Concept

Quadratic integer

Related lectures (30)

Cartesian Product and Induction

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

Integers and Rings

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

Properties of Division

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

Shor's algorithm: factoring integers

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

Elementary Algebra: Numeric Sets

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

Powers, Roots, etc.: Calculation Rules

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

Optimization Methods

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Subtraction: Absolute Value and Opposite

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

Mathematical Induction: Basics and Applications

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

Finite Element Method: Quadratic Elements

Explores the precision of finite element models and higher order asymptotic estimates.

Temporal Complexity: Concrete Example

Explores temporal complexity through a concrete example with positive and negative integers.

System Equivalence

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Finite Element Method: Higher Order Models

Explores precision of higher order finite element models and applications of quadratic finite elements in elastodynamics.

Priority of Operations

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

Basic Properties

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

Number Theory: GCD and LCM

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

Advanced Counting: Exercise 11

Covers the advanced counting topic of distinct n-duples of integers.

Operations in Z

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

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Order of Operations: Unnecessary Parentheses

Discusses the significance of moving parentheses before calculations and the rules for simplifying expressions and prioritizing operations.