Lectures related to Integer | EPFL Graph Search

Montgomery Multiplication

Covers Barrett reduction, Montgomery form of integers, and efficient Montgomery product computation.

Basic Properties

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

Integer Types in Java

Explains interpreting bit vectors as integers, two's complement, overflow, and integer type limits in Java.

Information Representation: Numbers and Operations

Covers the representation of numbers using binary patterns and computation operations.

Rudiments of Number Theory

Introduces modulo arithmetic, Euclid's algorithm, and congruence in number theory.

Properties of Division

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

Division in Rational Numbers

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

Rational Numbers: Construction and Properties

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

Complexity & Induction: Algorithms & Proofs

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

Multiplication in Rational Numbers

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

Operations in Z

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

Order of Operations: Unnecessary Parentheses

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

Properties of Subtraction

Covers the properties of subtraction and the distributivity of multiplication.

Cartesian Product and Induction

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

Integers Representation: Sign-and-Magnitude vs Two's Complement

Compares sign-and-magnitude with two's complement integer representations, emphasizing complexity differences and addressing overflow and underflow challenges.

Integers: Sets, Maps, and Principles

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

Bitwise Operators: Integers Types

Covers bitwise operators for integers and representing colors using 32-bit integers.

Powers, Roots, etc.: Calculation Rules

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

Problem-solving Strategies: Sum of N Integers (Recursive)

Covers the recursive algorithm for calculating the sum of the first N integers.

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.