When

Last 10 minutes of class on Wednesday, January 21, 2026.

Everyone takes the exam at the same time.

Scope

Computation, Theories of Computer Science.

Ground Rules

You will take the exam on Brightspace. There is 10 minute time limit, or 15 minutes for those with time-and-a-half accommodations.

Preparation Checklist

Do each of the following to maximize your preparation:

• (Optional) Go through Nicky Case’s How to Remember Everything Forever-ish.
• (Optional) Read Atul Gawande’s The Checklist.
• Review the recordings for class periods you missed, and for portions of the class sessions that you attended but feel you need to review.
• Work through the course notes on Computation and Theories of Computer Science.
• Watch the embedded videos in the course notes above.
• Follow some of the links within the course notes to outside articles and videos. This gives you access to new material as well as additional takes on the course content.
• Practice with the recall questions on the notes above.
• Make a pass over Gabe Robins’ A Brief History of Computing (Important).
• Read the Introduction and Chapters 1–2 of [Bernhardt] (Important).
• Skim the Introduction and Part I of [Petzold] (Important).
• Read the Preface and Sections 0.1 and 0.2 of [Sipser] (Not important but possibly useful).
• (Optional) Review my notes on Logic and Foundations of Mathematics.

Were you able to check off every box?

Things to Know

The learning objectives for the course up to this point in time include you having developed a familiarity with, and an ability to discuss:

• The story of computation
• Big moments in the history of computation
• The impact of Euclid, Babbage, Lovelace, Turing, Hopper, and others
• The scope and big ideas of each of the four theories of computer science: languages, automata, computability, and complexity

Outline of Course Content

The fact that active recall is better for acquiring long-term knowledge does not mean that outlines and concept maps are not useful. Learners should use multiple techniques—think “both and” rather than “either or.”

Computation and its History
    Definitions of Information, Computation, and Language
    Computation is the study of Languages and Automata
    To many, computing is pop culture
    Historical path to computer science as a discipline
        Ancient times
        Numerals
        Early computing recipes
        Early computing machines
        Ada Lovelace
        Logicism vs Formalism vs Intuitionism
        Hilbert’s Program
        Russell and Whitehead
        Formalization of Computing
            Lambda Calculus
            Gödel’s Recursive Functions
            Turing Machines
        Alan Turing’s paper
            Formalized effective computation
            Church-Turing Thesis
            Computational universality
            Showed Entscheidungsproblem was unsolvable
        Early electromechanical and electronic computers
        Programming Languages
        Language implementation
            Compilers
            Optimization
        Human-centric computing
        Modern Trends
    Computing: The Human Experience
    The four theories
        Language
        Automata
        Computability
        Complexity
    Philosophical Context: Denotational vs Operational
Theories of Computation, The Basics
    What is a theory?
        Organized body of knowledge with explanatory and predictive power
    Why study theory?
        To have a vocabulary for communication
        To reason from more fundamental and precise principles
        To predict and generate new knowledge
        To not flail and guess and have our thinking stuck in a box
    Big questions in computer science
        What is computation?
        What can and cannot be known through computation?
        What can and cannot be computed?
        What can and connt be efficiently computed?
    Language Theory
        Definition: how computations are expressed
        Symbols
        Alphabets
        Strings
        Languages
        Functions
    Automata Theory
        Definition: how computations are carried out
        Early computing machines
        How and why Turing came up with his machine model
        Representing a Turing Machine as a table
        Representing a Turing Machine as a state diagram
    Computability Theory
        Definition: what computations are (theoretically)possible
        Why not every function is computable
            The simple counting argument: there are more functions than programs
        Church-Turing Thesis
        The Halting Problem
    Complexity Theory
        Definition: what resources are required for computations
        Kinds of computability measures
        P vs. NP

About the Problems

This is a mini-quiz which tests for immediate understanding of topics and not your ability to work out problems over an extended duration of time. There is a strict time limit so that your immediate fluency is tested rather than your ability to search the web (or worse, ask a chatbot), since these things take time. There will be 5–10 questions, some will be multiple choice, some multi-select, and some matching. There are no free-form answers, so the exam will be autograded and you will see your score immediately after it is submitted.

All content on the assigned readings is fair game for questions, so do not neglect the readings, and by all means do the recall questions!