When we analyze an algorithm, we rarely want a single number — we want a statement about how the running time behaves as the input grows. Big O, Omega, and Theta are the three standard tools for making that statement precise. Big O gives an upper bound (the work grows no faster than this), Omega gives a lower bound (the work grows at least this fast), and Theta gives a tight bound (the growth is pinned between the two, up to constant factors).
In this course these notations are not interchangeable vocabulary; they encode different claims. Saying linear search is O(n) is a guarantee about the worst case, while saying any comparison sort is Omega(n log n) is a claim about an inherent limit, and saying merge sort is Theta(n log n) says both bounds coincide. Choosing the wrong notation can make a correct analysis say the wrong thing, which is why this topic focuses on the relationships among the three and on when each is the right reporting choice.
As you watch the videos below, pay attention to three things: the formal definitions with their constants c and n0, the picture of a function being sandwiched between scaled versions of another, and the logical relationship that f is Theta(g) exactly when f is both O(g) and Omega(g). Also note how speakers distinguish best/worst/average case from upper/lower/tight bound — these two ideas are related but are not the same thing, and conflating them is the most common error students make here.
A compact overview of all three asymptotic notations — Theta, Big O, and Omega — presented in about seven minutes. Based on its title and description, it introduces each notation in turn and is part of a short series that begins with a separate introduction video on analyzing algorithms. Expect formal definitions along with the constant-and-threshold conditions that make each bound precise.
Michael Sambol's algorithms videos are widely used by CS students for their brevity and fidelity to standard textbook definitions, and this one covers all three notations side by side, which is exactly the comparison this topic is built around.
An introductory treatment of asymptotic notation from the Back To Back SWE channel, aimed at learners meeting these symbols for the first time. Given the channel's interview-prep orientation, it likely emphasizes intuition about growth rates and how the notations are actually used when discussing algorithm efficiency, rather than heavy formal proof.
It offers a second, more conversational explanation of the same definitions, which helps if the formal version feels abstract, and it connects the notations to the practical habit of describing an algorithm's cost in interviews and code reviews.
A focused lesson on Big-Theta notation from the Mathispower4u channel. As a mathematics-oriented video, it most likely works through the formal definition with explicit constants and bounds and demonstrates verifying that one function is Theta of another through worked examples.
Theta is the notation students most often misuse, and a dedicated mathematical treatment reinforces the key relationship that a tight bound requires establishing both the upper and lower bound simultaneously.
Together these videos build directly toward MO1 and MO5: the Sambol and Back To Back SWE videos present Big O, Omega, and Theta as a related set so you can articulate what each one claims, and the Mathispower4u video on Theta reinforces why a tight bound is a stronger statement than either bound alone — the reasoning you need to justify your notation choice. The formal definitions and growth-rate intuition in these videos also underpin MO2 and MO3, since deriving best-, worst-, and average-case complexities and classifying loops or recursive halving all depend on comparing growth and discarding lower-order terms. Applying that vocabulary to concrete algorithm selection trade-offs (MO4) is left to the course readings, assignments, and worked examples that follow.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.