Logic and Proof Techniques

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Related lectures (26)

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Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Rational Numbers: Construction and Properties

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

Advanced Analysis II: Derivatives and Notations

Covers derivatives, notations, composition of functions, and multiple derivatives in advanced analysis.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

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.

Cartesian Product and Induction

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

Mathematical Analysis: Functions and Composition

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

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.