)

Workshop: Mathematical Data Management (45 min)

  • Project: Students organize sample mathematical datasets

  • Practice with real CSV files from mathematical experiments

  • Troubleshooting common issues

Week 1 Assessment: = - Practical skills check: Navigate and organize file system - Self-reflection: Comfort level with command line - Peer assessment: Help classmates with setup issues

Week 2: Version Control for Mathematical Research

Learning Objectives

  • Understand version control for mathematical research

  • Use Git for LaTeX document management

  • Set up GitHub for academic collaboration

Monday: Git Fundamentals for Mathematics (90 minutes)

Introduction to Version Control (30 min)

  • Why mathematicians need version control

  • Case study: Tracking changes in research papers

  • Demo: Git for LaTeX document collaboration

Git Basics Hands-on (60 min)

  • Initialize repository for a mathematical paper

  • Basic commands: add, commit, status

  • Mathematical Exercise: Version control a LaTeX document

Wednesday: Collaborative Mathematics with Git (90 minutes)

Branching for Research (45 min)

  • Creating branches for different paper sections

  • Merging collaborative work

  • Resolving conflicts in mathematical documents

GitHub for Academic Work (45 min)

  • Setting up academic GitHub account

  • Creating repositories for mathematical projects

  • Exercise: Collaborate on a mathematical proof document

Friday: Git Workshop & Project (90 minutes)

Mathematical Project Setup (90 min)

  • Group Project: Set up shared repository for mathematical analysis

  • Practice collaborative workflows

  • Code review for mathematical scripts

  • Issue tracking for research tasks

Week 2 Assessment: - Git workflow demonstration - Collaborative exercise evaluation - Repository organization quality

Week 3: Development Environment (VS Code)

Learning Objectives: - Set up integrated development environment - Configure VS Code for mathematical work - Understand extensions for LaTeX, Python, and data analysis

Monday: VS Code for Mathematics Students (90 minutes)

IDE Introduction (30 min)

  • Why use an integrated development environment

  • Overview of VS Code for mathematical work

  • Comparison with mathematical software interfaces

VS Code Setup and Configuration (60 min)

  • Installation and basic configuration

  • Essential extensions for mathematics: LaTeX, Python, Jupyter

  • Exercise: Set up workspace for mathematical project

Wednesday: LaTeX and Document Management (90 minutes)

LaTeX in VS Code (45 min)

  • LaTeX extension setup and configuration

  • Writing mathematical documents with live preview

  • Bibliography management integration

Version Control Integration (45 min)

  • Git integration in VS Code

  • Managing mathematical document versions

  • Exercise: Write and version a mathematical report

Friday: Data Analysis Environment (90 minutes)

Python and Jupyter Setup (45 min)

  • Python extension configuration

  • Jupyter notebook integration

  • Mathematical libraries overview

Mathematical Computing Workflow (45 min)

  • Project: Set up complete mathematical analysis environment

  • Integration with external mathematical software

  • Best practices for reproducible research

Week 3 Assessment: - Environment setup evaluation - LaTeX document creation - Integrated workflow demonstration

Week 4: Project Management for Research

Learning Objectives: - Apply project management to mathematical research - Use GitHub for research project organization - Understand Agile methods in academic context

Monday: Research Project Management (90 minutes)

Academic Project Management (45 min)

  • Adapting project management for mathematical research

  • Timeline management for research projects

  • Milestone setting for mathematical investigations

GitHub Projects for Research (45 min)

  • Setting up research project boards

  • Issue tracking for mathematical tasks

  • Exercise: Plan a semester research project

Wednesday: Collaborative Research Methods (90 minutes)

Research Team Workflows (45 min)

  • Organizing collaborative mathematical research

  • Code review for mathematical scripts

  • Documentation standards for mathematical projects

Agile Research Practices (45 min)

  • Sprint planning for research phases

  • Retrospectives for mathematical investigations

  • Workshop: Apply Agile methods to research project

Friday: Research Project Workshop (90 minutes)

Integrated Project Setup (90 min)

  • Capstone Project Start: Students begin semester-long mathematical project

  • Apply all learned tools in integrated workflow

  • Peer review and feedback session

Week 4 Assessment: - Project planning quality - Tool integration effectiveness - Collaboration skills demonstration

Weeks 5-8: Intermediate Skills Development

Weeks 5-6: Advanced Git and Collaboration - Advanced branching strategies for research - Large file management (Git LFS) for mathematical datasets - Continuous integration basics for mathematical projects

Weeks 7-8: Introduction to Containers and Automation - Basic containerization for reproducible mathematical computing - Simple automation scripts for mathematical workflows - Preparation for advanced topics

🟡 LEVEL 2: INTERMEDIATE TRACK (Weeks 5-10)

For students with some computational background

Week 5: Advanced Collaboration and Code Quality

Learning Objectives: - Implement advanced Git workflows - Apply code review processes to mathematical code - Establish quality standards for mathematical computing

Focus Areas: - Mathematical code review practices - Documentation standards for computational mathematics - Testing strategies for mathematical algorithms

Week 6: Containerization for Mathematical Research

Learning Objectives: - Understand containerization for reproducible research - Use Docker for mathematical software environments - Share computational environments with collaborators

Mathematical Applications: - Packaging mathematical software stacks - Reproducible numerical experiments - Cross-platform mathematical computing

Week 7: Project Management at Scale

Learning Objectives: - Manage complex mathematical research projects - Coordinate multiple research streams - Apply advanced project management tools

Week 8: Introduction to Automation

Learning Objectives: - Automate repetitive mathematical tasks - Set up basic continuous integration - Prepare for advanced computing workflows

Weeks 9-10: Integration and Advanced Preparation

  • Portfolio project development

  • Preparation for advanced HPC concepts

  • Research presentation and documentation

🔴 LEVEL 3: ADVANCED TRACK (Weeks 9-12)

For computationally experienced students

Week 9: High-Performance Computing and Containers

Learning Objectives: - Deploy mathematical software on HPC systems - Use advanced containerization (Apptainer/Singularity) - Understand HPC workflow management

Mathematical Applications: - Large-scale numerical simulations - Parallel mathematical computing - HPC cluster resource management

Week 10: CI/CD for Mathematical Research

Learning Objectives: - Implement continuous integration for mathematical projects - Automate testing of mathematical algorithms - Deploy mathematical software automatically

Week 11: Advanced Automation and Integration

Learning Objectives: - Create complex mathematical workflows - Integrate multiple computational tools - Optimize computational research pipelines

Week 12: Capstone Projects and Portfolio

Learning Objectives: - Complete comprehensive mathematical computing project - Demonstrate mastery of all course tools - Present integrated research workflow

📊 Assessment Strategies

Formative Assessment

Weekly Skills Checks: - Practical demonstrations of tool usage - Peer collaboration exercises - Self-reflection journals on learning progress

Project-Based Learning: - Ongoing mathematical research project - Portfolio development throughout semester - Regular peer review sessions

Summative Assessment

Midterm Portfolio Review (Week 6)

  • Demonstrate proficiency with foundational tools

  • Present mathematical project progress

  • Peer evaluation of collaboration skills

Final Project Presentation (Week 12)

  • Complete mathematical research project using all course tools

  • Documentation quality and reproducibility

  • Presentation to mathematical research community

Assessment Rubric Categories: 1. Technical Proficiency (40%) - Tool usage and integration 2. Mathematical Application (30%) - Relevance to mathematical research 3. Collaboration (20%) - Teamwork and peer interaction 4. Communication (10%) - Documentation and presentation quality

🚨 Common Challenges and Solutions

Challenge 1: Mathematics Students Intimidated by Command Line

Symptoms: - Students avoid using terminal - Preference for graphical interfaces - Fear of "breaking something"

Solutions: - Start with mathematical file organization examples - Use "safe" sandbox environments for practice - Pair programming with more confident students - Emphasize mathematical relevance in every command

Script for Encouragement:

"Think of the command line like mathematical notation - it seems complex at first, but it's actually a precise, powerful language for expressing exactly what you want the computer to do. Just like mathematical notation, once you learn the basics, it becomes much more efficient than everyday language."

Challenge 2: Students Don’t See Relevance to Mathematics

Symptoms: - "Why can’t I just use MATLAB/Mathematica?" - Resistance to learning new tools - Focus on immediate assignment completion over skill building

Solutions: - Always start lessons with mathematical use cases - Show real research workflows from mathematical faculty - Invite guest speakers from computational mathematics - Use mathematical datasets and problems in all exercises

Example Mathematical Connections: - Linux: "Managing output from long-running numerical simulations" - Git: "Collaborating on mathematical papers with advisors" - Containers: "Ensuring your numerical results are reproducible"

Challenge 3: Mixed Skill Levels in Same Class

Symptoms: - Advanced students bored with basics - Beginners overwhelmed by pace - Uneven group project contributions

Solutions: - Peer mentoring system (advanced students help beginners) - Tiered assignments with optional advanced components - Flexible deadlines based on starting skill level - Additional support sessions for beginners

Differentiated Assignment Example: - Basic: Use Git to track changes in a LaTeX document - Intermediate: Set up collaborative repository with branch protection - Advanced: Implement automated LaTeX compilation with CI/CD

Challenge 4: Time Management and Semester Integration

Symptoms: - Students overwhelmed by other mathematics courses - Difficulty seeing long-term value - Procrastination on practical assignments

Solutions: - Integrate with other mathematics courses when possible - Show immediate benefits (easier homework management) - Break large projects into weekly mini-deliverables - Connect with mathematics faculty for reinforcement

📚 Additional Resources for Instructors

Mathematical Example Repositories

Recommended Example Projects: 1. Numerical Analysis Project: Implementing and comparing root-finding algorithms 2. Statistical Analysis: Processing and visualizing mathematical survey data 3. LaTeX Collaboration: Co-authoring mathematical research paper 4. Simulation Study: Monte Carlo simulation with result management

Guest Speaker Suggestions

Potential Speakers: - Computational mathematics faculty showing research workflows - Industry mathematicians using these tools - Graduate students in computational mathematics - Mathematical software developers

Professional Development

Recommended Training for Instructors: - Understanding mathematics student learning styles - Computational mathematics teaching strategies - Industry trends in mathematical computing - Inclusive teaching practices for STEM

🎯 Success Metrics

Student Success Indicators

By End of Course, Students Should: - Confidently manage mathematical research projects using version control - Set up reproducible computational environments for mathematical work - Collaborate effectively on mathematical research using modern tools - Apply project management principles to mathematical investigations - Demonstrate integration of tools in cohesive mathematical workflow

Course Improvement Metrics

Track These Metrics: - Student confidence surveys (pre/post course) - Tool adoption in subsequent mathematical courses - Student feedback on mathematical relevance - Faculty feedback on student preparedness - Long-term tool usage tracking

End-of-Semester Student Reflection Questions

  1. How have these tools changed your approach to mathematical research?

  2. Which tools do you plan to continue using in future mathematics courses?

  3. What mathematical applications of these tools surprised you most?

  4. How confident do you feel collaborating on computational mathematics projects?

  5. What advice would you give to future mathematics students taking this course?

Remember: This curriculum guide should be adapted based on your specific student population, available resources, and institutional constraints. The key is maintaining focus on mathematical applications while building computational confidence gradually.