Quick Reference Guide

Your comprehensive resource for commands, formulas, algorithms, and best practices

Command Line - Git, Docker, Kubernetes, AWS CLI, Terraform
Physics & Math - Constants, equations, calculus
Algorithms - Big O, patterns, implementations
API & Network - REST, protocols, regex
Troubleshooting - Docker, Git, deployment issues
Best Practices - Code review, deployment, security
Recently Added - Latest additions to this reference

Command Line References

Git Commands

# Repository Management
git init                      # Initialize new repository
git clone <url>              # Clone remote repository
git remote -v                # List remote repositories
git remote add origin <url>  # Add remote repository

# Basic Operations
git add .                    # Stage all changes
git add <file>              # Stage specific file
git commit -m "message"     # Commit staged changes
git push origin <branch>    # Push to remote
git pull origin <branch>    # Pull from remote
git fetch                   # Fetch remote changes

# Branching
git branch                  # List branches
git branch <name>          # Create new branch
git checkout <branch>      # Switch branch
git checkout -b <branch>   # Create and switch
git merge <branch>         # Merge branch
git branch -d <branch>     # Delete branch

# History & Inspection
git status                 # Show working tree status
git log --oneline         # Show commit history
git diff                  # Show unstaged changes
git diff --staged         # Show staged changes
git show <commit>         # Show specific commit

# Undoing Changes
git reset HEAD~1          # Undo last commit (keep changes)
git reset --hard HEAD~1   # Undo last commit (discard changes)
git checkout -- <file>    # Discard file changes
git revert <commit>       # Create revert commit
git stash                 # Temporarily store changes
git stash pop            # Apply stashed changes

# Advanced
git rebase <branch>       # Rebase current branch
git cherry-pick <commit>  # Apply specific commit
git bisect start          # Start binary search
git reflog               # Show reference log

Docker Commands

Docker Command Reference

# Container Management
docker run <image>                    # Run container
docker run -d <image>                # Run detached
docker run -it <image> /bin/bash     # Interactive shell
docker ps                            # List running containers
docker ps -a                         # List all containers
docker stop <container>              # Stop container
docker start <container>             # Start container
docker rm <container>                # Remove container
docker logs <container>              # View logs
docker exec -it <container> /bin/bash # Enter container

# Image Management
docker images                        # List images
docker pull <image>                  # Pull image
docker build -t <tag> .             # Build image
docker push <image>                 # Push image
docker rmi <image>                  # Remove image
docker tag <source> <target>        # Tag image

# Docker Compose
docker-compose up                    # Start services
docker-compose up -d                # Start detached
docker-compose down                 # Stop services
docker-compose ps                   # List services
docker-compose logs -f              # Follow logs
docker-compose exec <service> bash  # Enter service

# System Management
docker system prune                 # Clean unused resources
docker volume ls                    # List volumes
docker network ls                   # List networks
docker inspect <object>             # Inspect object
docker stats                        # Show resource usage

Kubernetes Commands

kubectl Quick Reference

# Cluster Information
kubectl cluster-info              # Display cluster info
kubectl config view              # View config
kubectl get nodes                # List nodes
kubectl describe node <name>     # Node details

# Resource Management
kubectl get pods                 # List pods
kubectl get svc                  # List services
kubectl get deployments         # List deployments
kubectl get all                 # List all resources
kubectl get all -A              # All namespaces

# Creating Resources
kubectl create -f <file>        # Create from file
kubectl apply -f <file>         # Apply configuration
kubectl create deployment <name> --image=<image>
kubectl expose deployment <name> --port=<port>

# Debugging
kubectl logs <pod>              # View pod logs
kubectl logs -f <pod>           # Follow logs
kubectl exec -it <pod> -- /bin/bash  # Enter pod
kubectl describe pod <pod>      # Pod details
kubectl get events              # Cluster events

# Scaling & Updates
kubectl scale deployment <name> --replicas=<n>
kubectl set image deployment/<name> <container>=<image>
kubectl rollout status deployment/<name>
kubectl rollout undo deployment/<name>

# Deletion
kubectl delete pod <pod>        # Delete pod
kubectl delete -f <file>        # Delete from file
kubectl delete deployment <name> # Delete deployment

AWS CLI Commands

AWS CLI Essential Commands

# S3 Operations
aws s3 ls                           # List buckets
aws s3 ls s3://bucket              # List objects
aws s3 cp file s3://bucket/        # Upload file
aws s3 cp s3://bucket/file .      # Download file
aws s3 sync . s3://bucket/         # Sync directory
aws s3 rm s3://bucket/file         # Delete file
aws s3 mb s3://bucket              # Make bucket
aws s3 rb s3://bucket              # Remove bucket

# EC2 Operations
aws ec2 describe-instances          # List instances
aws ec2 start-instances --instance-ids <id>
aws ec2 stop-instances --instance-ids <id>
aws ec2 terminate-instances --instance-ids <id>
aws ec2 describe-images --owners self
aws ec2 create-snapshot --volume-id <id>

# IAM Operations
aws iam list-users                  # List users
aws iam list-roles                  # List roles
aws iam list-policies               # List policies
aws iam get-user --user-name <name>
aws iam create-user --user-name <name>

# Lambda Operations
aws lambda list-functions           # List functions
aws lambda invoke --function-name <name> output.json
aws lambda update-function-code --function-name <name> --zip-file fileb://function.zip

# CloudFormation
aws cloudformation list-stacks
aws cloudformation create-stack --stack-name <name> --template-body file://template.yaml
aws cloudformation update-stack --stack-name <name> --template-body file://template.yaml
aws cloudformation delete-stack --stack-name <name>

Terraform CLI Commands

Terraform Essential Commands

# Initialization & Setup
terraform init                  # Initialize working directory
terraform init -upgrade         # Update provider plugins
terraform version              # Show Terraform version

# Planning & Preview
terraform plan                 # Preview changes
terraform plan -out=tfplan     # Save plan to file
terraform plan -var="key=value" # Plan with variable
terraform plan -target=resource.name # Plan specific resource

# Apply Changes
terraform apply                # Apply changes (with prompt)
terraform apply -auto-approve  # Apply without confirmation
terraform apply tfplan         # Apply saved plan
terraform apply -var-file="vars.tfvars" # Apply with variable file

# Validation & Formatting
terraform validate             # Validate configuration
terraform fmt                  # Format configuration files
terraform fmt -check           # Check if formatting needed
terraform fmt -recursive       # Format all subdirectories

# State Management
terraform state list           # List resources in state
terraform state show <resource> # Show resource details
terraform state mv <src> <dst> # Move resource in state
terraform state rm <resource>  # Remove resource from state
terraform state pull          # Download remote state
terraform state push          # Upload local state

# Workspace Management
terraform workspace list       # List workspaces
terraform workspace new <name> # Create workspace
terraform workspace select <name> # Switch workspace
terraform workspace show      # Show current workspace
terraform workspace delete <name> # Delete workspace

# Import & Output
terraform import <resource> <id> # Import existing resource
terraform output              # Show all outputs
terraform output <name>       # Show specific output
terraform output -json        # Output as JSON

# Destruction
terraform destroy             # Destroy all resources
terraform destroy -target=resource.name # Destroy specific resource
terraform destroy -auto-approve # Destroy without confirmation

# Debugging & Troubleshooting
terraform show                # Show current state
terraform graph               # Generate dependency graph
terraform console             # Interactive console
terraform providers           # Show provider dependencies

# Advanced Operations
terraform taint <resource>    # Mark resource for recreation
terraform untaint <resource>  # Remove taint mark
terraform refresh             # Update state from real infrastructure
terraform force-unlock <lock-id> # Force unlock state

# Environment Variables
export TF_LOG=DEBUG           # Enable debug logging
export TF_LOG_PATH=terraform.log # Set log file path
export TF_VAR_name=value      # Set variable via environment

Physics Formulas & Constants

Fundamental Constants

Physical Constants

| Constant | Symbol | Value | Units | |———-|——–|——-|——-| | Speed of light | c | 2.998 × 10⁸ | m/s | | Planck constant | h | 6.626 × 10⁻³⁴ | J·s | | Reduced Planck constant | ℏ | 1.055 × 10⁻³⁴ | J·s | | Gravitational constant | G | 6.674 × 10⁻¹¹ | N·m²/kg² | | Elementary charge | e | 1.602 × 10⁻¹⁹ | C | | Electron mass | mₑ | 9.109 × 10⁻³¹ | kg | | Proton mass | mₚ | 1.673 × 10⁻²⁷ | kg | | Boltzmann constant | k_B | 1.381 × 10⁻²³ | J/K | | Avogadro’s number | N_A | 6.022 × 10²³ | mol⁻¹ | | Fine structure constant | α | 1/137.036 | dimensionless | | Vacuum permittivity | ε₀ | 8.854 × 10⁻¹² | F/m | | Vacuum permeability | μ₀ | 4π × 10⁻⁷ | H/m |

Key Physics Equations

Classical Mechanics

Newton's Laws:
F = ma                          # Second law
F₁₂ = -F₂₁                     # Third law

Kinematics:
v = v₀ + at                    # Velocity
x = x₀ + v₀t + ½at²           # Position
v² = v₀² + 2a(x - x₀)         # Velocity-position

Energy:
KE = ½mv²                      # Kinetic energy
PE = mgh                       # Gravitational PE
PE = ½kx²                      # Spring PE
W = F·d cos(θ)                # Work

Momentum:
p = mv                         # Linear momentum
L = r × p                      # Angular momentum
τ = r × F                      # Torque

Quantum Mechanics

Fundamental Equations:
iℏ ∂ψ/∂t = Ĥψ                # Schrödinger equation
Ĥ = -ℏ²/2m ∇² + V            # Hamiltonian
[x̂, p̂] = iℏ                   # Canonical commutation
ΔxΔp ≥ ℏ/2                   # Uncertainty principle

Quantum States:
|ψ⟩ = Σᵢ cᵢ|i⟩               # Superposition
⟨ψ|ψ⟩ = 1                    # Normalization
P = |⟨φ|ψ⟩|²                 # Transition probability

Hydrogen Atom:
E_n = -13.6 eV / n²          # Energy levels
r_n = n²a₀                   # Bohr radius
a₀ = 0.529 Å                 # Bohr radius constant

Electromagnetism

Maxwell's Equations:
∇·E = ρ/ε₀                    # Gauss's law
∇·B = 0                       # No magnetic monopoles
∇×E = -∂B/∂t                  # Faraday's law
∇×B = μ₀(J + ε₀∂E/∂t)        # Ampère-Maxwell law

Field Relations:
F = q(E + v×B)                # Lorentz force
E = -∇φ - ∂A/∂t              # Electric field
B = ∇×A                       # Magnetic field
c = 1/√(μ₀ε₀)                # Speed of light

Wave Equation:
∇²E - (1/c²)∂²E/∂t² = 0     # EM wave equation

Algorithms & Data Structures

Big O Complexity Reference

Time Complexity Cheat Sheet

Sorting Algorithms

Algorithm	Best	Average	Worst	Space
Bubble Sort	O(n)	O(n²)	O(n²)	O(1)
Selection Sort	O(n²)	O(n²)	O(n²)	O(1)
Insertion Sort	O(n)	O(n²)	O(n²)	O(1)
Merge Sort	O(n log n)	O(n log n)	O(n log n)	O(n)
Quick Sort	O(n log n)	O(n log n)	O(n²)	O(log n)
Heap Sort	O(n log n)	O(n log n)	O(n log n)	O(1)

Searching Algorithms

Algorithm	Best	Average	Worst	Space
Linear Search	O(1)	O(n)	O(n)	O(1)
Binary Search	O(1)	O(log n)	O(log n)	O(1)

Data Structures

Structure	Access	Insert/Delete	Search	Space
Array	O(1)	O(n)	O(n)	O(n)
Linked List	O(n)	O(1)	O(n)	O(n)
Hash Table	O(1)	O(1)	O(1) avg	O(n)
Binary Tree	O(log n)	O(log n)	O(log n)	O(n)
B-Tree	O(log n)	O(log n)	O(log n)	O(n)

Common Algorithm Patterns

Algorithm Templates

# Two Pointers
def two_pointers(arr):
    left, right = 0, len(arr) - 1
    while left < right:
        # Process
        if condition:
            left += 1
        else:
            right -= 1

# Sliding Window
def sliding_window(arr, k):
    window_sum = sum(arr[:k])
    max_sum = window_sum
    for i in range(k, len(arr)):
        window_sum += arr[i] - arr[i-k]
        max_sum = max(max_sum, window_sum)
    return max_sum

# Binary Search
def binary_search(arr, target):
    left, right = 0, len(arr) - 1
    while left <= right:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1

# DFS (Recursive)
def dfs(node, visited=None):
    if visited is None:
        visited = set()
    visited.add(node)
    for neighbor in node.neighbors:
        if neighbor not in visited:
            dfs(neighbor, visited)

# BFS (Iterative)
from collections import deque
def bfs(start):
    visited = set([start])
    queue = deque([start])
    while queue:
        node = queue.popleft()
        # Process node
        for neighbor in node.neighbors:
            if neighbor not in visited:
                visited.add(neighbor)
                queue.append(neighbor)

# Dynamic Programming
def dp_fibonacci(n):
    if n <= 1:
        return n
    dp = [0] * (n + 1)
    dp[1] = 1
    for i in range(2, n + 1):
        dp[i] = dp[i-1] + dp[i-2]
    return dp[n]

API Reference Patterns

RESTful API Conventions

REST API Best Practices

# Resource Naming
GET    /users              # List all users
GET    /users/{id}         # Get specific user
POST   /users              # Create new user
PUT    /users/{id}         # Update user (full)
PATCH  /users/{id}         # Update user (partial)
DELETE /users/{id}         # Delete user

# Nested Resources
GET    /users/{id}/posts   # User's posts
POST   /users/{id}/posts   # Create post for user

# Query Parameters
GET    /users?page=2&limit=20         # Pagination
GET    /users?sort=name&order=asc     # Sorting
GET    /users?filter[status]=active   # Filtering
GET    /users?fields=id,name,email    # Field selection

# HTTP Status Codes
200 OK                     # Successful GET, PUT
201 Created               # Successful POST
204 No Content            # Successful DELETE
400 Bad Request           # Invalid request
401 Unauthorized          # Authentication required
403 Forbidden             # No permission
404 Not Found             # Resource not found
409 Conflict              # Resource conflict
500 Internal Server Error # Server error

# Headers
Content-Type: application/json
Authorization: Bearer <token>
Accept: application/json
X-API-Version: v1
X-Request-ID: <uuid>

Common API Response Formats

API Response Patterns

// Successful Response
{
  "status": "success",
  "data": {
    "id": 123,
    "name": "John Doe",
    "email": "john@example.com"
  },
  "meta": {
    "timestamp": "2024-01-01T00:00:00Z"
  }
}

// Error Response
{
  "status": "error",
  "error": {
    "code": "VALIDATION_ERROR",
    "message": "Invalid email format",
    "details": {
      "field": "email",
      "value": "invalid-email"
    }
  }
}

// Paginated Response
{
  "status": "success",
  "data": [...],
  "pagination": {
    "page": 2,
    "per_page": 20,
    "total": 100,
    "total_pages": 5,
    "links": {
      "first": "/users?page=1",
      "prev": "/users?page=1",
      "next": "/users?page=3",
      "last": "/users?page=5"
    }
  }
}

Troubleshooting Flowcharts

Docker Troubleshooting

Docker Issue Resolution

Container Won't Start?
├─ Check logs: docker logs <container>
├─ Verify image: docker images
├─ Check resources: docker system df
└─ Inspect container: docker inspect <container>

Build Fails?
├─ Check Dockerfile syntax
├─ Verify base image exists
├─ Check build context size
└─ Review build cache: docker build --no-cache

Network Issues?
├─ List networks: docker network ls
├─ Inspect network: docker network inspect <network>
├─ Check container network: docker inspect <container> | grep Network
└─ Test connectivity: docker exec <container> ping <target>

Permission Errors?
├─ Check user in Dockerfile
├─ Verify volume permissions
├─ Use --user flag in docker run
└─ Check SELinux/AppArmor settings

Git Troubleshooting

Common Git Issues

Merge Conflicts?
├─ Identify conflicts: git status
├─ Open conflicted files
├─ Resolve conflicts manually
├─ Stage resolved files: git add <file>
└─ Complete merge: git commit

Accidentally Committed?
├─ Undo last commit: git reset HEAD~1
├─ Keep changes staged: git reset --soft HEAD~1
├─ Discard changes: git reset --hard HEAD~1
└─ Revert public commit: git revert <commit>

Wrong Branch?
├─ Stash changes: git stash
├─ Switch branch: git checkout <correct-branch>
├─ Apply changes: git stash pop
└─ Or cherry-pick: git cherry-pick <commit>

Lost Commits?
├─ Check reflog: git reflog
├─ Find lost commit
├─ Restore: git checkout <commit-hash>
└─ Create branch: git checkout -b recovered-branch

Best Practices Checklists

Code Review Checklist

Deployment Checklist

Mathematical Reference

Calculus Formulas

Derivatives and Integrals

Common Derivatives:
d/dx(xⁿ) = nxⁿ⁻¹
d/dx(eˣ) = eˣ
d/dx(ln x) = 1/x
d/dx(sin x) = cos x
d/dx(cos x) = -sin x
d/dx(tan x) = sec²x

Product Rule: d/dx(uv) = u'v + uv'
Chain Rule: d/dx(f(g(x))) = f'(g(x))g'(x)
Quotient Rule: d/dx(u/v) = (u'v - uv')/v²

Common Integrals:
∫xⁿ dx = xⁿ⁺¹/(n+1) + C  (n ≠ -1)
∫1/x dx = ln|x| + C
∫eˣ dx = eˣ + C
∫sin x dx = -cos x + C
∫cos x dx = sin x + C

Integration by Parts: ∫u dv = uv - ∫v du

Linear Algebra

Matrix Operations

Matrix Multiplication:
(AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ

Determinant (2×2):
|a b|
|c d| = ad - bc

Determinant (3×3):
|a b c|
|d e f| = a(ei-fh) - b(di-fg) + c(dh-eg)
|g h i|

Eigenvalues: det(A - λI) = 0
Trace: tr(A) = Σᵢ Aᵢᵢ
Transpose: (Aᵀ)ᵢⱼ = Aⱼᵢ

Special Matrices:
Identity: Iᵢⱼ = δᵢⱼ
Orthogonal: QᵀQ = QQᵀ = I
Hermitian: A† = A
Unitary: U†U = UU† = I

Network Protocols

Common Port Numbers

| Service | Port | Protocol | Description | |———|——|———-|————-| | SSH | 22 | TCP | Secure Shell | | Telnet | 23 | TCP | Unencrypted remote access | | SMTP | 25 | TCP | Email sending | | DNS | 53 | TCP/UDP | Domain name resolution | | HTTP | 80 | TCP | Web traffic | | HTTPS | 443 | TCP | Secure web traffic | | FTP | 20-21 | TCP | File transfer | | MySQL | 3306 | TCP | MySQL database | | PostgreSQL | 5432 | TCP | PostgreSQL database | | Redis | 6379 | TCP | Redis cache | | MongoDB | 27017 | TCP | MongoDB database | | Elasticsearch | 9200 | TCP | Elasticsearch API | | Kubernetes API | 6443 | TCP | K8s API server |

Regular Expressions

Regex Quick Reference

# Character Classes
.        Any character except newline
\d       Digit (0-9)
\D       Non-digit
\w       Word character (a-z, A-Z, 0-9, _)
\W       Non-word character
\s       Whitespace
\S       Non-whitespace
[abc]    Character set
[^abc]   Negated set
[a-z]    Range

# Quantifiers
*        0 or more
+        1 or more
?        0 or 1
{n}      Exactly n
{n,}     n or more
{n,m}    Between n and m

# Anchors
^        Start of string
$        End of string
\b       Word boundary
\B       Non-word boundary

# Groups
(...)    Capturing group
(?:...)  Non-capturing group
(?=...)  Positive lookahead
(?!...)  Negative lookahead

# Common Patterns
Email: ^[a-zA-Z0-9._%+-]+@[a-zA-Z0-9.-]+\.[a-zA-Z]{2,}$
URL: https?://[^\s]+
IP: \b(?:[0-9]{1,3}\.){3}[0-9]{1,3}\b
Phone: ^\+?1?\d{9,15}$

Quick Links

Documentation Resources

Online Tools

Regex101 - Regex testing
JWT.io - JWT decoder
Base64 Encode/Decode
JSON Formatter
Crontab Guru - Cron expression helper
YAML Validator

Performance Tools

GTmetrix - Web performance
WebPageTest - Performance testing
Can I Use - Browser compatibility
Bundle Phobia - NPM package size

Recently Added

Latest Additions & Updates

December 2025

Added Terraform CLI Commands section with comprehensive command reference
Enhanced Quick Navigation to include all major sections
Added Recently Added section for tracking updates

Previous Updates

Complete physics formulas and constants reference
Algorithm patterns and Big O complexity charts
RESTful API conventions and response formats
Docker and Git troubleshooting flowcharts
Code review and deployment checklists
Network protocols and port number reference
Regular expressions quick reference
Mathematical reference for calculus and linear algebra

Coming Soon

Python standard library quick reference
SQL query patterns and optimization tips
Shell scripting common patterns
CI/CD pipeline templates
Security best practices expanded section

Git Command Reference - Comprehensive Git guide
Docker Essentials - Complete Docker reference
Terraform Documentation - Infrastructure as Code guide
AI/ML Model Reference - Model architectures explained
Advanced Mathematics - Graduate-level formulas

*Last updated: 2025

Quick tip: Use Ctrl+F (Cmd+F on Mac) to search this page instantly*