Lectures related to Proof Techniques: Examples

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Proofs: Contraposition vs. Contradiction

Covers the concepts of contraposition and contradiction in proofs.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Proof Techniques: Direct, Contraposition, Cases

Covers proof techniques like direct, contraposition, and cases with examples.

Introduction to Proofs

Introduces informal proofs and their practical applications in computer science and mathematics, emphasizing the importance of proving theorems through direct and indirect methods.

Introduction to Proofs

Introduces informal proofs, explores practical applications, and explains theorem proofs using direct and indirect methods.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Fundamental Solutions

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

Linear Algebra: Properties and Operations

Explores subset properties, contraposition, and equivalence in linear algebra.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Implicit Functions: Unique Solutions and Class C Functions

Covers the proof of the theorem of implicit functions and the concept of class C functions.

Relative Homology: Exact Sequence

Covers the long exact sequence of relative homology groups and chain complexes.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Cartesian Product and Induction

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