Concept

Algebraic integer

Related lectures (30)

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

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

Basic Properties

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

Integers: Sets, Maps, and Principles

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

Functions and Integers

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

Advanced Counting: Exercise 11

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

Shor's algorithm: factoring integers

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

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Cartesian Product and Induction

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

Priority of Operations

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

Complexity & Induction: Algorithms & Proofs

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

Operations in Z

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

Powers, Roots, etc.: Calculation Rules

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

Subtraction: Absolute Value and Opposite

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

Properties of Subtraction

Covers the properties of subtraction and the distributivity of multiplication.

Mathematical Induction: Basics and Applications

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

Linear Algebra: Integers

Explores linear algebra over integers, emphasizing solutions to A.x=b equations and Hermite normal form.

Complexity of Algorithms: Proofs of Time Complexity

Covers the analysis of worst time complexity for algorithms and time complexity with real numbers and integers.

Discrete Log Problem: Pollard's Rho Method

Introduces Pollard's rho method for the discrete log problem and finding collisions efficiently in a cyclic group.

Closure Conversion: Representation and Transformation

Explores the representation and transformation of values, focusing on closure conversion and the challenges of representing functions in functional languages.