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Related lectures (23)

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Composition of Applications in Mathematics

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

Vector Spaces: Definition, R2

Introduces vector spaces with binary addition and scalar multiplication, exploring geometric examples in R2.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Cartesian Product and Induction

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

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Riemann Integral: Subdivisions and Volumes

Covers the concept of Riemann integral and volume calculation of closed pavements.

Constrained optimization: the basics

Covers the basics of constrained optimization, including tangent directions, trust-region subproblems, and necessary optimality conditions.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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.