Lecture

Powers, Roots, etc.: Calculation Rules

Related lectures (28)

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

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

Basic Properties

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

Function Composition and Integers

Covers function composition and integers, including properties and examples.

Integers and Rings

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

Integers: Elementary Concepts

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

Binary Integer Representation

Covers the binary representation of integers, including positive and negative numbers.

Complexity & Induction: Algorithms & Proofs

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

Properties of Division

Covers the properties of division in integers and the relationship between divisibility and unique quotients.

Integers: Sets, Maps, and Principles

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

Modular Arithmetic: Introducing Z/mZ

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

Subtraction: Absolute Value and Opposite

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

Functions and Integers

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

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Priority of Operations

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

Mathematical Induction: Basics and Applications

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

Rational Numbers: Construction and Properties

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

Operations in Z

Covers addition properties and operations in the set of integers Z.

Shor's algorithm: factoring integers

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

Properties of Subtraction

Covers the properties of subtraction and the distributivity of multiplication.