Lectures related to Functions and Integers

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

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

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Function Composition and Integers

Covers function composition and integers, including properties and examples.

Integers: Sets, Maps, and Principles

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

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Number Theory: GCD and LCM

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

Real Functions: Graphs and Properties

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Convex Functions

Covers the properties and operations of convex functions.

Terminologie: Functions Graph Discussion

Covers the terminology related to the graph of a function and intervals.

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.

Transformations Affines

Covers the concept of affine transformations in functions, including shifting and compressing functions.

Real Functions: Definitions and Properties

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.

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.

Logic and Proof Techniques

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

Number Theory: Greatest Common Divisor and Prime Factorization

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

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Shor's algorithm: factoring integers

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