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Mathematics

Channel | updated April 22, 2013

The Mathematics Department at MIT is a world leader in pure and applied mathematical research and education. In pure mathematics we explore exciting current research directions in most of the major fields. In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications. Our applied math group focuses on biology, combinatorics, computer science, scientific computing, numerical analysis, and areas of physical applied mathematics. Learn more

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Lecture 1: The "Game" of Mathematics
  • MIT OpenCourseWare,
  • Educational
Lecture 1: The "Game" of Mathematics

Video Description: Herb Gross introduces Calculus Revisited II — Functions of Several Variables — and discusses the over-arching theme "The Game of Mathematics". A game has objectives, rules, and definitions as well as strategies (logical plans) for meeting the objectives of the ...

Slow discharge of a LiFePO4 nanoparticle
  • Chemical Engineering,
  • Demonstration
Slow discharge of a LiFePO4 nanoparticle

At small currents, ordered stripes appear in a 100x100nm particle due to coherency strain.

Moderate discharge of a LiFePO4 nanoparticle
  • Chemical Engineering,
  • Demonstration
Moderate discharge of a LiFePO4 nanoparticle

At moderate current (I/I0=.01), phase separation is observed but with less ordering than at slow current.

Quasi-solid solution behavior in LiFePO4
  • Chemical Engineering,
  • Demonstration
Quasi-solid solution behavior in LiFePO4

Phase separation is suppressed as discharge rate is increased (I/I0=.03) and the critical current is approached. There is not enough time for complete phase-separation, and a quasi-solid solution forms.

Formation of {101} phase boundaries in a LiFePO4 ...
  • Chemical Engineering,
  • Demonstration
Formation of {101} phase boundaries in a LiFePO4 nanoparticle

When a LiFePO4 nanoparticle is held at 50% state of charge, coherency strain leads to the formation of {101} phase boundaries. Phase-field simulation of a 500x500nm particle.

Formation of {100} stripes in a LiFePO4 nanoparticle
  • Chemical Engineering,
  • Demonstration
Formation of {100} stripes in a LiFePO4 nanoparticle

When a LiFePO4 nanoparticle is held at 50% state of charge and cracks and dislocations cause a loss coherency in the [001] direction, a {100} stripe morphology is formed. Phase-field simulation of a 500x500nm particle.

Slope
  • Mathematics,
  • Feature
Slope

K-12 mathematics: presenting the concept of "Slope".

Benedict Gross
  • Mathematics,
  • Feature
Benedict Gross

A Celebration of Algebraic Geometry, August 25-28, 2011 Benedict Gross: On the arithmetic of pencils of quadrics

Kieran O'Grady
  • Mathematics,
  • Feature
Kieran O'Grady

A Celebration of Algebraic Geometry, August 25-28, 2011 Kieran O'Grady: Moduli of double EPW-sextics

Lucia Caporaso
  • Mathematics,
  • Feature
Lucia Caporaso

A Celebration of Algebraic Geometry, August 25-28, 2011 Lucia Caporaso: Brill-Noether theory over the moduli space of stable curves

Gavril Farkas
  • Mathematics,
  • Feature
Gavril Farkas

A Celebration of Algebraic Geometry, August 25-28, 2011 Gavril Farkas: Models of the Prym moduli space via special K3 surfaces

Claire Voisin
  • Mathematics,
  • Feature
Claire Voisin

A Celebration of Algebraic Geometry, August 25-28, 2011 Claire Voisin: Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal

Dan Abramovich
  • Mathematics,
  • Feature
Dan Abramovich

A Celebration of Algebraic Geometry, August 25-28, 2011 Dan Abramovich: The tropicalization of moduli space

David Smyth
  • Mathematics,
  • Feature
David Smyth

A Celebration of Algebraic Geometry, August 25-28, 2011 David Smyth: Stability of finite Hilbert points and moduli of singular curves

Rahul Pandharipande
  • Mathematics,
  • Feature
Rahul Pandharipande

A Celebration of Algebraic Geometry, August 25-28, 2011 Rahul Pandharipande: Kappa classes on the moduli spaces of curves

William Fulton
  • Mathematics,
  • Feature
William Fulton

A Celebration of Algebraic Geometry, August 25-28, 2011 William Fulton: Degeneracy loci formulas for bundles with symmetries

Robert Lazarsfeld
  • Mathematics,
  • Feature
Robert Lazarsfeld

A Celebration of Algebraic Geometry, August 25-28, 2011 Robert Lazarsfeld: Asymptotic syzygies of algebraic varieties

David Eisenbud
  • Mathematics,
  • Feature
David Eisenbud

A Celebration of Algebraic Geometry, August 25-28, 2011 David Eisenbud: Vector bundles on P^n and representations of GL_n

Jason Starr
  • Mathematics,
  • Feature
Jason Starr

A Celebration of Algebraic Geometry, August 25-28, 2011 Jason Starr: Pseudo ideal sheaves and weak approximation over function fields of curves

Brendan Hassett
  • Mathematics,
  • Feature
Brendan Hassett

A Celebration of Algebraic Geometry, August 25-28, 2011 Brendan Hassett: Families of quartic del Pezzo surfaces

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