COSC 110 MIDTERM REVIWER

• Computational Thinking


  A problem-solving approach that involves breaking down large and complex problems into smaller and more manageable parts
• Steps of computational thinking

  1. Define the problem

  2. Decompose

  3. Pattern recognition

  4. Abstraction

  5. Algorithm design

  6. Evaluation
• Algorithm


  A step-by-step set of instructions or a sequence of actions designed to solve a specific problem or perform a particular task
• Procedure


  A systematic way of executing an algorithm
• Types of computation


  • Numerical algorithms
  • Symbolic computation
• Numerical algorithms


  • Focus on approximating solutions to mathematical problems using numerical values, emphasize efficiency and numerical stability
• Symbolic computation


  • Involves manipulating mathematical expressions symbolically, treating variables as symbols rather than numerical values, focus on exact representations of mathematical objects and expressions
• Data Collection, Representation, and Analysis

  1. Data Collection: Gathering information from various sources

  2. Data Representation: Structuring and organizing data for analysis

  3. Data Analysis: Inspecting, cleaning, transforming, and modeling data to uncover patterns, trends, and relationships
• Problem decomposition


  1. Identify main objectives

  2. Decompose into sub-problems

  3. Assign tasks and prioritize
• Importance of computational thinking

  • Problem-Solving Skills
  • Transferability
  • Automation and Efficiency
  • Data Literacy
  • Critical Thinking and Creativity
  • Preparation for the Future
  • Collaboration and Communication
• Applications of computational thinking

  • Developing software and applications
  • Designing algorithms for data analysis
  • Solving optimization problems
  • Creating simulations and models
• Abstraction


  The process of focusing on essential qualities while ignoring irrelevant details; allows us to manage complexity by hiding unnecessary implementation details
• Types of Abstraction


  • Data Abstraction
  • Procedural Abstraction
  • Control Abstraction
• Benefits of Abstraction


  • Simplicity
  • Modularity
  • Reusability
  • Scalability
• Challenges and Considerations of Abstraction

  • Performance
  • Trade-offs
  • Complexity Management
• Automation


  The use of technology to perform tasks with minimal human intervention
• Benefits of Automation


  • Efficiency
  • Accuracy
  • Scalability
  • Productivity
• Automation Techniques


  • Algorithmic Automation
  • Scripting and Programming
  • Workflow Automation
• Challenges and Considerations of Automation

  • Algorithm Selection
  • Error Handling
  • Validation and Verification
  • Maintenance
• Simulation


  The imitation of the operation of a real-world process or system over time
• Benefits of Simulation


  • Prediction
  • Understanding
  • Risk Mitigation
  • Cost Savings
• Simulation Techniques


  • Monte Carlo Simulation
  • Finite Element Analysis (FEA)
  • Agent-Based Modeling
• Challenges and Considerations of Simulation

  • Model Accuracy
  • Computational Resources
  • Complexity Management
• Parallelization


  Breaking down computational tasks into smaller subtasks that can be executed simultaneously on multiple processors or cores
• Benefits of Parallelization


  • Speedup
  • Scalability
  • Efficiency
• Parallelization Techniques


  • Data Parallelism
  • Task Parallelism
• Challenges and Considerations of Parallelization

  • Load Balancing
  • Communication Overhead
  • Synchronization
• Practical Applications of Parallelization

  • Numerical Parallelization Example
  • Symbolic Parallelization Example
• Computational Error


  The discrepancy between the computed value and the true value of a quantity, arising due to limitations in hardware, algorithms, or mathematical representations
• Types of Computational Errors

  • Round-off Error
  • Truncation Error
  • Symbolic Error
• Numeric Computation Errors


  • Round-off Error: Addition/Subtraction of numbers with different precision
  • Truncation Error: Approximating integrals using numerical methods
• Techniques to Mitigate Numeric Errors

  • Use higher precision arithmetic
  • Implement error analysis techniques
  • Employ adaptive algorithms that adjust step sizes based on error estimates
• Techniques to Address Symbolic Errors

  • Utilize exact arithmetic when possible
  • Employ algebraic simplification techniques cautiously
  • Incorporate error bounds in symbolic computations
• Application and Importance of Computational Errors

  • Scientific Computing
  • Engineering
  • Finance
• Case Study - Theriac 25: One notable real-world example where computational errors led to significant consequences is the case of the Therac-25 radiation therapy machine incidents in the 1980s
• Data abstraction - It focuses on hiding implementation details of data structures while providing operations to manipulate them.