Lecture

Properties of Division

Related lectures (28)

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the extension of addition and multiplication operations in rational numbers.

Explores division in rational numbers and the extension of addition from integers.

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Covers absolute value, subtraction in integers, and comparisons between integers.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Covers basic properties of natural numbers, including order relations and inverses.

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.

Covers function composition and integers, including properties and examples.

Covers the rules of calculation for powers, roots, and more, focusing on positive numbers and integers.

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Explains the importance of parentheses in simplifying mathematical operations and notations.

Covers the basics of Shor's algorithm for factoring integers and the steps involved in the quantum algorithm.

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.