Integers and Rings

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Related lectures (28)

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Shor's algorithm: factoring integers

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

Number Theory: GCD and LCM

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

Number Theory: Greatest Common Divisor and Prime Factorization

Introduces greatest common divisor, prime factorization, and the Euclidean Algorithm.

Logic and Proof Techniques

Covers integers, rationals, logic, proof techniques, functions, and relations using examples and truth tables.

Arithmetic Fundamentals: Equivalence and Irreducibility

Covers the fundamental theorem of arithmetic, focusing on equivalence and irreducibility of integers.

Basic Properties

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

Linear Algebra: Reciprocity and Equivalence

Explores reciprocity, equivalence, and proof techniques in linear algebra, emphasizing logical reasoning and mathematical rigor.

Mathematical Induction: Basics and Applications

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

Complexity & Induction: Algorithms & Proofs

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

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.