Introduction to Mathematical Concepts and Course Mechanics

Flashcards based on the introductory lecture covering definitions, notation, proofs, axioms, and course tools.

Even number

An integer $n$ that can be written as $n = k + k$ for some integer $k$.

Floor of $x$

Denoted $\lfloor x \rfloor$, the greatest integer at most $x$ (e.g., $\lfloor -0.5 \rfloor = -1$).

Ceiling of $x$

Denoted $\lceil x \rceil$, the least integer at least $x$ (e.g., $\lceil \pi \rceil = 4$).

Mathematical proof

A deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

Axioms

Certain basic or original assumptions that, along with accepted rules of inference, can be used in principle to construct every mathematical proof.

Lean proof assistant

A software system used in the final part of class to cover the formalization of mathematical examples.

Wooclap

The platform through which students submit their group work on class worksheet exercises.