Lecture Notes: Introduction to Computer Science

Overview of Computers

Computers were initially built to solve arithmetic problems.
They have evolved to perform a variety of tasks:
- Running the internet
- Graphics processing
- Simulating complex systems like the universe
Fundamental operation of computers is based on flipping zeros and ones.
Modern smartphones have more computing power than the entire world in the 1960s.
Historical context: Apollo moon landing could be simulated on a few Nintendo consoles.

Key Areas in Computer Science

Theoretical Computer Science
- Alan Turing: Father of theoretical computer science.
- Turing Machine: A fundamental model that describes a general-purpose computer.
  - Components include:
    - An infinitely long tape (akin to RAM)
    - A head for reading/writing symbols
    - A state register
    - A list of instructions (held in memory).
- Lambda Calculus: Basis for programming language research.
- Computability Theory: Classifies problems based on solvability.
  - Example: Halting problem – cannot predict if a program will stop.
- Computational Complexity: Categorizes problems by how resource-intensive they are.
  - Some problems are theoretically solvable but impractical due to resource constraints.
- Algorithms:
  - Defined as a set of instructions independent of hardware.
  - Efficiency varies between algorithms.
  - Studied in algorithmic complexity.
- Information Theory: Studies properties of information.
  - Applications include data compression, coding theory, and cryptography.
Computer Engineering
- Focuses on designing computers that solve diverse problems efficiently.
- CPU: Core of computer that handles tasks; uses scheduling to allocate resources effectively.
- Computer Architecture: Different architectures serve various functions (CPUs, GPUs, FPGAs).
- Programming Languages: Tools for human-computer interaction, ranging from low-level to high-level languages.
  - Compilers convert code into CPU instructions.
- Operating Systems: Essential software controlling how programs interact with hardware.
Software Engineering
- The art of writing efficient, error-free software.
- Considerations include problem-solving, data communication, performance measurement, and graphics.
- Optimization Problems: Common in real-world applications; seek the best solutions within constraints.
- Boolean Satisfiability: A foundational problem with implications in AI.

Real World Applications of Computer Science

Artificial Intelligence: Developing computers that can make decisions based on data.
- Machine Learning: Algorithms enable learning from data.
- Computer Vision: Making sense of images; involves image processing techniques.
- Natural Language Processing: Understanding human language; uses knowledge representation.
Big Data: Managing and analyzing large datasets.
Internet of Things: Enhances data collection through everyday objects.
Computational Science: Uses computing to address scientific inquiries.
Human-Computer Interaction: Designing intuitive computer systems.
Robotics: Enabling physical manifestations of computer intelligence.

Future of Computer Science

Continued evolution in a field that remains dynamic despite hardware limitations.
Potential societal impacts over the next hundred years.

Additional Resources

For further learning, check out brilliant.org, which offers courses on computer science topics.