Mathematical Induction: Basics and Applications

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Related lectures (44)

Integers and Rings Log in to Mediaspace to watch this video

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

Untitled Log in to Mediaspace to watch this video

Cardinality and Group Theory Log in to Mediaspace to watch this video

Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.

Group Actions and Functors Log in to Mediaspace to watch this video

Covers group quotient, group actions, and functors connecting sets and G-sets.

Coordinate Systems Log in to Mediaspace to watch this video

Covers the concept of systems of coordinates and the geometric interpretation of base changes.

Untitled Log in to Mediaspace to watch this video

Arithmetic Fundamentals: Equivalence and Irreducibility Log in to Mediaspace to watch this video

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

Cheeger's Inequalities Log in to Mediaspace to watch this video

Explores Cheeger's inequalities for random walks on graphs and their implications.

Wireless Receivers: OFDM Log in to Mediaspace to watch this video

Covers the fundamentals of Orthogonal Frequency Division Multiplexing (OFDM) in wireless communication systems.

Subgroups Criteria: Propositions and Examples Log in to Mediaspace to watch this video

Covers the criteria for subgroups and provides examples and proofs.

Differentiability in Analysis Log in to Mediaspace to watch this video

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Number Theory: Operations and Equivalence Log in to Mediaspace to watch this video

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Hermite Normal Form: Computation & Properties Log in to Mediaspace to watch this video

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Optimal Transport: Cyclically Monotone Sets Log in to Mediaspace to watch this video

Covers cyclically monotone sets in optimal transport theory and their properties.

Quantum Order Finding with QPE Log in to Mediaspace to watch this video

Covers the Quantum Order Finding algorithm using Quantum Phase Estimation (QPE), focusing on Shor's factoring algorithm.

Euclidean Algorithm: GCD Calculation Log in to Mediaspace to watch this video

Covers the Euclidean algorithm for GCD calculation and algorithmic complexity analysis.

Cauchy Sequences and Induction Log in to Mediaspace to watch this video

Covers Cauchy sequences, convergence, and induction in mathematical analysis.

Poisson Paradigm: Qualitative / Quantitative Log in to Mediaspace to watch this video

Covers the Poisson Paradigm, including the First/Second Moment Method and Martingales, discussing dependency graphs and Chernoff bounds.

Newtonian Potential: Bounded Domains Log in to Mediaspace to watch this video

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Fundamental Solutions Log in to Mediaspace to watch this video

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

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